Satellite platform distributed cooperative control method based on inner-outer loop game

Abstract

The application relates to a kind of distributed cooperative control methods based on inner and outer ring game, belong to automatic control technical field. Considering the control constraint and optimization performance index of each subsystem, an auxiliary decoupling decision variable is designed for each subsystem to guarantee the distributed Nash equilibrium solution, and the inner ring distributed node control with each subsystem as the main part is realized. Considering the coupling relationship between various loads and the platform, the overall high-precision control optimization index containing the performance index weight of each subsystem is established, the weight of each subsystem is mapped to the platform connection graph, and the outer ring edge control algorithm based on the platform connection graph is designed. Two Nash equilibriums of outer ring edge control and inner ring node control form an interactive Stackelberg equilibrium, which expands the standard Stackelberg differential graph equilibrium control input. Through sequential adjustment of inner and outer ring control input, the attitude stability and whole satellite attitude pointing accuracy are improved, which can be applied to high-precision and high-stability control of large on-orbit assembly structures such as modular reconfigurable spacecraft, large-size antenna and optical load.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of automatic control, and particularly relates to a satellite platform distributed cooperative control method based on inner-outer loop game. BACKGROUND

[0002] High-precision quantitative remote sensing takes time-varying atmosphere, hydrosphere and biosphere as observation targets, and needs to be configured with multiple large high-precision loads such as optical and microwave to realize precise collaborative observation of multiple elements. The radiation and geometric deviation introduced by the spatial position and pose difference of the traditional multi-platform observation method becomes the main error term restricting high-precision quantitative remote sensing, and it is urgent to develop a large multi-mission satellite platform supporting on-orbit assembly. With the continuous docking of on-orbit assembly modules, the structural topology form of the large satellite platform is changing, and it also involves the collision of the satellite platform and the assembly load, and the time-varying characteristics of the structural mass characteristics, collision and other complex factors are easy to induce the attitude drift and vibration of the large space combination structure. In addition, the space complex environment such as solar pressure, thermal radiation and rarefied atmosphere will also affect the attitude stability of the large space assembly structure. Due to the energy transmission and strong dynamic coupling between the platform and the load subsystem, it directly affects the global pointing stability of the large space structure, and relates to the success of the on-orbit assembly and high-precision observation after assembly. Therefore, it is urgent to solve the high-precision high-stability distributed cooperative robust control problem of the large satellite platform supporting on-orbit assembly considering the space complex environmental forces, strong coupling and nonlinearity.

[0003] At present, in the field of high-precision high-stability control of large satellite platforms, the following aspects are mainly concentrated: (1) decentralized control: the large satellite platform control problem is decomposed into several independent subsystem control problems, and then the control input mode is designed; (2) distributed control, which is different from the former, when designing the subsystem control input, the distributed control input will consider the neighbor information within a certain range around the subsystem, and set up information interaction between the controllers to form a distributed cooperative control network. In the past control of large satellite platforms, usually considering the performance differences of each subsystem and platform, the existing means rely on experience weight to balance the performance of local subsystem and platform, causing the performance of a single subsystem to be over-optimized, leading to the decline of the precision of other subsystems, and it is difficult to meet the control demand of high-precision high-stability. In addition, there may be a large variance in the optimization gradient of each subsystem, leading to a long time to obtain the optimal solution of the system, and even the phenomenon that the optimal solution cannot be obtained. SUMMARY

[0004] The technical problem solved by the application is to overcome the deficiencies in the prior art, and the application provides a distributed cooperative control method based on inner-outer loop game for the high-precision high-stability control problem of a large satellite platform, which improves the attitude stability and the control precision of the whole satellite attitude pointing.

[0005] The technical scheme of the present application is as follows: a satellite platform distributed cooperative control method based on inner and outer ring game, which comprises the following steps:

[0006] S1, a multi-subsystem interconnection model of an on-orbit assembled satellite platform is established, and a connection graph is formed The multi-subsystem interconnection model of the on-orbit assembled satellite platform collectively refers to the satellite platform subsystems and the load subsystems as subsystems, and the subsystems are represented as vertices of the connection graph, the vertex set of the connection graph, the coupling control relationship between the subsystems is the edge of the connection graph, the edge set of the subsystems;

[0007] S2, the distributed edge control is set as an outer ring leader, and the distributed node control is set as an inner ring follower, the control input of the inner ring follower and the outer ring leader is sequentially adjusted, and the cooperative control of the satellite platform and each load is realized, and the specific sequential adjustment process is as follows:

[0008] S2.1, the outer ring edge control input Π of the fixed subsystem i i and the set of the outer ring edge control input of all the neighbor subsystems of the fixed subsystem i -i , the topological coupling weight l of the subsystem i and the subsystem j is determined ij , i≠j, the control constraint of each subsystem and the optimization performance index are considered, an auxiliary decoupling decision variable is constructed for each subsystem, the distributed stable control of the inner ring node of the platform subsystem and each load subsystem is carried out, and each subsystem satisfies the Nash equilibrium condition;

[0009] S2.2, on the basis of the inner ring node control input U of the fixed subsystem i i and the set of the inner ring node control input of all the neighbor subsystems of the fixed subsystem i -i , a control optimization index containing the performance index weight of each subsystem is established, each subsystem weight is mapped into the connection graph, the outer ring edge control based on the connection graph is carried out by adjusting the edge weight of the connection graph, and the edge control input satisfies the Nash equilibrium;

[0010] S2.3, whether the Stackelberg equilibrium is satisfied after the execution of steps S2.1 and S2.2 is judged, if yes, the process is ended, and if not, the steps S2.1 and S2.2 are continuously executed.

