Multi-unmanned trolley system consistency control method based on disturbance observer under switching topology

Abstract

The invention discloses a distributed consistency control method suitable for a multi-unmanned trolley system, and designs a control strategy based on a preset time disturbance observer for the problem that communication topology dynamic change and external disturbance interference are difficult to consider at the same time. In system modeling, each trolley is modeled as a second-order nonlinear system, and external disturbance is generated by a heterogeneous external source system. In the design of the controller, a disturbance observer with a preset time convergence characteristic is introduced, and strict convergence of disturbance estimation errors can be realized in finite time. Control input is fused with three parts of neighbor state difference feedback, leader tracking and disturbance compensation, and it is ensured that the system can still achieve a consistent target in a complex dynamic environment. By constructing a combined Lyapunov function and combining a Markov jump system theory, it is proved that a system state error and a disturbance estimation error converge to zero after a preset time. A simulation result verifies the effectiveness and stability of the method under communication switching and non-ideal disturbance interference.

Description

Technical Field

[0001] The present invention belongs to the field of collaborative control of multiple unmanned vehicle systems, and specifically relates to a distributed consistency control method based on a preset time disturbance observer under the conditions of Markov switching topology and external disturbances generated by heterogeneous exogenous systems. The method is suitable for scenarios such as unmanned vehicle systems, robotic arm clusters, and drone formations. Background Art

[0002] With the rapid development of technologies such as autonomous driving, intelligent manufacturing, and collaborative robotics, multi-unmanned vehicle systems, as a typical example of multi-agent systems, have shown broad application prospects in aspects such as formation maintenance, task allocation, and path coordination. Among them, consistency control, as a fundamental issue in the coordinated operation of systems, has become a research hotspot.

[0003] Existing research mainly focuses on two aspects: one is the control strategy based on a fixed communication topology. This type of method has a clear structure and is easy to analyze, but when the communication topology changes dynamically, the system performance often decreases significantly; the other is the robust control method or disturbance observation method for external disturbances, which can enhance the system stability, but most of them do not combine the dynamic characteristics of the communication topology and are difficult to adapt to the frequently changing network environment in reality.

[0004] In recent years, some literature has attempted to introduce mechanisms such as adaptive control or distributed estimation to simultaneously address topology changes and disturbances. However, these approaches typically require the disturbance to satisfy strong a priori assumptions or are only applicable to topological systems with low-frequency switching, limiting their scope of application.

[0005] Furthermore, existing disturbance observers often use asymptotic or exponential convergence mechanisms, resulting in estimation errors that gradually approach zero over a long period of time, making it difficult to meet the practical needs of rapid disturbance compensation in highly dynamic environments. The preset-time disturbance observer, however, is a new control tool that achieves strict convergence of the disturbance estimation error within a preset finite time. It does not rely on prior information about the disturbance or asymptotically adjustable parameters, and offers the advantages of fast response and strong robustness. This type of structure provides a new and feasible path for achieving efficient and consistent control in the face of frequent communication switching and complex disturbances.

[0006] Therefore, it is urgent to design a distributed consistency control method that integrates a preset time disturbance observer and takes into account the random switching of communication topology and the external disturbance compensation capability, so as to improve the coordination ability and system robustness of the multi-unmanned vehicle system in complex dynamic environments. Summary of the Invention

[0007] Existing consistency control methods for multi-unmanned vehicle systems find it difficult to simultaneously adapt to the Markov random switching characteristics of the communication topology and the influence of heterogeneous external disturbances. Specifically, the performance of control strategies based on fixed topologies significantly degrades in dynamic network environments, existing disturbance observation methods do not incorporate the dynamic characteristics of topology, resulting in insufficient robustness, and traditional adaptive or distributed estimation methods rely on strong prior assumptions or are only applicable to low-frequency switching scenarios, limiting the system coordination capabilities in complex dynamic environments.

[0008] To address the above technical issues, the present invention proposes a distributed consistency control method that introduces a preset time disturbance observer under a switching topology. The core innovation of this method lies in: by designing a disturbance observer with a preset time convergence characteristic, the disturbance estimation error is strictly converged to zero within a pre-set finite time, without relying on prior disturbance information or asymptotic adjustment mechanisms. This significantly improves the system's response speed and compensation accuracy to highly dynamic disturbances, ensuring stable and consistent operation of the system under frequent communication switching and complex disturbances.

