A method for heterogeneous dynamic feedback control of multi-mode state-dependent switching continuous linear systems

Abstract

This invention discloses a heterogeneous dynamic feedback control method for multi-mode state-dependent switching continuous linear systems. It employs a heterogeneous dynamic feedback switching control architecture, independently designing optimal-order controllers for multiple operating conditions such as coarse satellite acquisition and fine control. While ensuring optimal local performance in each mode, it achieves coordinated operation of heterogeneous subsystems, significantly improving the flexibility and specificity of the control system design. Addressing the energy surge and impact issues caused by abrupt changes in state dimension during heterogeneous switching, this invention proposes a dynamic initial value adjustment strategy for the controller based on multi-Lyapunov function extremum optimization. This strategy calculates and resets the internal state of the new controller in real time, effectively reducing switching disturbances, ensuring continuous and smooth control signals, and suppressing transient oscillations and hard switching shocks during mode switching. Simultaneously, a dimension-reduced state-dependent switching rule based on nested ellipsoids is designed to reduce the observation requirements of high-dimensional augmented states. Combined with dwell time analytical constraints, it is theoretically proven that the closed-loop system is globally uniformly bounded under bounded disturbances, enabling asymptotic convergence and smooth transition from coarse to high-precision modes in noisy environments.

Description

Technical Field

[0001] This invention relates to spacecraft control, and more particularly to a method for heterogeneous dynamic feedback control of a multi-mode state-dependent switching continuous linear system. Background Technology

[0002] In complex systems with significant multimodal characteristics, such as drag-free satellite attitude control, motion regulation of precision manufacturing equipment, and stabilization control of spaceborne gravitational wave detection platforms, systems often need to dynamically switch between different operating conditions (e.g., startup phase, steady-state operation phase, high-precision tracking phase) to adapt to the differentiated requirements for robustness, response bandwidth, tracking accuracy, and anti-interference capabilities under different scenarios. The control performance of such complex systems directly determines the achievement of core indicators of high-end equipment, and breakthroughs and optimizations in their control technology have become key to driving technological upgrades in related fields. However, existing switching control schemes still have significant technical bottlenecks in adapting to heterogeneous controller architectures, suppressing transient impacts during switching, and optimizing switching decision logic, making it difficult to meet the extreme requirements of high-precision missions for control system stability, smooth dynamic response, and local optimal performance.

[0003] The core limitation of traditional switching system stability theory lies in its widespread use of the same-order controller assumption, which assumes that all controllers for all subsystems have the same state dimension. While this simplifies stability analysis, it fundamentally contradicts practical engineering requirements. In real-world multi-mode control tasks, the operating characteristics, disturbance intensity, and performance requirements of systems differ significantly across modes. For example, during system startup or coarse-tuning, robustness and response speed are prioritized, typically employing simple, low-order controllers. Conversely, during steady-state operation or fine-tuning, high-precision tracking at the nanometer or micrometer level is required, often necessitating the design of high-order, fine-tuning controllers with more correction and filtering modules. Existing same-order theoretical frameworks are incompatible with such heterogeneous controller architectures, forcing engineers to unify controller order by artificially increasing the dimension of low-order controllers or simplifying the structure of high-order controllers. This compromise directly sacrifices local optimal control performance in specific modes, making it difficult for control systems to simultaneously meet the ultimate targets of robustness, response speed, and tracking accuracy across the entire operating range, severely hindering the improvement of core performance in complex systems.