[0011] Preferably, the Stackelberg equilibrium is as follows:

[0012] for the outer ring edge control input Π of the subsystem i i and the set of the outer ring edge control input of all the neighbor subsystems of the subsystem i -i , there is the outer ring edge control input as follows: iBest inner-loop nodal control input of subsystem i when such that:

[0013]

[0014]

[0015] where J i is the inner-loop nodal control cost function of subsystem i, is the set of best inner-loop nodal control inputs of all neighboring subsystems of subsystem i when -i

[0016] For any inner-outer loop coordinated control pair {Π, U(Π)}, there exists a best outer-loop edge control input such that:

[0017]

[0018]

[0019] where Γ i is the outer-loop edge control cost function of subsystem i, U(Π) is the corresponding inner-loop nodal control input when the outer-loop edge control input is Π, is the best outer-loop edge control input of subsystem i, is the best inner-loop nodal control input of subsystem i when the outer-loop edge control input is Π i is the set of best inner-loop nodal control inputs of all neighboring subsystems of subsystem i when the outer-loop edge control input is Π i

[0020] Preferably, in the on-orbit assembled satellite platform multi-subsystem interconnection model, the rigid body motion of the plurality of subsystems is represented by a set of differential equations as follows:

[0021]

[0022] Y i = C i X i

[0023] wherein, and Y i ∈ R 6 are the state variable and the output variable of subsystem i, respectively; U' i ∈ R 6 is the control variable of subsystem i, which is superimposed by the outer-loop edge control input Π i and the inner-loop nodal control input U i , U' j ∈ R​​​​​6 The control input of the neighbor subsystem j of the subsystem i is also composed of the outer loop control input and the inner loop node control input, q ie The attitude angle quaternion of the subsystem i is ω i The attitude angular velocity of the subsystem i is A i The characteristic matrix of the subsystem i is B B i The inertia expansion matrix of the subsystem i is C I a The inertia of the subsystem i is I i The output matrix of the subsystem i is C i = I 6×6 , Φ ij The coupling coefficient of the state quantity of the neighbor subsystem j to the state quantity of the subsystem i is B ij The coupling coefficient of the control quantity of the neighbor subsystem j to the state quantity of the subsystem i is B

[0024] Preferably, in the step S2.1, the optimal inner loop node control input of the subsystem i is :

[0025]

[0026] Wherein, The algebraic sum of the i-th row of the adjacency matrix of the subsystem i is G i The weight in the system cooperative tracking error of the subsystem i adjusts the proportion of the consistency error of the subsystem i and its neighbor subsystems -i and the expected instruction error of the subsystem i, so as to obtain better control precision, R i The value function V i of the subsystem i is determined by the weight matrix in the value function V i (δ -i , δ i ), which adjusts the tracking error and the control energy consumption, so as to achieve the optimal control effect with the minimum energy consumption, B i The inertia expansion matrix of the subsystem i is C The linear value decomposition function of the value function V i (δ -i , δ i ) of the subsystem i is decoupled from the coupling between the cooperative error δ -i of the subsystem i and the cooperative error δ i of its neighbor subsystems -i, and satisfies: The cooperative tracking error of the subsystem i is δ j The cooperative tracking error of the subsystem j is δ -i The set of the cooperative tracking errors of all the neighbor subsystems of the subsystem i is represented by δ cost function value decomposition function for subsystem i with respect to the state variable X of subsystem i i .

[0027] Preferably, in said step S2.1 the set of optimal inner-loop nodal control inputs of the N+1 subsystems reaching a global Nash equilibrium condition is:

[0028]

[0029] wherein, is the set of optimal inner-loop nodal control inputs of all the neighbor subsystems of subsystem i, J i is the cost function of subsystem i, is the optimal cost function of subsystem i, is the optimal inner-loop nodal control input of subsystem i, U i is the inner-loop nodal control input of subsystem i.

[0030] Preferably, in said step S2.2 the set of edge control inputs Π of all the subsystems satisfies the following condition:

[0031]

[0032]

[0033]

[0034]

[0035] wherein, is the derivative of Π i with respect to time t, is the partial derivative of the optimization control objective function of subsystem i with respect to the edge control input Π i of subsystem i, e i is the tracking error of subsystem i; e j is the tracking error of subsystem j, e ij = y ij - Π j is the coordination error, y ij is the estimate of the edge control input Π j of neighbor subsystem j by subsystem i, l ij is the topological coupling weight of subsystem i with respect to subsystem j, i≠j, is the auxiliary control quantity for automatically adjusting the topological coupling weight l ij of subsystem i with respect to subsystem j, is the auxiliary compensation adaptive law for .