[0009] The present invention adopts the following technical solutions:

[0010] 1. System Modeling and Topology Modeling: Each vehicle in a multi-robot system is modeled as a second-order nonlinear system, where the state consists of position and velocity, and the control input is also affected by external disturbances. The system's communication relationships are modeled as a directed graph, whose topology changes randomly over time using a Markov process, providing greater real-world adaptability.

[0011] 2. Disturbance modeling and observer design: External disturbances are not directly assumed to be known or bounded, but are generated by a class of linear heterogeneous exogenous systems. A disturbance observer with preset time convergence performance is designed. This observer uses auxiliary variable construction combined with a time-varying function control law to achieve the convergence of the disturbance estimation error to zero within a predetermined time, thereby improving the real-time performance of disturbance compensation and the robustness of the system.

[0012] 3. Consistency Control Protocol Design: Based on information from neighboring cars, the controller is designed by integrating the output of a preset time disturbance observer. The control input consists of three parts: a neighbor state difference feedback term, a leader tracking term, and a disturbance compensation term. It has the following structural characteristics:

[0013] (1) The state feedback part realizes the consistency goal of the system;

[0014] (2) The disturbance compensation part uses a preset time observer to achieve rapid disturbance suppression;

[0015] (3) The control gain is designed based on the Lyapunov function to ensure the mean square stability of the system under topology jumps.

[0016] 4. Stability and Performance Analysis: By constructing a joint Lyapunov function and combining it with Markov jump system theory, it is demonstrated that under the combined effects of topology switching and disturbance interference, both the system state error and the disturbance estimation error converge to zero after a preset time, achieving the system's global consistency control goal.

[0017] Compared with the prior art, the present invention has at least the following advantages:

[0018] By modeling the dynamic switching of communication topology through Markov process and introducing a preset time disturbance observer, the disturbance error can be strictly converged within a limited time, which significantly improves the robustness and response speed of the system in complex networks and disturbance environments. The control protocol does not rely on the disturbance prior model or switching frequency assumption, is suitable for high-frequency dynamic topology, has strong adaptability and fast convergence speed, and can effectively ensure the efficient coordination and precise control of multiple unmanned vehicle systems in complex dynamic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Attachment Figure 1 :Schematic diagram of the communication topology of a multi-unmanned vehicle system. (a) Communication topology (b) Communication topology (c) Joint graph

[0020] Attachment Figure 2 : Error curve between the estimated disturbance value and the actual disturbance of each car.

[0021] Attachment Figure 3 : Perturbation estimation error of each car. (a) Perturbation estimation error in the X direction, (b) Perturbation estimation error in the Y direction.

[0022] Attachment Figure 4 : Velocity error of each car. (a) Velocity error in the X direction, (b) Velocity error in the Y direction.

[0023] Attachment Figure 5 : Position error of each car. (a) Position error in the X direction, (b) Speed ​​error in the Y direction. DETAILED DESCRIPTION

[0024] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0025] 1. Communication topology and Markov switching modeling

[0026] Use a directed graph G(t) to describe the information interaction structure between multiple unmanned vehicles. is the weighted adjacency matrix of G, where a ij represents the weight of the edge from node i to node j. If there is no edge between nodes i and j, then aij =0, otherwise a ij =1; further construct the Laplace matrix based on the adjacency matrix To measure the connectivity of the network.

[0027] On this basis, the leader node is introduced to construct a topology with a leader Use the matrix B(t)=diag{b1,b2,...,b N Describe the connection relationship between the leader and the follower, and define the topology control matrix H(t) = L(t) + B(t) and its symmetric form

[0028] exist Switch in Define a random variable σ(t), when σ(t) satisfies the formula, and G(t)=G m , G m yes 's subgraph.

[0029] σ(t)=m,m=1,2,...,s (1)

[0030] Define the Markov transition rate matrix as follows:

[0031]

[0032] where q mn >0 is the transition from state m to state n; if m≠n, q mn =-∑ m≠n q mn , o(μ) is an infinitesimal quantity of higher order than μ.

[0033] The present invention satisfies the following two assumptions:

[0034] Assumption 1: Each communication topology G m ,m=1,2,...,s,is a balanced graph, and the joint graph of all possible communication topologies Contains a directed spanning tree with the leader as the root node.

[0035] Assumption 2 The Markov transition rate matrix Q is ergodic.