[0004] More critically, the dimensionality mismatch caused by switching between different modal controllers can lead to severe transient shocks, and the shortcomings of existing solutions in switching rule design and stability analysis further exacerbate the operational risks of the system. Due to the differences in the internal state dimensions of different modal controllers, the system faces abrupt changes in the state space structure at the moment of mode transition. The jump in the controller state dimension directly causes state discontinuity, resulting in severe transient shocks. These shocks not only cause abrupt changes in control quantities but may also damage the stability of the closed-loop system. Under strong disturbances, they may even induce system divergence and instability, posing a serious threat to the operational safety of high-value platforms such as spacecraft and precision manufacturing equipment. Meanwhile, traditional state-dependent switching rules rely solely on the single external state of the controlled object for decision-making, failing to integrate internal controller state information. This results in insufficient effective information for switching decisions and an inability to accurately adapt to the multidimensional dynamic changes of the system. Although some cutting-edge research (such as the "pseudo-continuity" theory) attempts to address the problem of heterogeneous switching, it often imposes stringent topological constraints on the switching logic (e.g., prohibiting the system from returning to a higher-dimensional mode after switching from a "higher-dimensional mode to a lower-dimensional mode"), significantly weakening the universality of the control strategy under complex operating conditions. Furthermore, existing stability analysis methods for heterogeneous switching systems (such as stability conditions based on linear matrix inequalities) fail to fully cover the state transition at the moment of switching and lack analytical estimation of dwell time, making it difficult to theoretically guarantee the global stability of the system. In high-end applications such as spaceborne gravitational wave detection and ultra-precision machining, traditional solutions also suffer from insufficient noise suppression capabilities and discontinuous control quantities, leading to abrupt state changes during switching and failing to meet the stringent requirements of high-precision scientific measurement and precision manufacturing. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of closed-loop system switching instability and transient impact caused by inconsistent (different orders) of modal controllers in complex multi-mode control systems, overcome the dependence of existing switching control theory on the isomorphism of subsystems, and provide a general dynamic feedback switching control method with different orders.

[0006] This invention provides a method for heterogeneous dynamic feedback control of a multi-mode state-dependent switching continuous linear system, comprising: Establish the continuous-time linear state-space equation of the controlled object, and provide N dynamic feedback controllers of different orders for N different working modes, where N is a natural number greater than 1. Based on the continuous-time linear state-space equation of the controlled object, nested ellipsoidal regions are constructed in the low-dimensional state space of the controlled object based on the energy function, where each ellipsoidal region has N different working modes. Determine whether the monitored physical quantity crosses the energy boundary of each ellipsoidal region; if so, trigger a switch in the working mode. When switching signal switching modes, the transient impact caused by the change of controller order is eliminated by resetting the initial value.

[0007] In one embodiment of the present invention, it further includes: Based on the energy decay characteristics of the system under bounded perturbation, a minimum residence time constraint Tmin is set; The minimum dwell time constraint Tmin must satisfy: ; ϵ is the width parameter of the switching boundary buffer, b1 is a constant related to the system decay rate, C is the energy threshold of the switching surface, and M1 is the maximum possible energy jump value at the moment of switching. This is the effect of the disturbance ω(t) on the energy derivative of the system.

[0008] In one embodiment of the present invention, establishing the continuous-time linear state-space equation of the controlled object and designing N dynamic feedback controllers of different orders for N different operating modes includes: Establish a model of the controlled object; Design a group of controllers of different orders for the controlled object model; Construct a closed-loop augmentation system.

[0009] In one embodiment of the present invention, the dynamic equation of the controlled object is: ; in, The state of the controlled object, To control the input, For external disturbances, y p (t) represents the measurement output, A p B p D p C p This is a system matrix with corresponding dimensions.

[0010] In one embodiment of the present invention, the design of a heterogeneous controller group for the controlled object model includes: For the i-th operating mode, i∈{1,2,…,N}, design the i-th dynamic feedback controller, whose state-space equation is: ; in, Let n be the internal state of the i-th controller, and the controller order n in different modes. i They can be different.

[0011] In one embodiment of the present invention, the construction of the closed-loop augmentation system includes: Define the augmented state vector of the i-th subsystem Then the state equation of the i-th closed-loop subsystem is: ; Among them, the closed-loop system matrix A i It is composed of a controlled object matrix and a controller matrix.