[0036] Preferably, in the step S2, the overall control optimization index is:

[0037]

[0038] wherein, is the value function of the subsystem i outer loop edge control cost function i is the value function of the subsystem i outer loop edge control cost function i is the outer loop edge control input of the subsystem i.

[0039] Preferably, the optimal outer loop edge control input of the subsystem i satisfies the following Nash equilibrium:

[0040]

[0041] wherein, is the optimal outer loop edge control input of all neighbor subsystems of the subsystem i.

[0042] Yet another technical solution provided by the present application is to provide a computer readable storage medium, the computer readable storage medium stores a computer program, and the computer program is executed by a processor to realize the steps of the method of the first technical solution.

[0043] Another technical solution provided by the present application is to provide a terminal device, comprising a memory and a processor and a computer program stored in the memory and executable on the processor, characterized in that: the processor executes the computer program to realize the steps of the method of the second technical solution.

[0044] Compared with the prior art, the present application has the following beneficial effects:

[0045] (1) The present application forms a sequential Stackelberg equilibrium by two Nash equilibriums of outer loop edge control and inner loop node control, and adjusts the inner and outer loop control inputs sequentially to improve the attitude stability and the accuracy of the whole satellite attitude pointing control.

[0046] (2) The Stackelberg equilibrium principle proposed in the present application realizes high-precision cooperative control of multiple subsystems of a satellite ground station through sequential cooperative regulation of the inner loop (follower) and the outer loop (leader), and realizes high-precision control effect through the fusion of inner and outer loop control.

[0047] (3) The inner loop control of the present application considers the control constraints and optimization performance indicators of various types of load local subsystems, designs an inner loop distributed node controller that meets multiple constraints, and realizes the stability of the subsystem under multiple constraints to support the high-precision edge control of the outer loop.

[0048] (4), the outer loop control considers the coupling relationship of various load subsystems and platform subsystems, establishes a total high-precision control optimization index containing the performance index weight of each subsystem, maps the weight of each subsystem to the platform connection graph, and designs an outer loop edge control algorithm based on the platform connection graph;

[0049] (5), on the basis of the inner loop distributed node stable control, the auxiliary control amount of the topological coupling weight l ij of the subsystem i and the subsystem j and the auxiliary compensation adaptive law are automatically adjusted to realize the high-precision collaborative regulation and control of the satellite platform multi-subsystem by the outer loop, and the high-precision control effect is realized by fusing the inner and outer loop controls;

[0050] (6), the application can be applied to the high-precision and high-stability control of large on-orbit assembly structures such as modular reconfiguration spacecraft, large-size antennas and optical loads. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 The figure is a framework diagram of the large satellite platform distributed collaborative control method based on the inner and outer loop game of the embodiment of the application. DETAILED DESCRIPTION

[0052] The specific embodiments of the application will be further described below in combination with the drawings of the specification.

[0053] As Figure 1 The figure is a framework diagram of the large satellite platform distributed collaborative control method based on the inner and outer loop game, and the distributed collaborative control method based on the inner and outer loop game specifically includes the following steps:

[0054] Step 1: according to the influence of the assembly modules of the large satellite platform and the complex space environment (light pressure, gravity gradient, etc.) on the structure vibration and attitude drift during on-orbit operation, an on-orbit assembly satellite platform multi-subsystem interconnection model is established, the bidirectional influence mechanism between the platform subsystem and the load subsystem is analyzed, and a master-slave decision mechanism of the double loop is established; specifically including the following sub-steps:

[0055] Step 1.1: according to the assembly modules of the large satellite platform and the operating environment (light pressure, gravity gradient, etc. disturbance factors), in the on-orbit assembly satellite platform multi-subsystem interconnection model, the multi-subsystem interconnection system of N load subsystems and one platform subsystem is considered, and the individual rigid body motion of the platform subsystem and the load subsystem can be expressed as a group of differential equations as follows:

[0056]

[0057] Y i =C i X i

[0058] wherein, and Y i ∈R 6 are the state and output of subsystem i respectively; U′ i ∈R 6 are the control of subsystem i, which is composed of outer-loop edge control input and inner-loop node control input U i and U i are the outer-loop edge control input and inner-loop node control input of subsystem i respectively; U′ j ∈R 6 are the control of neighbor subsystem j of subsystem i, which is also composed of outer-loop edge control input and inner-loop node control input, q ie is the attitude quaternion of subsystem i, ω i is the attitude angular velocity of subsystem i; A i is the characteristic matrix of subsystem i, B i is the inertia expansion matrix of subsystem i, I a is the inertia of subsystem i, C i is the output matrix of subsystem i, C i = I 6×6 , Φ ij is the coupling coefficient of neighbor subsystem j state quantity to subsystem i state quantity, -i is the neighbor node set of subsystem i, B ij is the coupling coefficient of neighbor subsystem j control quantity to subsystem i state quantity.

[0059] Considering that the platform subsystem and the load subsystem N+1 subsystems form a connection graph The on-orbit assembled satellite platform multi-subsystem interconnection model unifies the satellite platform subsystem and the load subsystem as a subsystem, which is represented as a vertex of the connection graph, is the vertex set of the connection graph, is the edge set of the subsystem, and the neighbor node of node subsystem i is denoted as The coupling control relationship between the subsystems is the edge of the connection graph.

