Unknown non-homodromous multi-agent system output feedback consistency control method based on preset performance

Abstract

The invention relates to an unknown non-homonymous multi-agent system output feedback consistency control method based on preset performance, and the method comprises the steps: building a Nussbaum function through preset performance control, and designing a reduced-order dynamic gain Kalman filter; a controller is designed by using a backstepping method and a dynamic surface technology, and the output consistency of the multi-agent system is realized.

Description

Technical Field

[0001] The invention relates to an output feedback consistency control method of an unknown non-codirectional multi-agent system based on preset performance. Background Art

[0002] In the field of engineering, many complex practical systems, such as the precision control of robotic arms, the dynamic navigation of self-driving cars, and the attitude control of aerospace vehicles, often have internal operating mechanisms that are difficult to accurately describe using simple linear models. Instead, they require more sophisticated nonlinear system modeling to capture their rich dynamic characteristics.

[0003] Many existing control methods, such as feedback linearization, sliding mode control, and adaptive control, have shown good performance in dealing with nonlinear systems with clear control directions (i.e., the direction of the input's influence on the system state or output is known), but they are unable to cope with the challenge of unknown control directions that are common in actual engineering applications. The unknown nature of the control direction greatly increases the difficulty of system analysis and design, because traditional control strategies often rely on prior knowledge of the system's dynamic characteristics, while the fuzziness of the control direction breaks this foundation.

[0004] To address this problem, designing an adaptive tracking control scheme that can effectively deal with nonlinear systems with unknown control directions and uncertainties has become a key issue that needs to be solved in the field of control theory and application. This not only requires the control algorithm to be able to learn online and adapt to the unknown characteristics of the system, but also to ensure the stability and tracking performance of the system when the control direction is unknown, which places extremely high demands on the innovation, robustness and adaptability of the control strategy. Summary of the invention

[0005] The purpose of the present invention is to provide an output feedback consistency control method for an unknown non-codirectional multi-agent system based on preset performance.

[0006] The present invention adopts the following technical solution:

[0007] A method for output feedback consistency control of unknown non-codirectional multi-agent systems based on preset performance is proposed. The preset performance control is used to construct the Nussbaum function and design a reduced-order dynamic gain Kalman filter. The backstepping method and dynamic surface technology are used to design a controller to achieve the output consistency of the multi-agent system.

[0008] Furthermore, the unknown non-co-directional multi-agent system is:

[0009]

[0010] Among them, x i 、ui and i are the state, control input and output of the system respectively, θ i and are the unknown system parameters and the known smooth nonlinear function, is a known nonlinear smooth function, b i is an unknown non-zero parameter whose magnitude and sign are completely unknown and different between different agents.

[0011] Furthermore, the preset performance control includes:

[0012] (1) Time-varying scaling function: β(t) increases monotonically with time, β(0) = 1, and 0 f 01;

[0013] (2) Preset function:

[0014] in, is a positive constant, and ω i yes

[0015] (3) Normalization function:

[0016] in, is the error;

[0017] (4) Barrier function:

[0018] in,

[0019] p i The derivative of (t) is:

[0020] in, μ 1 =μβρ,

[0021] Furthermore, the Nussbaum function is:

[0022] V(t) is a positive definite, smooth and radially unbounded function.

[0023]

[0024] Among them, c i is an appropriate constant, is the Nussbaum function, c i is a smooth function, and V(t), c i (t), ​It is bounded on the domain [0,∞).

[0025] Furthermore, the reduced-order dynamic gain Kalman filter is:

[0026]

[0027] in,

[0028] represents a vector whose i-th entry is 1 and the rest are 0;

[0029]

[0030] Design dynamic gain:

[0031]

[0032] Among them, g i ≤[1 / (2σ i2 )],

[0033] ρ、δ i14 , and is a normal number, 0 t 01;

[0034] Symmetric positive definite matrix P i and the positive constant σ i1 , σ i2 、a i satisfy:

[0035]

[0036] in, D i =diag{0,1,…,n i -2}

[0037]

[0038] Furthermore, the state estimation expression of the i-th follower agent is in, as an estimation error.

[0039] Furthermore, using backstepping method and dynamic surface technology, the controller is designed as:

[0040]

[0041] in, δ i(n-1)1 Is a normal number. ​

[0042] The beneficial effects of the present invention are as follows: the present invention first performs preset performance control design, and does not require initial errors, then constructs Nussbaum functions to handle the unknown initial directions of multi-agents, and designs a reduced-order dynamic gain Kalman filter to reconstruct the unmeasurable state variables of the followers, wherein the adaptive compensation component relaxes some constraints on parameter selection. At the same time, the impact of network attacks on the system is considered, and in the case of DOS attacks, a new communication channel is established to achieve system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is the attack time set by the present invention.