[0012] In one embodiment of the present invention, based on the continuous-time linear state-space equation of the controlled object, nested ellipsoidal regions are constructed in the low-dimensional state space of the controlled object based on energy functions, wherein each ellipsoidal region has N different operating modes, including: Divide the state space into regions and define a nested ellipsoidal region R. i As work areas for different control modes: ; in, Let C0 be a positive definite symmetric matrix, and let Ci be the energy threshold constant defining the ellipsoidal boundary, where C0 = 0 and CN = +∞.

[0013] In one embodiment of the present invention, determining whether the monitored physical quantity crosses the energy boundary of each ellipsoidal region, and triggering a working mode switch if so, includes: Real-time monitoring of the status of the controlled object x p When the state trajectory crosses the boundary of the ellipsoid, the switching signal σ(t) changes abruptly. In a dual-mode system, the switching rules are as follows: ; Wherein, Ω represents the preset inner region.

[0014] In one embodiment of the present invention, when switching signal switching modes, eliminating transient impacts caused by changes in controller order through initial value reset includes: When the switching signal σ(t) is at time t k When switching from mode j to mode i, a quadratic Lyapunov function is selected for the i-th subsystem. And matrix P i According to the state x of the controlled object p and controller state x c,i Divide into blocks: ; ; Where P i,2 Corresponding to the controller state part, and being a positive definite matrix, P i,1 Corresponding controlled object state x p Its own quadratic term, P i,12 Corresponding controlled object state x p With the i-th controller state xc,i Cross-coupling terms between them, P i,21 With P i,12 Together they constitute the state intersection term; Take the partial derivative with respect to the controller state and set it to zero: ; Calculate and assign the optimal initial value.

[0015] In one embodiment of the present invention, the optimal initial state x of the activation controller i is... c,i(tk) for: .

[0016] The present invention has the following beneficial effects: (1) Breaking the isomorphic limitation and achieving full compatibility of controllers of different orders. The present invention theoretically removes the strict constraint of traditional switching systems that subsystems must have the same dimension (same order). By constructing an augmented system framework based on dynamic feedback, this scheme allows for the independent synthesis of the optimal order H∞ controller for different operating modes (such as the coarse acquisition mode and scientific measurement mode of satellites) (for example, mode 1 uses a 4th order controller and mode 2 uses a 5th order controller). This function enables the control system design to accurately match the frequency band and accuracy requirements under different operating conditions, avoiding the introduction of redundant dynamics or the sacrifice of control performance in order to achieve the desired order.

[0017] (2) Eliminating transient shocks and achieving a smooth, seamless transition. To address the energy surge caused by abrupt dimensional changes during mode transitions, this invention features transient energy minimization. By implementing a dynamic controller initial value adjustment strategy, the system can automatically search for and start a new controller from a local minimum point on the Lyapunov energy surface during mode transitions. Simulation results show that in drag-free satellite control missions, this function ensures the continuity of the control input u(t) and the system state x. p The smooth transition without abrupt changes in (t) effectively suppresses mechanical resonance and overshoot induced by hard switching.

[0018] (3) Establishing residence time constraints to ensure global robust stability. This invention integrates a stability criterion based on multiple Lyapunov functions (MLF). By analytically calculating the minimum residence time Tmin and embedding it into the control logic, this scheme can force the system to meet the energy dissipation requirements in a single mode. Theoretical derivation proves that even in harsh environments with bounded external disturbances ω(t), this function can still guarantee the global uniformity and boundedness of the closed-loop system, completely eliminating the risk of Zeno phenomenon or finite escape instability caused by frequent switching, and significantly improving the survivability and control accuracy of the system in complex environments.

