Design method of dynamic event-triggered manipulator system controller based on adjacent modal dependency

Abstract

The present invention discloses a design method for a dynamic event-triggered manipulator system controller based on adjacent modal dependency. With the help of an auxiliary system, the unknown interconnected terms are processed using the cyclic small gain condition, and the closed-loop system is stochastically stable and satisfies H ∞ Sufficient conditions for performance. The relaxation matrix is ​​used to address the nonlinearity caused by adjacent modes, and a new controller design condition is proposed using linear matrix inequalities. Compared with traditional methods, this method can be applied to robotic arm systems with unknown interconnections and does not require knowledge of the real-time operating modes of all subsystems, thus saving considerable costs.

Description

Technical Field

[0001] The present invention relates to a design method for a dynamic event-triggered robotic arm system controller based on adjacent modal dependency. Background Art

[0002] Markov systems, as a special class of stochastic hybrid systems, have attracted widespread attention. Such systems have random jump parameters, modeled by the transitions of a Markov chain. Markov systems can capture sudden changes in the controlled plant's modes and therefore have a wide range of applications in the field of system control in engineering applications.

[0003] In addition, the limited network bandwidth of the robotic arm system inevitably leads to many problems, such as packet collisions, network attacks, and limited bandwidth. It is particularly important to reduce the frequency of communication transmissions without sacrificing ideal stability and performance. Compared with traditional time triggering, the event triggering mechanism shows absolute advantages in saving network resources and reducing the number of control tasks executed. It can effectively alleviate the burden of network communication and has become a research hotspot for more and more scholars at home and abroad. The event triggering mechanism no longer samples at a fixed time. The update of the controller or filter is determined by certain events. Only when the new sampling state or measurement output does not meet the triggering condition will their input be updated; otherwise, the input signal remains unchanged. This paper proposes a new adjacent modality-dependent event triggering scheme. Since the acquisition cost of modal information is very high, the adjacent modality-dependent event triggering mechanism does not need to know the modal information of the entire system, which can save a certain amount of cost.

[0004] The modal information of each subsystem must be transmitted promptly and accurately to the control units of all other subsystems. However, in the practical application of large decentralized systems, this random and frequent exchange of information can easily lead to a waste of resources. Moreover, the timeliness and accuracy of information transmission are affected by the quality of information network transmission and cannot be guaranteed. This makes decentralized control methods based on full modal dependence difficult to implement in practice. Therefore, this paper proposes a state feedback control method based on adjacent modal dependence. This method does not require the control unit of a subsystem to know the modal information of any other subsystems during control system operation. Summary of the Invention

[0005] The purpose of this invention is to design a robot system controller based on dynamic event triggering based on adjacent modal dependence, which can improve the stability and H performance of the robot system under the condition of not knowing the operation mode of all subsystems and limited bandwidth. ∞ performance and save certain costs.

[0006] The specific technical solution of the present invention is as follows: a dynamic event-triggered state feedback control problem with adjacent modal dependencies of an unknown interconnected robotic arm system, comprising the following steps:

[0007] The mathematical model of the robotic arm system is as follows:

[0008]

[0009] Where i∈1,2, Indicates the system status, represents the control input, Indicates the measurement output, w i (t) represents the disturbance, A i (r i (t))、B i (r i (t))、D i (r i (t))、E i (r i (t))、C i (r i (t))、G i (r i (t))、H i (r i (t)) has appropriate dimensions. It is the unknown Internet satisfaction

[0010] in and d i >0. r i (t) represents the local operation mode, [r1(t) r2(t),..., r.(t)] represents the global operation mode, then, we define a bijective function: So we can get It can be seen that the relationship between the local operating mode and the global operating mode.