[0044] Figure 2 This is the communication topology diagram of the multi-agent system of the present invention under normal conditions and under DOS attack.

[0045] Figure 3 This is a multi-agent trajectory diagram that does not consider preset performance in the present invention.

[0046] Figure 4 Multi-agent trajectory diagram considering preset performance for the present invention.

[0047] Figure 5 This is a multi-agent error curve diagram without considering the preset performance of the present invention.

[0048] Figure 6 Multi-agent error graph considering preset performance for the present invention. DETAILED DESCRIPTION

[0049] The content of the present invention is fully described below through specific embodiments and drawings.

[0050] Example

[0051] By using preset performance control, a smooth, bounded, strictly monotonically decreasing positive performance function is introduced to ensure transient / steady-state error response, convergence speed and overshoot; a reduced-order dynamic gain Kalman filter is designed to reconstruct the unmeasurable state variables of the follower; a Nussbaum function is constructed to deal with the problem of unknown control direction in multi-agents; and a controller is designed using backstepping and dynamic surface technology to achieve output consistency of the multi-agent system.

[0052] The information exchange between agents is represented by a directed graph G = (V, E), where V = {0, 1, ..., N} represents a set of nodes or agents. A represents the set of edges connected by nodes, where the root node 0 is the leader. Define A = [a ij ] is the adjacency matrix. If agent j can directly transmit data to agent i, then aij >0, otherwise a ij =0, and a ii =0.

[0053] 1. Preset performance control design

[0054] (1) Time-varying scaling function:

[0055] β(t) increases monotonically with time, β(0) = 1, and 0 f 01.

[0056] (2) Preset function:

[0057]

[0058] in, is a positive constant, and ω i yes

[0059] (3) Normalization function:

[0060]

[0061] in, Is the error

[0062] (4) Barrier function:

[0063]

[0064] in,

[0065] p i The derivative of (t) is:

[0066]

[0067] in, μ 1 =μβρ,

[0068] 2. Design Nussbaum function to handle the problem of unknown initial direction of intelligent agent

[0069] V(t) is a positive definite, smooth and radially unbounded function.

[0070]

[0071] c i is an appropriate constant, is the Nussbaum function, c i is a smooth function, and V(t), c i ​(t), It is bounded on the domain [0,∞).

[0072] 3. Agent system design

[0073] Consider a class of high-order nonlinear MAS, including N agents numbered from 1 to N, but the initial control directions of all agents are unknown.

[0074]

[0075] Among them, x i 、u i and i are the state, control input and output of the system respectively, θ i and are the unknown system parameters and the known smooth nonlinear function, is a known nonlinear smooth function. b i is an unknown non-zero parameter whose magnitude and sign can be completely unknown and different between different agents.

[0076] 4. Reduced-order dynamic gain Kalman filter design

[0077] Since each agent only has known output states, a reduced-order dynamic gain filter is built to estimate the state of the MAS.

[0078]

[0079] in,

[0080] represents a vector whose i-th entry is 1 and the rest are 0.

[0081]

[0082] Design dynamic gain:

[0083]

[0084] Among them, g i ≤[1 / (2σ i2 )], ρ、δ i14 , and is a normal number, 0 t 01. Symmetric positive definite matrix P i and the positive constant σ i1 , σ i2 、a i satisfy:

[0085] ​

[0086] in, D i =diag{0,1,…,n i -2}

[0087]

[0088] The state estimation expression of the i-th follower agent is definition ε i =[ε i2 ,…,ε in ] T as an estimation error.

[0089] 5. Controller design

[0090] First, perform the following coordinate transformation

[0091]

[0092] Among them, α i,(s-1) , They are virtual controller and filtered virtual controller respectively.

[0093] In order to reduce the computational complexity, a dynamic function α is provided i,s

[0094]

[0095] t is is the filter time constant, q is is a positive constant, where q i1 =d i +a i0 , the rest are 1, To satisfy is a time-varying smooth function. is a normal number.

[0096] According to the above formula,

[0097]

[0098] in, M is =sup|B is |, It is M is estimates;

[0099]

[0100] (1) The first step of the backstep method:

[0101] Designing a virtual controller:

[0102]

[0103] in, δ i11 ,δ i12 ,δ i13 ,δ i14 is a normal number, They are κ i The estimated value of

[0104]

[0105] The adaptive rate is designed as:

[0106]

[0107] (2) Backstepping method, steps 2 to (n-1):

[0108] Design the virtual controller as:

[0109]

[0110] where c is ,δ is1 ,δ is2 ,δ i(s-1)1 Is a normal number.