[0036] 2. System modeling and parameter setting

[0037] The dynamic model of the i-th unmanned vehicle is:

[0038]

[0039] Among them, qi 、v i and Represent the position, speed and acceleration of the unmanned vehicle respectively; When input vector, is an external disturbance.

[0040] The dynamic model of leadership is:

[0041]

[0042] in, represent the desired position and velocity respectively;

[0043] make The state space form of the system is:

[0044]

[0045] in,

[0046] 3. Design a preset time disturbance observer

[0047] To describe the many different types of disturbances that the car may face, the external disturbance ω of the system is i Generated by the following heterogeneous exogenous systems:

[0048]

[0049] Among them, i is the state of disturbance, ω i is the external disturbance, E i and F i is the observable gain matrix.

[0050] To realize the unknown disturbance ω i To accurately estimate , the preset disturbance observer is designed as follows.

[0051] Construction error auxiliary variable Π i :

[0052] Π i =v i -ρ i (7)

[0053] And define the state update law ρ of the disturbance observer i for:

[0054]

[0055] The disturbance estimate is then expressed as:

[0056]

[0057] Among them, k i and c i is the gain constant, is the disturbance estimate of the i-th car, μ(t) is the preset time convergence factor, defined as:

[0058]

[0059] Wherein, T is the preset time, and h>0 is the set power parameter.

[0060] 4. Coherence Controller Design

[0061] The control input of the i-th unmanned vehicle is defined as:

[0062]

[0063] Where K is the gain matrix to be designed.

[0064] 5. Stability analysis

[0065] In order to verify that the proposed consistency controller can achieve consistent control and disturbance suppression of the system under the conditions of Markov switching topology and disturbance compensation, this paper constructs the following Lyapunov function:

[0066]

[0067] in, Indicates the state error between the follower and the leader, represents the disturbance estimation error, σ(t)=m, m=1,2,…,s represents the communication topology mode number under Markov process control, P σ(t) 、P 1,σ(t) is the Lyapunov matrix under the corresponding mode.

[0068] (1) Analysis of the error convergence of disturbance observer

[0069] For auxiliary variable π i Taking the derivative and substituting it into formula (8) we can get:

[0070]

[0071] Construct the Lyapunov function term:

[0072]

[0073] Taking its derivative and substituting it into formula (13) we can get:

[0074]

[0075] Among them, the coefficient is a bounded positive function, so this term will not lead to divergence. Arranging it can be obtained:

[0076]

[0077] Where δ(t) is The disturbance term caused by boundedness.

[0078] because When t→T - When μ(t)→0, and combined with the preset time convergence lemma, we can see that there is a finite time T>0 such that:

[0079]

[0080] Therefore, the disturbance estimation error is completely eliminated within the preset time.

[0081] (2) Controller stability analysis

[0082] After t≥T, the disturbance compensation is fully effective and the system can be regarded as a disturbance-free situation. The controller is simplified to:

[0083]

[0084] At this time, the derivative of the Lyapunov function becomes:

[0085]

[0086] Considering that the communication topology obeys Markov switching, the transfer rate matrix is ​​Q = (q mn ), construct Lyapunov function in each mode The total derivative of the system satisfies:

[0087]

[0088] Based on Assumptions 1 and 2, if there exists a family of positive matrices {P m} and the control gain K so that the above inequality holds for all modes, then the system achieves mean square consistency under the Markov switching network.

[0089] 6. Simulation verification and result analysis

[0090] A system consisting of six unmanned vehicles is selected for detailed description. Vehicle 0 is the leader, and the remaining vehicles (numbered 1 to 5) are followers. Simulation verification is performed on the Matlab platform.

[0091] The initial values ​​of each car are as follows (unit: m; m / s):

[0092] q0(0)=[2π / 3,4π / 5] T,v0(0)=[0.1,0.2] T ;

[0093] q1(0)=[π,-5π / 6] T ,v1(0)=[-0.2,0] T ;

[0094] q2(0)=[π / 6,3π / 2] T ,v2(0)=[0.1,-0.1] T ;

[0095] q3(0)=[-3π / 4,11π / 12] T ,v3(0)=[0.3,-0.1] T ;

[0096] q4(0)=[3π / 4,-1π / 4] T ,v4(0)=[0.4,-0.2] T ;

[0097] q5(0)=[5π / 12,-π] T ,v5(0)=[0.2,-0.4] T .