[0011]

[0012] Where dt>0,

[0013] The event detector determines whether newly sampled data should be sent to the controller by using the following threshold conditions:

[0014]

[0015] where ε i (ξ i (t))∈[0,1) is a given scalar parameter that sets the detection threshold, Ω i (ξ i (t))>0 is the event trigger matrix to be determined in the design, x i(kT) represents the current sampling state, x i (t k T) represents the latest sampling state, h i (kT) represents the dynamic factor and satisfies:

[0016]

[0017] If the sampled data meets the event trigger threshold condition, the data will be stored and sent to the controller at the same time.

[0018] Convert the event-triggered network Markov jump system into a new time-delay system:

[0019]

[0020]

[0021] Design the state feedback controller as: i (t) = K i (ξ i (t))x i (t k T),

[0022] where K i (ξ i (t)) is the gain of the controller.

[0023] Since the adjacent mode-dependent controller cannot directly control the local mode-dependent robotic arm system, we need to use an auxiliary system.

[0024]

[0025] The event trigger mechanism and controller designed for the auxiliary system are:

[0026]

[0027]

[0028] in

[0029] The closed-loop system of the robot assist system can be written as:

[0030]

[0031] Design the Lyapunov function as:

[0032] in

[0033] definition

[0034]

[0035] in

[0036]

[0037] Considering the event triggering conditions, we can get

[0038]

[0039]

[0040] Consider the condition of small loop gain

[0041] If the above conditions are met, we can get

[0042]

[0043]

[0044] Then consider the following Lyapunov function

[0045]

[0046] Easy to get

[0047] If the auxiliary system controller gains and weighting matrices satisfy the following conditions:

[0048]

[0049] The adjacent mode-dependent controller can stabilize the robotic arm system

[0050] And the linear matrix inequality is

[0051]

[0052]

[0053] According to the lemma, we first write the matrix as in We can get

[0054] in We can get

[0055]

[0056] in

[0057] Then introduce the slack variable matrix

[0058] Can get

[0059]

[0060]

[0061]

[0062]

[0063] when When is fixed, the above matrix inequality becomes LMI. Therefore, a global mode-dependent event-triggered state feedback controller can be obtained.

[0064] Then, based on the relationship between the global mode and the local operating mode, an event-triggered state feedback controller related to the adjacent modes can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0066] Figure 2 A state diagram of a system 1 using a state feedback controller according to an embodiment of the present invention;

[0067] Figure 3 A state diagram of a system 2 using a state feedback controller according to an embodiment of the present invention;

[0068] Figure 4 This is an event triggering diagram of an adjacent mode-dependent state feedback controller system 1 using the method proposed in the present invention;

[0069] Figure 5 This is an event triggering diagram of an adjacent mode-dependent state feedback controller system 2 using the method proposed in the present invention;

[0070] Figure 6 The modal diagram of a state feedback controller system using adjacent mode dependence is shown in FIG. DETAILED DESCRIPTION

[0071] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0072] like Figure 1 As shown in the figure, the design method of the dynamic event-triggered robotic arm system controller based on adjacent modal dependence includes the following steps:

[0073] Step 1: Set the initial values ​​of various parameters;

[0074] Step 2: Update event trigger threshold parameters;

[0075] Step 3: Use threshold parameters to verify event-triggered measurement and update trigger status x i (t k T);

[0076] Step 4: Use trigger state x i (t k T) Generate control input u in real time i (t)

[0077] Step 7: According to the control input u i (t) The resulting state updates the system parameters.

[0078] An embodiment of the present invention is described below:

[0079] Consider the event-triggered state feedback control problem of an interconnected robotic arm system with unknown adjacent modal dependencies. The corresponding mathematical model is:

[0080]

[0081]

[0082] Figure 1 is a flow chart of the method of an embodiment of the present invention; applying the proposed method, the system state diagram obtained by using the adjacent mode dependent state feedback controller is as follows Figure 2 、 Figure 3 As shown in the diagram, the event triggering diagram of the system using the state feedback controller is as follows: Figure 4 、 Figure 5 As shown in the figure, the Markov process diagram under the state feedback controller is as follows Figure 6 As shown, it can be seen that the designed adjacent mode-dependent state feedback controller can stabilize the robotic arm system;

[0083] References

[0084] [1]Guan,C.,Fei,Z.,Feng,Z.,Shi,P.(2020).Stability and stabilization ofsingular Markovian jump systems by dynamic event-triggered controlstrategy.Nonlinear Ahalysis:Hybrid Systems,38,100943.

