Reference signal fast adaptive distributed tracking method based on adaptive estimation and robust controller

Abstract

The invention belongs to the field of autonomous estimation and rapid tracking control of unknown reference signals by multiple agents, and particularly relates to a reference signal rapid adaptive distributed tracking method based on adaptive estimation and a robust controller. Re-parameterizing the reference signal containing unknown parameters, and converting the reference signal into an observable system through a filtering transformation technology; constructing a reference signal unknown parameter rapid distributed estimation module, and designing an unknown parameter adaptive distributed observer based on an adaptive method and a finite time theory; constructing a reference signal fast robust tracking control module, and designing a fast robust tracking controller based on a sliding mode algorithm and a finite time theory; and constructing a closed-loop system stability analysis module, and proving finite time convergence of the multi-agent distributed tracking system. According to the invention, the practicability and reliability of the multi-agent tracking system in the field are obviously improved.

Description

Technical Field

[0001] The invention belongs to the field of autonomous estimation and rapid tracking control of unknown reference signals by multiple intelligent agents, and particularly relates to a method for rapid adaptive distributed tracking of reference signals based on adaptive estimation and a robust controller. Background Art

[0002] With the development of computer networks, sensor technology and communication technology, the research on multi-agent tracking systems has attracted widespread attention. Compared with a single agent tracking a target, a multi-agent tracking system can complete various complex tasks, such as patrolling, detection, and rescue, with high performance, high flexibility and high robustness. In fact, a multi-agent tracking system is a system composed of multiple interacting agents that work together to track the target and solve problems that a single agent cannot solve independently. In a multi-agent tracking system, each agent is independent, but through collaboration, more complex tasks and goals can be achieved. For example, in autonomous driving technology, multiple vehicles need to coordinate driving to maintain formation and safe distance. In military or civilian missions, multiple drones can share visual or position information, collaborate to complete tasks covering a large area, or form specific flight formations to improve efficiency.

[0003] In a multi-agent tracking system, if all agents can receive target information, it is easy to realize multi-agent tracking of the target. However, in real life, due to limited communication or insufficient resources, usually only some agents can receive target information, which is the main research direction in this field. Among them, when the target reference signal is known, a distributed estimator is designed for each agent so that each agent can obtain the output signal of the target. However, the existing methods mainly focus on the state estimation of the reference signal, rather than the parameter estimation, which leads to unsatisfactory results when processing reference signals with unknown parameters. Among them, when parameter and state estimation need to be performed simultaneously, most methods still have deficiencies in parameter estimation accuracy. With the gradual deepening of the research on multi-agent tracking systems, the current technology lacks a comprehensive solution that can effectively handle reference signals with unknown parameters in multi-agent tracking systems. For this situation, it is necessary to design a distributed estimator to realize the autonomous estimation of the reference signal and its unknown parameters, and at the same time design a tracking controller so that the output signal of each agent can quickly track the reference signal with unknown parameters within a limited time. In addition, in practical applications, the convergence time of the system is an important indicator for evaluating the performance of the controller. In the existing technology, most control algorithms can only guarantee asymptotic convergence and cannot meet the high requirements for speed and accuracy in practical applications. Asymptotic stability can only ensure that the system state converges only to the neighborhood of the equilibrium point, and the time to converge to the equilibrium point is infinite, which is a defect of the asymptotically stable algorithm. Finite-time control has a faster convergence speed and better anti-interference performance than asymptotically stable control, and can converge to the equilibrium point within a finite time. Therefore, it is more practical to study multi-agent tracking systems based on finite-time theory.

[0004] In summary, the current research mainly has the following problems: (1) Most algorithms in the existing technology have a slow convergence speed, such as the asymptotic convergence algorithm, which is not conducive to practical applications that require rapid response to drone formations or autonomous driving fleets; (2) The methods of the existing technology usually require a certain understanding of the partial state or parameters of the reference signal, which is not applicable when the parameters of the reference signal are completely unknown; (3) The existing technology may not be able to maintain good stability when facing external interference such as wind or sound waves, and is easily affected by external environmental factors. To this end, we propose a fast adaptive distributed tracking method for reference signals based on adaptive estimation and robust controller. Summary of the invention

[0005] The purpose of the present invention is to provide a fast adaptive distributed tracking method of reference signals based on adaptive estimation and robust controllers, and to construct a multi-agent reference signal fast adaptive distributed tracking system model, which takes into account the unknown parameters in the reference signal, as well as the influence of external interferences such as wind, interference signals, and sound waves on intelligent systems such as drones and unmanned vehicles, and improves the convergence speed of the system based on finite time theory. It provides a new modeling idea for the autonomous estimation and fast tracking control of unknown reference signals by multi-agents, enriches the research methods in this field, and the designed distributed observer and fast robust tracking controller significantly improve the practicality and reliability of multi-agent tracking systems in this field.