[0111] (3) Backstepping method step n:

[0112] The controller is designed to

[0113]

[0114] in δ i(n-1)1 Is a normal number.

[0115] Lemma 1: There exist two positive constants N 0 and t a satisfy:

[0116]

[0117] Then a nonlinear system has an average residence time t a The attack time σ(t).

[0118] Among them, N σ (T,t) is the number of DOS attacks within the time [t,T).

[0119] Theorem 1: For the entire multi-agent nonlinear system, for each attack time σ(t), if the average residence time t a >(lnμ / C), then the controller u i , virtual controller Adaptive rate It can be guaranteed that all variables in the closed-loop system are bounded.

[0120] in,

[0121] Effect example

[0122] Consider a multi-agent system consisting of a leader and four agents. The structure of the i-th agent is as follows:

[0123]

[0124] The parameter selections are as follows:

[0125] f 11 = sinx 11 ,f 21 = sinx 21 ,f 31 =x 31 cosx 31 ,f 41 =x 41 cosx 41

[0126] f 12 = sinx 12 ,f 22 =sinx 22 ,f 32 =x 32 cosx 32 ,f 42 =x 42 cosx 42

[0127] Φ 322 =cosy 3 ,Φ 422 =cosy 4 ,θ i1 =0.5,θ i2 =0.7.

[0128] The Nussbaum function is designed as:

[0129]

[0130] Preset performance control parameters:

[0131] bf =0.001,

[0132] The reduced-order filter is designed as:

[0133]

[0134] Among them, k 12 =0.5,k 22 =0.2,k 32 =0.2,k 42 =0.3, l i (0)=1.

[0135] The virtual controller is designed to:

[0136]

[0137] Among them, δ i11 =δ i12 =0.5,δ i13 =2,δ i14 =1, c 11 =0.4, c 21 =0.1, c 31 =0.1, c 41 =0.2,

[0138] The controller is designed to:

[0139]

[0140] The initial value is chosen as x 11 (0) = 0.3, x 21 (0) = -0.2, x 31 (0) = 0.2, x 41 (0) = -0.3, the expected trajectory is y d =0.5sin(2t).

[0141] The present invention uses Matlab simulation to verify the technical effect, and obtains the motion of the multi-agent system in 0 to 10 seconds through simulation. Figure 3 to Figure 6 It can be found that in the case of unknown initial direction, all agents can quickly approach the preset trajectory regardless of whether there is preset performance control. Figure 3 and Figure 5 It can be seen that the initial error is large and deviates more from the preset trajectory; Figure 4 and Figure 6 It can be seen that the preset performance control works. In summary, the designed control method is effective and reasonable.

Claims

1. A method for output feedback consistency control of unknown non-codirectional multi-agent systems based on preset performance, characterized in that: Using preset performance control, construct Nussbaum function and design reduced-order dynamic gain Kalman filter; The controller is designed using backstepping and dynamic surface technology to achieve consistency in the output of the multi-agent system.

2. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 1 is characterized in that: The unknown non-co-directional multi-agent system is: Among them, x i 、u i and i are the state, control input and output of the system respectively, θ i and are the unknown system parameters and the known smooth nonlinear function, is a known nonlinear smooth function, b i is an unknown non-zero parameter whose magnitude and sign are completely unknown and different between different agents.

3. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 2 is characterized in that: Preset performance controls include: (1) Time-varying scaling function: β(t) increases monotonically with time, β(0) = 1, and 0 f 01;​ (2) Preset function: Where l is a positive constant and ω i yes (3) Normalization function: in, is the error; (4) Barrier function: in, p i The derivative of (t) is: in, μ1=μβρ, 4. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 3 is characterized in that: The Nussbaum function is: V(t) is a positive definite, smooth and radially unbounded function. Among them, c i is an appropriate constant, is the Nussbaum function, c i is a smooth function, and V(t), c i (t), It is bounded on the domain [0,∞).

5. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 4 is characterized in that: The reduced-order dynamic gain Kalman filter is: in, represents a vector whose i-th entry is 1 and the rest are 0; Design dynamic gain: Among them, g i ≤[1 / (2σ i2 )], ρ、δ i14 , and is a normal number, 0 t 01;​ Symmetric positive definite matrix P i and the positive constant σ i1 , σ i2 、a i satisfy: in, D i =diag{0,1,…,n i -2} 6. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 5 is characterized in that: The state estimation expression of the i-th follower agent is in, as an estimation error.

7. The output feedback consistency control method of unknown non-co-directional multi-agent system based on preset performance according to claim 6 is characterized in that: Using backstepping and dynamic surface techniques, the controller is designed as: in, δ i(n-1)1 Is a normal number.

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