[0019] Furthermore, the technical solution of this invention can be applied to the aerospace field. For example, the controlled object may include one or more of the following: artificial satellites, deep space probes, manned spacecraft, space telescopes and scientific payloads, spacecraft actuators and movable parts, on-orbit servicing and operation devices, and controlled structures in microgravity environments. Its technical effect is that it can significantly improve control accuracy. Attached Figure Description

[0020] Figure 1 A flowchart of a heterogeneous dynamic feedback control method for a multi-mode state-dependent switching continuous linear system according to an embodiment of the present invention is shown. Figure 2 A closed-loop architecture diagram of a multi-mode state-dependent switching continuous linear system according to an embodiment of the present invention is shown. Figure 3 A schematic diagram of state space partitioning in one embodiment of the present invention is shown; Figure 4 A multi-mode smooth switching diagram under nominal operating conditions is shown in an embodiment of the present invention; and Figure 5 A control quantity curve variation diagram is shown in one embodiment of the present invention. Detailed Implementation

[0021] In the following description, the invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be practiced without one or more specific details or with other alternatives and / or additional methods, materials, or components. In other instances, well-known structures, materials, or operations are not shown or described in detail so as not to obscure the inventive points of the invention. Similarly, for illustrative purposes, specific quantities, materials, and configurations are set forth to provide a comprehensive understanding of embodiments of the invention. However, the invention is not limited to these specific details.

[0022] In this invention, the various embodiments are merely intended to illustrate the solutions of the invention and should not be construed as limiting.

[0023] In this specification, references to "an embodiment" or "this embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily refer to the same embodiment in all instances.

[0024] Furthermore, the numbering of the steps in the methods of the present invention does not limit the execution order of the method steps. Unless otherwise specified, the method steps may be executed in different orders.

[0025] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0026] Figure 1 A flowchart of a method for heterogeneous dynamic feedback control of a multi-mode state-dependent switching continuous linear system according to an embodiment of the present invention is shown.

[0027] like Figure 1 As shown, in this embodiment, the heterogeneous dynamic feedback control method for a multi-mode state-dependent switching continuous linear system includes: S1. Construct a multi-mode, different-order switching system model, establish the continuous-time linear state-space equation of the controlled object, and design N dynamic feedback controllers of different orders for N different operating modes: First, a model of the controlled object is established, and the dynamic equations of the controlled object are described as follows: ; in, The state of the controlled object, To control the input, For external disturbances, y p (t) represents the measurement output, A p B p D p C p A system matrix with corresponding dimensions; Secondly, a heterogeneous controller group is designed. For the i-th operating mode, i∈{1,2,…,N}, the i-th dynamic feedback controller is designed, and its state-space equation is: ; in, Let n be the internal state of the i-th controller, and the controller order n in different modes. i They can be different; Finally, construct the closed-loop augmented system and define the augmented state vector of the i-th subsystem: Then the state equation of the i-th closed-loop subsystem is: ; Among them, the closed-loop system matrix A i It is composed of a controlled object matrix and a controller matrix.

[0028] S2. Construct reduced-dimensional state dependency switching rules. In order to achieve automatic switching between different modes, in the low-dimensional state space R of the controlled object... m The design of nested ellipsoidal regions based on energy functions: First, divide the state space into regions: define a series of nested ellipsoidal regions R. i As an effective working area for different control modes: ; in, The matrix is ​​positive definite symmetric, Ci is the energy threshold constant defining the ellipsoidal boundary, C0=0, CN=+∞; Real-time monitoring of the status of the controlled object x p When the state trajectory crosses the boundary of the ellipsoid, the switching signal σ(t) changes abruptly. In one embodiment of the present invention, for a dual-mode system, the switching rule is as follows: ; Wherein, Ω represents the preset inner region.

[0029] S3. Perform dynamic optimization of controller initial values ​​at the switching time: When the switching signal σ(t) is at time t k When switching from mode j to mode i, a quadratic Lyapunov function is selected for the i-th subsystem. And matrix P i According to the state x of the controlled object p and controller state x c,i Divide into blocks: ; ; Where P i,2 Corresponding to the controller state part, and being a positive definite matrix, P i,1 Corresponding controlled object state x p Its own quadratic term, P i,12 Corresponding controlled object state x p With the i-th controller state x c,i Cross-coupling terms between them, P i,21 With P i,12 Together they constitute the state intersection term; Take the partial derivative with respect to the controller state and set it to zero: ; Calculate and assign the optimal initial value, and activate the optimal initial state x of controller i. c,i(tk) for: .