[0060] Based on the established on-orbit assembled satellite platform multi-subsystem interconnection model, whether the platform subsystem or the load subsystem has a unified model architecture, when control is performed, the motion of subsystem i is affected by the coupling of the system state (X j ) and the control quantity (U′ j ) of subsystem j, and similarly, the motion of subsystem j is affected by the coupling of the system state (X i ) and the control quantity (U′ i) coupling effect. Therefore, there is a bidirectional coupling effect between the subsystems, which breaks the control mode of the whole system as a unified whole after the platform subsystem and the load subsystem are assembled, and introduces the modeling concept of a multi-subsystem interconnected system, which can more finely depict the dynamics and kinematics characteristics of the on-orbit assembly, thus providing a new perspective to design the controller and further improving the stability and control accuracy of the whole multi-subsystem.

[0061] 2. Based on the analysis of the interconnected double-loop control target, considering the control constraints (such as coupling constraints between subsystems, collision, etc.) and the optimization performance index (minimum energy consumption, etc.) of each subsystem, a new differential game method is proposed to construct an auxiliary decoupling decision variable for each subsystem, ensuring that: 1) global Nash equilibrium, 2) each subsystem i only uses the information of the system itself and its neighbor nodes;

[0062] Step 2.1: According to the multi-subsystem interconnected system composed of the platform subsystem and the load subsystem established in step 1, in order to achieve stable control, the cooperative tracking error δ i of subsystem i is defined based on the connection graph

[0063]

[0064] where l ij is the topological coupling weight between subsystem i and subsystem j, i≠j, in the present application, the connection graph is defined as L=[l ij ], if (i,j)∈C, then l ij >0; when , l ij =0. (i,j)∈C indicates that there is an edge from subsystem j to subsystem i.

[0065] G i is the weight in the cooperative tracking error of subsystem i, which adjusts the proportion of the consistency error of subsystem i and its neighbor subsystem-i and the expected command error of subsystem i, so as to obtain better control accuracy. In the problem of multi-subsystem cooperative consistency, the main goal of each subsystem is to design its control input so that it can cooperate with the platform subsystem, i.e. to satisfy lim t→∞ (X i -X0)=0,i=1,2,…,N+1,0 is a zero vector with dimension N+1. X0 is the expected state quantity of the subsystem.

[0066] The subsystem error dynamic system can be established as:

[0067]

[0068] where D ithe algebraic sum of the i-th row of the adjacency matrix L, i.e., D i =∑ j l ij . U i is the inner-loop node control input of subsystem i, U j is the inner-loop node control input of subsystem i.

[0069] Step 2.2: Under the fixed outer-loop edge control input Π i and the set of outer-loop edge control inputs of all neighboring subsystems of subsystem i, Π -i , the control objective of the platform subsystem / payload subsystem i is not only to keep consistent with the leader, but also to optimize the individual performance index of the subsystem, forming the following cost function:

[0070]

[0071] where δ -i is the set of neighboring node tracking errors of subsystem i, and U -i is the set of neighboring node control inputs of subsystem i, satisfying: r i (δ i ,δ -i ,U i ,U -i )≥0 is the integral factor of the quadratic performance index function, used to evaluate the control performance of subsystem i. When and only when δ i =δ -i =0, r i (δ i ,δ -i ,U i ,U -i ) = 0, indicating that the collaborative control objective of the platform subsystem and the payload subsystem is achieved at this time, so that the input U i of the control subsystem i is U i = 0. Further, the value function V i (δ i ,δ -i ) of the inner-loop node control cost function J i of subsystem i is established:

[0072]

[0073] Thus, the control design objective of subsystem i in the differential graph game is to obtain the following optimal controller:

[0074]

[0075] where U is the optimal inner-loop node control input of subsystem i.

[0076] Step 2.3: On the basis of the neighbor node control input U -i of subsystem i, the optimal inner loop node control input of subsystem i satisfies the following condition:

[0077]

[0078] On this basis, the definition of global Nash equilibrium balance can be further obtained. For N+1 subsystems composed of satellite platforms and payloads, the N+1 element control input of the global Nash equilibrium condition is:

[0079]

[0080] wherein, denotes the control input set of all other subsystems except subsystem i. constitutes the set of optimal cost functions of all subsystems.

[0081] Under the premise that the subsystem is a rational person, Nash equilibrium plays an important role in non-cooperative games, representing the optimal control effect: after considering the optimal control input set of all neighbor subsystems, no subsystem i will actively change its control optimal control input to obtain a smaller cost function.