[0098] The communication topology of the multi-unmanned vehicle system is shown in Figure and Switch between them, both of these graphs are equilibrium graphs, such as Figure 1 (a) and (b); and Joint graph of Contains a directed spanning tree with the leader as the root node, such as Figure 1 (c)

[0099] Transfer rate matrix And its initial distribution is ι = [1 / 3, 2 / 3].

[0100] The disturbance to each follower car is caused by the following external system:

[0101]

[0102] in,

[0103] The initial disturbance value of each follower car is set as follows:

[0104] ζ1(0)=[0.4,0.2] T ζ2(0)=[-0.3,0.8] T ;

[0105] ζ3(0)=[0.3,0.2] T ζ4(0)=[0.4,0.5] T ζ5(0)=[-0.2,0.3] T .

[0106] The disturbance observer uses a preset time structure, and the preset time parameters are set as: T = 5s, h = 3

[0107] The control parameter of the disturbance observer is: i =8,c i =10. Set uniformly for all followers.

[0108] The controller parameters are set as follows: Control gain matrix The feasibility is verified by LMI method and the system stability conditions are met.

[0109] The simulation integration time step is set to 0.01s, and the simulation results are as follows Figures 3 to 5 As shown: Figure 2 The error curve between the disturbance estimation value and the actual disturbance of each car is shown. It can be seen that the disturbance estimation error tends to 0 within the preset time, which verifies that the disturbance observer has the preset time convergence performance. Figure 4 and Figure 5 In the figure, we can see that the position and velocity errors of each follower car relative to the leader converge to 0 in a finite time, indicating that the position state and velocity state have achieved consistency.

[0110] Simulation results show that the proposed distributed consistency control strategy based on preset time disturbance observer can effectively estimate and compensate for external disturbances, maintain system stability and achieve global consistency control even when the communication topology changes frequently, verifying the effectiveness and robustness of the proposed method.

Claims

1. A method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology, characterized in that: The method comprises the following steps: (1) Establish a multi-robot system model, where each robot is modeled as a second-order nonlinear system with position and velocity states, and the control input is also affected by external disturbances; (2) Establish the communication topology of the multi-robot system, adopt the leader-follower model, use a directed graph to model the communication relationship, and describe the random switching characteristics of the communication topology through the Markov process; (3) Modeling external disturbances as unknown disturbance signals generated by a linear heterogeneous exogenous system; (4) Design a disturbance observer with a preset time convergence characteristic, construct auxiliary variables and their high-order derivatives, and use time-varying functions to achieve the disturbance estimation error convergence to zero within the set time; in order to achieve the consistency control target of the system after the preset time; (5) Based on the neighbor car state information and the disturbance observer estimate, a consistency controller is constructed. The control input includes the neighbor state difference feedback term, the leader tracking term, and the disturbance compensation term. (6) Through the Lyapunov method and Markov jump system theory, the mean square stability of the system under topology switching and disturbance interference is analyzed to ensure that the system achieves global consistency within a limited time.

2. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1 is characterized in that : The dynamic model of the unmanned vehicle is expressed as: in, 、 and Represent the position, speed and acceleration of the unmanned vehicle respectively; When input vector, is an external disturbance; make , , then the state space form of the system is: in, , .

3. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1 is characterized in that : The Markov random switching of the communication topology consists of a finite number of balanced directed graphs, and their joint graph contains a directed spanning tree with the leader as the root node.

4. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1 is characterized in that: The external disturbance Generated by heterogeneous exogenous systems of the following form: in, is a state of disturbance, is an external disturbance, is the observable gain matrix.

5. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1 is characterized in that: The preset time function in the disturbance observer is: in For preset time, is the power parameter set.

6. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1, characterized in that: The disturbance observer estimates the disturbance in the form of: in, yes Estimated value of; preset time convergence factor Defined by the fifth item; Auxiliary variables for construction; is the design parameter.

7. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1, characterized in that: The consistency control protocol is in the form of: in, is the control gain matrix to be designed; for the state of being a leader; is the connection weight between followers; represents the connection weight with the leader; For the The disturbance estimate of the car.

8. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1 is characterized in that: The Lyapunov function constructed in the system stability analysis is a family of mode-dependent functions, and the topological mode switching is controlled by the Markov generator matrix.

9. The method for consistency control of a multi-unmanned vehicle system based on a disturbance observer under a switching topology according to claim 1, characterized in that: The controller will start at the preset time Afterwards, the disturbance estimation error is returned to zero, and the system state error converges to zero in the mean square sense, meeting the global consistency control goal.

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