[0030] S4. Determine the minimum dwell time to ensure stability: To prevent system instability caused by frequent switching, a minimum residence time constraint is set based on the system's energy decay characteristics under bounded disturbances. The minimum residence time Tmin is calculated as follows: After entering the i-th mode, the system must maintain that mode for at least Tmin time. The analytical estimate of this time satisfies: ; ϵ is the width parameter of the switching boundary buffer, b1 is a constant related to the system decay rate, C is the energy threshold of the switching surface, and M1 is the maximum possible energy jump value at the moment of switching. This is derived from the optimization problem... Sure, This is the effect of the disturbance ω(t) on the energy derivative of the system.

[0031] In this embodiment, the core improvement of the invention lies in the deep integration of the stability theory of multiple Lyapunov functions (MLF) with the principle of optimal control. In a system switching between different order modes, when the system switches from mode j (corresponding to controller order nj) to mode i (corresponding to controller order ni), the traditional direct switching method causes discontinuous jumps in the system state vector in the phase space due to the abrupt change in the state space dimension. This results in a violent positive impulse (i.e., ΔV>0) in the Lyapunov energy function V(x), which manifests as control jitter and transient overshoot. To address this technical problem, the invention fully utilizes the degrees of freedom of the controller state xc,i(tk) at the moment of switching, defines the Lyapunov function Vi(x) as a metric of the system's generalized energy, and analytically calculates the initial controller state that minimizes the total energy of the current system by solving the extremum condition ∂Vi / ∂xc,i=0. This technical strategy is mathematically equivalent to forcibly constraining the system state to the local minimum potential energy point of the new modal energy surface. Through this active initial value reset operation, the system can instantly offset the potential energy difference when the dimension changes, achieving the continuous or decreasing value of the Lyapunov function (ΔV≤0), fundamentally suppressing the transient shock caused by dimension mismatch, and achieving a smooth and seamless transition between different order controllers.

[0032] For conventional state-dependent switching methods, they typically rely on fully augmented states (including controller states). However, in heterogeneous systems, the physical meaning of augmented states changes with mode variations, making it difficult to define switching boundaries uniformly. To address this technical deficiency, this invention is based on the physical state x of the controlled object. p To maintain continuity, a series of nested ellipsoidal invariant sets are constructed in a low-dimensional common state space. This design utilizes the principle of topological mapping to project the stability constraints of a high-dimensional heterogeneous system onto a low-dimensional physical space, where the switching rules depend only on the physical state x. p The switching logic is decoupled from the controller order relative to the energy boundary. This dimensionality reduction not only reduces the computational load on the observer but also improves the system's robustness to unmodeled dynamics by directly triggering mode transitions through the energy level of the physical state.

[0033] The stability of a switching system is determined by the balance between "energy dissipation during subsystem operation" and "energy jump at the moment of switching." If the switching frequency is too high, the accumulated jump energy will exceed the energy dissipation capacity of the subsystem, leading to system divergence. This invention establishes a minimum dwell time Tmin based on the energy balance inequality through rigorous derivation. This constraint forces the system to operate for a sufficient time in a single mode to dissipate the energy injected by the disturbance ω(t) and the residual potential energy generated by the switching. Theoretically, this design ensures that the Lyapunov function of the closed-loop system generally decreases along the operating trajectory (or converges to the bounded region), rigorously proving the globally consistent boundedness of the system under bounded disturbances, and completely avoiding the Zeno phenomenon (i.e., infinitely fast switching) and finite escape instability risks that may be caused by switching at different orders.

[0034] Figure 2 A closed-loop architecture diagram of a multi-mode state-dependent switching continuous linear system according to an embodiment of the present invention is shown.

[0035] Figure 3 A schematic diagram of state space partitioning in one embodiment of the present invention is shown.

[0036] like Figure 2 and Figure 3 As shown, this invention addresses the technical deficiency of traditional switching logic, which relies on a fully augmented state composed of "controlled object state + controller state." It proposes a novel switching structure design, the core improvement of which lies in optimizing the signal connection method of the switching decision module. This switching decision module establishes a signal connection only with the physical state output terminal of the controlled object, and is completely independent of the internal state x of the controller. c (t) creates a coupling relationship.