[0085] [2]Gu,Y.,Shen,M.,Ahn,C.K.(2023).Dynamic event-triggered fault-tolerant control through a new intermediate observer.International Journal ofRobust and Nonlinear Control,33(16),9804-9825.

[0086] [3]Zhang L,Sun Y,Pan Y,et al.Network-based robust event-triggeredcontrol for continuous-time uncertain semi-Markov jump systems[J].International Journal of Robust and Nonlinear Control,2021,31(1):306-323.

[0087] [4]Liu,D.,Yang,G.H.(2019).Decentralized event-triggered outputfeedback control for a class of interconnected large-scale systems.ISAtransactions,93,156-164.

Claims

1. A method for designing a controller for a dynamic event-triggered robotic arm system based on adjacent modal dependencies, characterized by: Use linearization technology to establish a mathematical model of the robotic arm system; In order to reduce the waste of limited network resources, a dynamic event triggering scheme based on adjacent modality dependence is proposed; Design a state feedback controller triggered by dynamic events based on adjacent modal dependencies; Among them, the mathematical model of the robotic arm system is as follows: Where i∈1,2, Indicates the system status, represents the control input, Represents the measurement output, represents disturbance, A i (r i (t))、B i (r i (t))、D i (r i (t))、E i (r i (t))、C i (r i (t))、G i (r i (t))、H i (r i (t)) has appropriate dimensions, It is the unknown Internet satisfaction in and d i >0, r i (t) represents the local operation mode, [r1(t) r2(t), ..., r i (t)] represents the global operation mode and defines the bijective function: So we can get It can be seen that the relationship between the local operation mode and the global operation mode, r(t) has the following transition probability Where dt>0, The event triggering mechanism of adjacent modal dependency is as follows: in is a given scalar parameter that sets the detection threshold, is the event trigger matrix to be determined in the design, x i (kT) represents the current sampling state, x i (t k T) represents the latest sampling state, h i (kT) represents the dynamic factor and satisfies: If the sampled data meets the event trigger threshold condition, the data will be stored and sent to the controller at the same time, and then we transform the event-triggered Markov process system into a new time-delay system in satisfy Based on the above-mentioned adjacent-modal-dependent dynamic event triggering mechanism, an adjacent-modal-dependent state feedback controller is designed to stabilize the robotic arm system. The controller is described as follows: in is the controller gain. Since the adjacent mode-dependent controller cannot directly control the local mode-dependent robotic arm system, we need to use the following auxiliary systems: The event trigger mechanism and controller designed for the auxiliary system are: in The closed-loop system of the robot assist system can be written as:

2. According to the method for designing a controller for a dynamic event-triggered manipulator system based on adjacent modal dependence in claim 1, the manipulator system performs stability analysis and controller design, characterized in that: The unknown interconnected terms are processed by the cyclic small gain condition to ensure the random stability of the auxiliary closed-loop system and the H ∞ performance; The relaxation matrix variables are introduced to derive the linear solution conditions of the adjacent mode dependent state feedback controller; The Lyapunov function is: definition in Considering the event triggering conditions, we can get Finally got Consider the condition of small loop gain If the above conditions are met, we can get Then consider the following Lyapunov function And the cycle small gain condition is satisfied Easy to get If the auxiliary system controller gains and weighting matrices satisfy the following conditions: The adjacent mode-dependent controller can stabilize the robotic arm system, and the matrix inequality condition is: Further, the matrix is ​​written as in the form of We can get in We can get in Then introduce the slack variable matrix Can get when When fixed, the above matrix inequality becomes LMI, and the state feedback controller is obtained According to the relationship between the global operating mode and the adjacent mode, the event triggering status feedback related to the adjacent mode can be obtained.

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