[0082] Step 2.4, for the cooperative stable control problem of platform subsystem and payload subsystem, according to the complex space environment such as solar pressure, thermal radiation, rarefied atmosphere, system time-varying uncertainty and vibration and other complex disturbance factors, the following value function quadratic performance index function of inner loop node control cost function J i of subsystem i is established:

[0083]

[0084] wherein, δ i is the cooperative tracking error of subsystem i, δ j is the cooperative tracking error of subsystem j, is the vector formed by the cooperative tracking error of subsystem i and subsystem j, Q ij is the weight matrix that determines the proportion of cooperative tracking error δ i in the value function V i (δ i , δ -i ) of inner loop node control cost function J ij of subsystem i, and R i is the inner loop node control cost function J ivalue function V i (δ i ,δ -i ) of subsystem i, R ij is the weight matrix determining the input proportion of the inner-loop node control of subsystem i in the value function V i (δ i ,δ -i ) of subsystem i, l ij is the topological coupling weight between subsystem i and subsystem j, i≠j.In the present application, the connection graph is defined as The adjacency matrix is L=[l ij ].If (i,j)∈C, l ij >0; when , l ij =0.(i,j)∈C indicates that there is an edge from subsystem j to subsystem i.Meanwhile, in order to realize the distributed inner-loop node control, the value function V i (δ i ,δ -i ) of the inner-loop node control of subsystem i needs to only depend on δ i , but not δ i and δ -i .

[0085] Step 2.5, the present application designs an auxiliary compensation term decouples the value function V i (δ i ,δ -i ) of the cost function of the subsystem, so that the distributed solution and the global Nash equilibrium are established at the same time.On this basis, the Hamilton-Jacobi (HJ) equation of the inner-loop node control of subsystem i is established:

[0086]

[0087] R j is the weight matrix determining the input proportion of the inner-loop node control of subsystem j in the value function V j (δ j ,δ j ) of the cost function J -j .

[0088] Further, the HJ equation is solved to obtain the optimal control input of each subsystem, which is specifically:

[0089]

[0090] wherein, δ i is the cooperative tracking error of subsystem i, δ jLet the cooperative tracking error of subsystem j be . Q is the vector formed by the cooperative tracking error of subsystems i and j. ij J is the control cost function of the link point within subsystem i. i Value function V i (δ i ,δ -i The cooperative tracking error δ is determined in the process. ij The weight matrix of proportions, R i J is the control cost function of the link point within subsystem i. i Value function V i (δ i ,δ -i The weight matrix R that determines the proportion of control inputs at internal nodes is used in the process. ij V is the value function of subsystem i. i (δ i ,δ -i The weight matrix that determines the proportion of control inputs at the nodes in the neighboring subsystem j of subsystem i is called the weight matrix. ij Let i≠j be the topological coupling weight between subsystem i and subsystem j. In this invention, a connection graph is defined. The adjacency matrix is ​​L = [l ij If (i,j)∈C, then l ij >0; when At that time, l ij =0. (i,j)∈C indicates that there exists an edge from subsystem j to subsystem i. The designed decoupling matrix, the cooperative error δ of decoupled subsystem i. i The cooperative error δ with its neighboring subsystem -i -i The coupling between them.

[0091] Furthermore, the value function V of the corresponding cost function of subsystem i i (δ i ,δ -i )for:

[0092]

[0093] This makes the value function V of the cost function of subsystem i. i (δ i ,δ -i The linear value decomposition function of the cost function of subsystem i is capable of being derived from the value function of subsystem i. It is obtained by superposition, specifically:

[0094]

[0095] in,

[0096] Step 2.6: According to the definition of distributed control, The optimization of the inner loop node control of the platform subsystem and each load subsystem is only dependent on δ i , by making The Hamilton function of the subsystem i can be obtained as follows:

[0097]

[0098] Further, the Hamilton function of the subsystem i can be obtained as follows:

[0099]

[0100] Further, by The inner loop node distributed optimal control input of the subsystem i can be obtained as follows:

[0101]

[0102] So far, the inner loop node distributed stable control algorithm of the platform subsystem and each load subsystem has been completed.

[0103] Step 3: Further considering the vibration coupling effect between each type of load subsystem and the platform subsystem, the external disturbance transmission effect and the coupling effect of the internal moving parts of the subsystem, an overall high-precision control optimization index containing the performance index weight of each subsystem is established, the weights of each subsystem are mapped to the platform connection graph, and an outer loop edge control algorithm based on the platform connection graph is designed by adjusting the edge weight of the platform subsystem and the load subsystem connection graph. The edge weight of the platform subsystem and the load subsystem connection graph is determined according to the importance of the edge in the overall system precision.

[0104] Specifically, the following sub-steps are included:

[0105] Step 3.1: Considering the vibration coupling effect between each type of load subsystem and the platform subsystem, the external disturbance transmission effect and the coupling effect of the internal moving parts of the subsystem, in the designed outer loop edge control algorithm, on the basis of the given inner loop node control U i , U -i The control goal of the subsystem i is to minimize the outer loop edge control cost function Γ i The value function

[0106]

[0107] Wherein, Π i The outer loop edge control input of the subsystem i Π = [Π1, Π2, …, Π N+1 ] T Is the edge control input set of the subsystem.

[0108] Step 3.2: Set the control input and cost performance function of each subsystem only effective for the subsystem itself, and not effective for other subsystems. Further, the subsystem can obtain Nash equilibrium through the following dynamic process:

[0109]

[0110]

[0111] where, y ij is the estimated value of subsystem i to the neighbor subsystem j edge control input Π j l ik is the topological coupling weight of subsystem i and subsystem k i≠k.

[0112] Step 3.3: Based on the optimal outer loop edge control input group For the introduction of the following control input Nash equilibrium:

[0113]

[0114] where, is the optimal outer loop edge control input of subsystem i. is the optimal outer loop edge control input of all neighbor subsystems of subsystem i.