[0037] The design logic of this switching structure is based on the physical state x of the controlled object. p By leveraging the inherent continuity of (t), and through topological mapping and energy constraint modeling, a series of nested ellipsoidal invariant sets (such as...) are constructed in a low-dimensional common phase space. Figure 3 The regions R1, R2, ..., Rn shown in the diagram represent the stability boundaries of different operating modes, with each ellipsoidal invariant set corresponding to a different operating mode. In actual engineering implementation, there is no need for real-time reconstruction, dimensional matching, or full observation of the internal state of the high-dimensional controller, whose dimensions change with mode switching. Instead, it is sufficient to collect the physical quantities of the controlled object in real time using sensors (e.g., displacement and velocity in a satellite attitude control system, or directly measurable physical parameters such as position and angular velocity in an industrial servo system), and determine whether the energy value corresponding to that physical quantity crosses the preset ellipsoidal invariant set boundary to trigger the corresponding mode switching command.

[0038] The structural design offers significant technical advantages: on the one hand, by separating the connection between the switching decision and the internal state of the controller, the information interaction topology of the system is greatly simplified, reducing redundant overhead in signal transmission and data processing, and improving the response speed of the switching decision; on the other hand, it completely avoids the problem of singularity in switching logic judgment caused by the abrupt change in the augmented state dimension due to the change in the controller order during the switching process (such as fuzzy boundary definition, switching command conflict, etc.), thus ensuring the uniqueness and reliability of the switching decision.

[0039] Meanwhile, this invention incorporates an active initial value adjustment strategy in the controller unit to address the core shortcomings of traditional switching structures. In traditional controller switching, the state register of the controller to be activated is often initialized by direct zeroing or random assignment, leading to a mismatch between the controller state and the physical state of the controlled object, causing transient disturbances during switching. In contrast, the controller structure designed in this invention introduces a real-time optimization calculation loop, which maintains signal synchronization with the switching decision module: when the rising edge of the switching trigger signal σ(t) arrives (i.e., the instant the mode switching command officially takes effect), the optimal initial value x, calculated in real-time based on the Lyapunov energy minimization principle, is applied through a hardware-level hard-connection path (or a logic-level priority signal channel). c,i (tk) (tk is the switching time) is instantaneously injected into the status register of the controller to be activated.

[0040] This dynamic reset structure, combining hardware and logic, ensures precise alignment of state manifolds between controllers of different orders at the physical implementation level. Even if the controller orders corresponding to the switching modes are different (nj≠ni), the initial state of the controller to be activated can be aligned with the current physical state x of the controlled object through the immediate injection of optimal initial values. p (tk) forms an adaptive dynamic association, eliminating manifold misalignment caused by differences in state dimensions. This structural design provides a key structural foundation for achieving a smooth transition without disturbance or overshoot during different-order switching, ensuring the continuity and stability of the system output at the moment of switching.

[0041] Figure 4 A diagram showing the smooth switching of multiple modes under nominal operating conditions in one embodiment of the present invention is shown.

[0042] Figure 5 A control quantity curve variation diagram is shown in one embodiment of the present invention.

[0043] In this embodiment, the optimal use of the present invention is manifested in high-precision multi-mode attitude and orbit control for drag-free satellite platforms in space gravitational wave detection missions. This scenario requires the satellite to achieve cross-scale control from micrometer to picometer levels throughout the entire process from release and capture to scientific measurement using a group of controllers of different orders (such as a 4th-order coarse-precision controller K1, a 4th-order high-precision transition controller K2, and a 5th-order ultra-high-precision scientific controller K3).

[0044] in, ; ; .

[0045] like Figure 4 and Figure 5 As shown, in this embodiment, under an on-orbit environment free from strong external disturbances (such as high-energy particle impacts in space, extreme magnetic field interference, etc.), the satellite starts from its initial large deviation state upon entering orbit, and, relying on the nested ellipsoidal invariant set and switching logic designed in this invention, traverses the preset energy boundary step by step, eventually converging stably to a scientific measurement mode that meets the requirements for high-precision measurement. The entire process achieves a smooth, disturbance-free transition, and the specific stages are as follows: 1. Initial capture phase (near initial mode): After the satellite is released into orbit, due to factors such as orbit insertion error and residual disturbances in the separation mechanism, there are significant initial position and velocity deviations (typical deviation index is position deviation > 10⁻). 6 m, where the velocity deviation is adapted to the dynamic characteristics of the position deviation of this magnitude), at this time the system state trajectory is located within the outermost ellipsoidal invariant set (such as the R1 region) of the low-dimensional phase space mentioned above. For this large deviation initial state, the system automatically activates the 4th-order low-order coarse-precision controller K1 according to the preset switching rules. This controller is adapted to the rapid stabilization requirements of large deviation scenarios. Its control parameters are optimized for energy dissipation and can guide the state xp (satellite position and velocity physical quantities) of the controlled object to rapidly approach the origin of the phase space (i.e., the ideal operating point) from the initial deviation point with a high response speed while ensuring system stability. In this process, the system state trajectory always remains smooth and continuous, without obvious overshoot and jitter, laying a stable foundation for subsequent mode switching.

[0046] 2. Mode transition and switching phase (transition mode): When the system state trajectory under the action of the fourth-order low-order coarse-precision controller K1 continues to converge, and the energy value corresponding to the physical state xp of the controlled object touches the preset ellipsoidal invariant set boundary (such as the nested boundary between R1 and the inner R2, i.e., the "switching surface" mentioned above), the system switching decision module triggers the dimensionality reduction switching logic based on the low-dimensional physical state monitoring results. This switching process strictly follows the active initial value optimization strategy designed in this invention: When switching from the 4th-order low-order coarse-precision controller K1 to the 4th-order high-precision transition controller K2, at the moment the rising edge of the switching trigger signal σ(t) arrives, the real-time optimization loop calculates the optimal initial state xc,2(tk) of K2 that is suitable for the current xp(tk), and injects it into the state register of K2 instantly through the hard connection path to achieve a seamless connection between K1 and K2. After a brief transition through K2, the system state trajectory further converges to the boundary of the inner ellipsoidal invariant set (such as the boundary between R2 and the innermost R3), triggering the secondary switching logic. Similarly, the optimal initial state xc,3(tk) of K3 is calculated through the initial value optimization strategy, completing the smooth switching from the 4th-order high-precision transition controller K2 to the 5th-order ultra-high-precision controller K3. After K3 is activated, the system state trajectory is constrained within the innermost ellipsoidal invariant set (R3 region), and the system officially enters the scientific measurement mode. In this mode, the high-order characteristics and ultra-high precision control capabilities of K3 can meet the stringent requirements of satellite scientific measurement missions for attitude / position stability (such as nanometer-level position accuracy and micro-radian-level attitude accuracy).

[0047] like Figure 4 and Figure 5 As shown, at the instants of the two switching events (K1→K2 is a same-order switching event, K2→K3 is a different-order switching event), although the order of the controller and the control parameters change, the state trajectory of the satellite's core controlled object (blue solid line) remains continuous without any jumps, and the corresponding control output (red curve) also remains smooth and continuous. This fully verifies the effectiveness of the "low-dimensional switching decision + active initial value adjustment" technical solution of this invention, and successfully achieves a seamless and smooth transition of the satellite from large deviation orbit insertion to high-precision scientific measurement mode, fully meeting the high stability and high reliability requirements of the aerospace field for the dynamic switching process of on-orbit equipment.

[0048] Although various embodiments of the invention have been described above, it should be understood that they are presented by way of example only and not as limitations. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the breadth and scope of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined solely by the appended claims and their equivalents.