[0115] Step 3.4: Establish the overall high-precision control optimization index containing the performance index weight of each subsystem, map the weight of each subsystem to the platform connection topology , through the adaptive adjustment of the edge weight of the platform subsystem and the load subsystem connection graph, design the following distributed adaptive edge control input to realize Nash equilibrium:

[0116]

[0117]

[0118]

[0119]

[0120] where, is the auxiliary control quantity for automatically adjusting the edge weight value of subsystem i and subsystem j, is the auxiliary control quantity for automatically adjusting the topological coupling weight l ij of subsystem i and subsystem j, is the auxiliary compensation adaptive law of , which satisfies

[0121] Step 3.5, introduce the coordination error eij =y ij -Π j , the dynamic system can be further updated as:

[0122]

[0123]

[0124]

[0125]

[0126] where, is the value function of the outer-loop edge control cost function Γ i of subsystem i, is the derivative of Π i with respect to time t, is the partial derivative of the optimization control objective function of subsystem i with respect to the edge control input Π i of subsystem i, e i is the tracking error of subsystem i; e j is the tracking error of subsystem j, e ij =y ij -Π j is the coordination error, y ij is the estimated value of the edge control input Π j of neighbor subsystem j by subsystem i, l ik is the topological coupling weight between subsystem i and subsystem k, i≠k. In the present application, the connection graph is defined as The adjacency matrix is L=[l ik ]. If (i, k)∈C, then l ij >0; when , l ij =0. (i, k)∈C indicates that there is an edge from subsystem k to subsystem i.

[0127] So far, the designed outer-loop edge control input Π i is optimized, and finally reaches the Nash equilibrium.

[0128] 4. Unlike the standard Stackelberg equilibrium, there is a Nash equilibrium in both the inner-loop follower and the outer-loop leader. Combining the two equilibriums together constitutes an interactive Stackelberg equilibrium, which expands the control input of the standard Stackelberg differential graph equilibrium. By sequentially adjusting the control input of the inner-loop follower and the outer-loop leader, the cooperative optimization high-precision high-stability control of the satellite platform and each load is realized. The specific steps are as follows:

[0129] Step 4.1: Based on the designed internal node distributed stable control algorithm and distributed outer loop edge control algorithm, establish the sequential game decision process:

[0130] 1) Fixed outer ring edge control input Π i ,Π -i Determine the topological coupling weights l between the platform subsystem and the payload subsystem. ij Based on this, the platform subsystem and the load subsystem are coordinated and stabilized by a distributed control algorithm, laying the foundation for high-precision and high-stability control objectives.

[0131] 2) Control input U at fixed nodes i U -i Based on this, the distributed edge control algorithm further refines the consideration of the coupling effect between the subsystems to achieve the expected high-precision and high-stability control objective.

[0132] To achieve high-precision and stable control of the platform and payload subsystems, distributed edge control plays a dominant role in the decision-making process. It not only imposes its decisions on the internal node control inputs (the topological connection diagram of the platform and payload subsystems) but also adjusts the control inputs based on the node control inputs. Therefore, the distributed edge control inputs are designated as the leader, and the distributed node control inputs as the followers, thus forming a sequential Stackelberg differential graph game.

[0133] Step 4.2: On one hand, the inner-loop distributed stable empty control collaboratively optimizes to Nash equilibrium; on the other hand, the edge weights of the outer-loop edge control collaborative conditional connection graph form the outer-loop Nash equilibrium, resulting in a sequential alternation. The following Stackelberg equilibrium is introduced:

[0134] (1) For the outer loop control input Π of subsystem i i The set of outer loop control inputs of all neighboring subsystems of subsystem i, Π -i There exists an outer loop control input of Π i Optimal internal link control input of subsystem i Make:

[0135]

[0136] Established;

[0137] (2) For any inner and outer loop coordinated control pair {Π,U(Π)}, there exists an optimal outer loop side control input for subsystem i. Make:

[0138]

[0139] Established;

[0140] When designing within the Stackelberg countermeasure framework, following the control input U of distributed nodes... i At that time, the leader's side control input Π i ,Π -i It is given and permissible; therefore, the control cost function J at each node within subsystem i is... i Value function V i (δ i ,δ -i The distributed optimization problem of Π can be viewed as a standard quadratic tracking control problem, where Π i ,Π -i This is considered an externally sourced bounded signal to achieve Nash equilibrium in the node control system. Secondly, when designing the leader-side control input, U at this time... i U -i Treating it as a bounded external bounded signal, further controlling the outer loop cost function This enables the edge control input to reach Nash equilibrium; ultimately, based on the Nash equilibrium formed by the inner and outer loops, the two reach Stackelberg equilibrium, thus achieving the expected high-precision and high-stability control objective.