Claims

1. A method for heterogeneous dynamic feedback control of a multi-mode state-dependent switching continuous linear system, characterized in that, include: Establish the continuous-time linear state-space equation of the controlled object, and provide N dynamic feedback controllers of different orders for N different working modes, where N is a natural number greater than 1. Based on the continuous-time linear state-space equation of the controlled object, nested ellipsoidal regions are constructed in the low-dimensional state space of the controlled object based on the energy function, where each ellipsoidal region has N different working modes. Determine whether the monitored physical quantity crosses the energy boundary of each ellipsoidal region; if so, trigger a switch in the working mode. When switching signal switching modes, the transient impact caused by the change of controller order is eliminated by resetting the initial value.

2. The method according to claim 1, characterized in that, Also includes: Based on the energy decay characteristics of the system under bounded perturbation, a minimum residence time constraint Tmin is set; The minimum dwell time constraint Tmin must satisfy: ； ϵ is the width parameter of the switching boundary buffer, b1 is a constant related to the system decay rate, C is the energy threshold of the switching surface, and M1 is the maximum possible energy jump value at the moment of switching. This is the effect of the disturbance ω(t) on the energy derivative of the system.

3. The method according to claim 1, characterized in that, The process of establishing the continuous-time linear state-space equation of the controlled object and designing N dynamic feedback controllers of different orders for N different operating modes includes: Establish a model of the controlled object; Design a group of controllers of different orders for the controlled object model; Construct a closed-loop augmentation system.

4. The method according to claim 3, characterized in that, The dynamic equation of the controlled object is: ； in, The state of the controlled object, To control the input, For external disturbances, y p (t) represents the measurement output, A p B p D p C p This is a system matrix with corresponding dimensions.

5. The method according to claim 3, characterized in that, The design of heterogeneous controller groups for the controlled object model includes: For the i-th operating mode, i∈{1,2,…,N}, design the i-th dynamic feedback controller, whose state-space equation is: ； in, Let n be the internal state of the i-th controller, and the controller order n in different modes. i They can be different.

6. The method according to claim 3, characterized in that, The construction of the closed-loop augmentation system includes: Define the augmented state vector of the i-th subsystem Then the state equation of the i-th closed-loop subsystem is: ； Among them, the closed-loop system matrix A i It is composed of a controlled object matrix and a controller matrix.

7. The method according to claim 1, characterized in that, The continuous-time linear state-space equation based on the controlled object constructs nested ellipsoidal regions in the low-dimensional state space of the controlled object based on an energy function, wherein each ellipsoidal region has N different operating modes, including: Divide the state space into regions and define a nested ellipsoidal region R. i As work areas for different control modes: ； in, Let C0 be a positive definite symmetric matrix, and let Ci be the energy threshold constant defining the ellipsoidal boundary, where C0 = 0 and CN = +∞.

8. The method according to claim 1, characterized in that, The step of determining whether the monitored physical quantity crosses the energy boundary of each ellipsoidal region, and triggering a switch in the working mode if so, includes: Real-time monitoring of the status of the controlled object x p When the state trajectory crosses the boundary of the ellipsoid, the switching signal σ(t) changes abruptly. In a dual-mode system, the switching rules are as follows: ； Wherein, Ω represents the preset inner region.

9. The method according to claim 1, characterized in that, When switching signal switching modes, the process of eliminating transient impacts caused by changes in controller order through initial value reset includes: When the switching signal σ(t) is at time t k When switching from mode j to mode i, a quadratic Lyapunov function is selected for the i-th subsystem. And matrix P i According to the state x of the controlled object p and controller state x c,i Divide into blocks: ； ； Where P i,2 Corresponding to the controller state part, and being a positive definite matrix, P i,1 Corresponding controlled object state x p Its own quadratic term, P i,12 Corresponding controlled object state x p With the i-th controller state x c,i Cross-coupling terms between them, P i,21 With P i,12 Together they constitute the state intersection term; Take the partial derivative with respect to the controller state and set it to zero: ； Calculate and assign the optimal initial value.

10. The method according to claim 9, characterized in that, The optimal initial state x of the activation controller i c,i(tk) for: 。

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