[0141] In summary, the satellite platform distributed cooperative control method based on inner and outer loop game theory proposed in this invention includes the following steps:

[0142] S1. Establish an interconnection model of multiple subsystems on the on-orbit assembled satellite platform and generate a connection diagram. The on-orbit assembled satellite platform multi-subsystem interconnection model collectively refers to the satellite platform subsystem and payload subsystem as subsystems, which are represented as vertices in the connectivity graph. Let be the set of vertices in the connectivity graph, and let be the edges of the connectivity graph representing the coupling control relationships between subsystems. The edge set of the subsystem;

[0143] S2. Set the distributed edge control as the outer loop leader and the distributed node control as the inner loop follower. By sequentially adjusting the control inputs of the inner loop follower and the outer loop leader, the coordinated control of the satellite platform and each payload is achieved. The specific sequential adjustment process is as follows:

[0144] S2.1, Fixed subsystem i outer loop control input Π i The set of outer loop control inputs of Π and all its neighboring subsystems -i Determine the topological coupling weights l between subsystem i and subsystem j. iji≠j, considering the control constraints and the optimization performance index of each subsystem individual, an auxiliary decoupling decision variable is constructed for each subsystem, the inner loop node control of the platform subsystem and each load subsystem is distributedly stabilized, so that each subsystem satisfies the Nash equilibrium condition;

[0145] S2.2, fixing the inner loop node control input U i of the subsystem i and the set U -i of the inner loop node control inputs of all neighboring subsystems of the subsystem i i On this basis, a control optimization index containing the performance index weight of each subsystem is established, the weight of each subsystem is mapped into the connection graph, the outer loop edge control based on the connection graph is performed by adjusting the edge weight of the connection graph, so that the edge control input satisfies the Nash equilibrium;

[0146] S2.3, judging whether the Stackelberg equilibrium is satisfied after the execution of steps S2.1 and S2.2, if yes, ending, otherwise, continuing to execute steps S2.1 and S2.2.

[0147] The Stackelberg equilibrium is as follows:

[0148] For the outer loop edge control input Π i of the subsystem i -i , there exists the optimal inner loop node control input i of the subsystem i when the outer loop edge control input is Π i , so that:

[0149]

[0150] is established;

[0151] Wherein, J i is the inner loop node control cost function of the subsystem i , U -i is the set of the optimal outer loop edge control inputs of all neighboring subsystems of the subsystem i

[0152] For any inner-outer loop collaborative control pair {Π, U(Π)}, there exists the optimal outer loop edge control input of the subsystem i , so that:

[0153]

[0154] is established;

[0155] Wherein, Γ i is the outer loop edge control cost function of the subsystem i , U(Π) is the corresponding inner loop node control input when the outer loop edge control input of the subsystem is Π. For the optimal outer loop control input of subsystem i, The outer loop control input is Π i The optimal internal link control input for subsystem i; The outer loop control input is Π i The set of optimal internal node control inputs of all neighboring subsystems of subsystem i.

[0156] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements as follows: Figure 1 The steps of the method are described.

[0157] This invention provides a terminal device, including a memory and a processor, and a computer program stored in the memory that can run on the processor. When the processor executes the computer program, it implements the following... Figure 1 The steps of the method are described.

[0158] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computationally usable program code.

[0159] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, systems, and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks within the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 A means for a process or multiple processes and / or a function specified in one or more boxes within a block.

[0160] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0161] These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 These computer program instructions can also be loaded into a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks.

[0162] The present application has been disclosed with reference to the preferred embodiments thereof while it is understood that the application is capable of making modifications and variations thereto without departing from the scope of the application. Accordingly, the detailed description and examples are to be regarded as illustrative in nature and not restrictive.

Claims

1. A satellite platform distributed cooperative control method based on inner-outer loop game, characterized in that, Comprising the following steps: S1, establish a multi-subsystem interconnection model of an on-orbit assembly satellite platform and form a connection graph The multi-subsystem interconnection model of the on-orbit assembly satellite platform collectively refers to satellite platform subsystems and load subsystems as subsystems, and the subsystems are represented as vertices of a connection graph, The coupling control relationship between the subsystems is an edge of the connection graph, The edge set is the subsystem. S2, the distributed edge control is set as the outer ring leader, the distributed node control is set as the inner ring follower, the control input of the inner ring follower and the outer ring leader is adjusted sequentially to realize the cooperative control of the satellite platform and each load, and the specific sequential adjustment process is as follows: S2.1, the outer-loop control input set Π of subsystem i i and all its neighboring subsystems -i , determine the topological coupling weight l between subsystem i and subsystem j ij i≠j, considering the individual control constraints and optimization performance indicators of each subsystem, construct an auxiliary decoupling decision variable for each subsystem, and perform distributed stable control on the inner-loop nodes of the platform subsystem and each load subsystem to make each subsystem satisfy the Nash equilibrium condition; S2.2, the inner loop node control input U of the fixed subsystem i i and the set U of all its neighboring subsystem inner loop node control inputs -i On this basis, the control optimization index containing the performance index weight of each subsystem is established, the weight of each subsystem is mapped to the connection graph, the outer loop edge control based on the connection graph is performed by adjusting the edge weight of the connection graph, so that the edge control input satisfies the Nash equilibrium; S2.3, judging whether the Stackelberg equilibrium is met after steps S2.1 and S2.2 are executed, if yes, ending, otherwise, continuing to execute steps S2.1 and S2.

2.

2. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 1, characterized in that The Stackelberg equilibrium is as follows: For the outer loop control input Π of subsystem i i The set of outer loop control inputs of all neighboring subsystems of subsystem i, Π -i There exists an outer loop control input of Π i Optimal internal link control input of subsystem i Make: The Stackelberg equilibrium is as follows: where J i is the inner-loop node control cost function for subsystem i, is the set of all neighbor subsystem inner-loop node control inputs for subsystem i -i is the set of all neighbor subsystem optimal outer-loop edge control inputs for subsystem i For any inner-outer loop coordinated control pair {Π, U(Π)}, there exists an optimal outer-loop boundary control input for subsystem i such that: The Stackelberg equilibrium is as follows: where Γ i is the cost function of the outer-loop edge control of subsystem i, U(Π) is the corresponding inner-loop node control input of subsystem i when the input of the outer-loop edge control is Π, is the optimal inner-loop node control input of subsystem i when the input of the outer-loop edge control is Π is the optimal inner-loop node control input of subsystem i when the input of the outer-loop edge control is Π i ; is the set of optimal inner-loop node control inputs of all neighboring subsystems of subsystem i when the input of the outer-loop edge control is Π i .

3. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 1, characterized in that, In the on-orbit assembly satellite platform multi-subsystem interconnection model, the rigid body motion of the plurality of subsystems is represented as a group of differential equations as follows: Y i = C i X i where, and Y i ∈R 6 are the state and output of subsystem i respectively; U' i ∈R 6 is the control of subsystem i, which is composed of outer-loop edge control input and inner-loop node control input U i and U i ; U' j ∈R 6 is the control of neighbor subsystem j of subsystem i, which is also composed of outer-loop edge control input and inner-loop node control input q ie is the attitude quaternion of subsystem i, ω i is the attitude angular velocity of subsystem i; A i is the characteristic matrix of subsystem i, B i is the inertia expansion matrix of subsystem i, I a is the inertia of subsystem i, C i is the output matrix of subsystem i, C i = I 6×6 , Φ ij is the coupling coefficient of neighbor subsystem j state to subsystem i state, -i is the neighbor node set of subsystem i, B ij is the coupling coefficient of neighbor subsystem j control to subsystem i state.

4. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 3, characterized in that, In said step S2.1, the optimal inner loop node control input of subsystem i is given by: : where D i″ is the algebraic sum of the i-th row of the adjacency matrix of the subsystem, G i is the weight in the system cooperative tracking error of the subsystem i, which adjusts the consistency error of the subsystem i and its neighbor subsystem -i and the proportion of the expected command error of the subsystem i to obtain better control precision, R i is the value function V i of the subsystem i, and i is the weight matrix in the decision of the control input proportion in the value function V -i (δ i ,δ i ), which adjusts the tracking error and the control energy consumption to achieve the optimal control effect with the minimum energy consumption, B i is the rotational inertia expansion matrix of the subsystem i, which constructs is the value function V -i of the subsystem i, and i is the linear value decomposition function of the value function V -i (δ i ,δ j ), which decouples the coupling between the cooperative error δ -i of the subsystem i and the cooperative error δ -i of its neighbor subsystem -i, and satisfies: δ i is the cooperative tracking error of the subsystem i, δ j is the cooperative tracking error of the subsystem j, and δ -i represents the set of the cooperative tracking errors of all the neighbor subsystems of the subsystem i, is the value decomposition function of the cost function of the subsystem i is the partial derivative with respect to the state quantity X i of the subsystem i.

5. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 4, characterized in that, The step S2.1, the set of optimal inner loop node control inputs of N+1 subsystems The global Nash equilibrium condition is reached when: wherein, J is a set of optimal inner-loop node control inputs for all neighboring subsystems of subsystem i, i C is a cost function for subsystem i, C is an optimal cost function for subsystem i, U is an optimal inner-loop node control input for subsystem i, i U is an inner-loop node control input for subsystem i.

6. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 1, characterized in that In the step S2.2, the edge control input set Π of all the subsystems satisfies the following condition: in, For Π i The derivative with respect to time t, The side control input Π of the optimal control objective function of subsystem i with respect to subsystem i i The partial derivative of e i e represents the tracking error of subsystem i; j Let e ​​be the tracking error of subsystem j. ij =y ij -Π j For the cooperative error, y ij For subsystem i, the control input Π is used to control the neighboring subsystem j. j The estimated value, l ij The topological coupling weights of subsystem i and subsystem j are i≠j. To automatically adjust the topological coupling weights l between subsystem i and subsystem j ij Auxiliary control quantity, for The auxiliary compensation adaptive law.

7. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 1, characterized in that In the step S2, the control optimization index is: wherein, is the value function of the outer-loop edge control cost function Γ i for subsystem i, Π i is the outer-loop edge control input for subsystem i.

8. The satellite platform distributed cooperative control method based on inner-outer loop game according to claim 1, characterized in that Optimal outer loop edge control input for subsystem i satisfies the Nash equilibrium: wherein, is the best outer-loop control input for all neighboring subsystems of subsystem i.

9. An electronic device, comprising: Comprising: Memory: for storing computer readable instructions; And A processor for running the computer readable instructions to execute the method of any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, A computer program is stored thereon, and the computer program is run by the processor to realize the method of any one of claims 1-8.

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