[0006] The technical solution adopted by the present invention is as follows:

[0007] A method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller is characterized by comprising the following steps:

[0008] Step 1: construct a multi-agent reference signal fast adaptive distributed tracking system based on an unknown parameter observer and a robust controller, wherein the multi-agent reference signal fast adaptive distributed tracking system based on an unknown parameter observer and a robust controller comprises: a reference signal unknown parameter model construction module, a reference signal unknown parameter fast distributed estimation module, a reference signal fast robust tracking control module, and a closed-loop system stability analysis module;

[0009] Step 2: In the reference signal unknown parameter model construction module, establish an observable model of the reference signal containing unknown parameters;

[0010] Step 3: In the reference signal unknown parameter fast distributed estimation module, for the observable model generated in step 2, an unknown parameter adaptive distributed observer is designed based on an adaptive method and finite time theory, so that when only some agents can detect the reference signal, each agent can use only limited communication information to achieve autonomous estimation of the reference signal and its unknown parameters within a limited time;

[0011] Step 4: In the reference signal fast robust tracking control module, the reference signal information estimated in step 3 is used to design a fast robust tracking controller based on a sliding mode algorithm and finite time theory, so that the output signal of each intelligent agent can achieve fast tracking of the reference signal containing unknown parameters within a finite time;

[0012] Step 5: In the closed-loop system stability analysis module, a proof of finite-time convergence of a multi-agent reference signal fast adaptive distributed tracking system is provided; on the basis of steps 1 to 4, by designing a Lyapunov function, it is proved that the multi-agent reference signal fast adaptive distributed tracking system based on an unknown parameter observer and a robust controller, under the action of the distributed observer designed in step 3 and the robust tracking controller designed in step 4, enables each agent to achieve fast estimation and stably tracking of the reference signal within a finite time when only some agents can detect the reference signal.

[0013] Preferably, in step 1: the reference signal unknown parameter model building module is mainly used to establish an observable model for the reference signal containing unknown parameters;

[0014] The reference signal unknown parameter fast distributed estimation module enables each intelligent agent to autonomously estimate the unknown parameters of the reference signal based on the state information obtained by the sensor and the communication network;

[0015] The reference signal fast robust tracking control module enables the intelligent agent to achieve safe and stable tracking of the reference signal under the influence of external disturbances;

[0016] The closed-loop system stability analysis module is mainly used to provide a finite-time convergence proof for a multi-agent reference signal fast adaptive distributed tracking system.

[0017] Preferably, in step 2, since sinusoidal signals can form various periodic signals, the reference signal to be tracked is specifically represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase; the reference signal containing unknown parameters is re-parameterized through a parameter transformation method, and converted into an observable system that is easier to control and observe through filtering transformation technology.

[0018] Preferably, the specific steps in step 2 are as follows:

[0019] Step 201: The reference signal to be tracked is represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase:

[0020]

[0021] in, ω k and ψ k Respectively represent the amplitude, frequency and phase of the sinusoidal signal, y N+1 is the output signal of the system to be tracked;

[0022] Step 202: Based on the mathematical expression of the reference signal to be tracked proposed in step 201, the reference signal containing unknown parameters is re-parameterized through parameter transformation, that is, the reference sinusoidal signal (1) to be tracked can be regarded as the output of the following virtual linear system:

[0023]

[0024] Among them, and in And θ=[θ 1 ,θ 2 ,…,θ l ] T is based on l unknown parameters Reversible reparameterization of ;

[0025] Step 203: Based on the virtual linear system (2) proposed in step 2.2), (2) is converted into an observable system through filtering transformation:

[0026]

[0027] in, is the filter transformation vector,

[0028]

[0029]

[0030]

[0031]

[0032] Preferably, the specific method in step 3 is as follows:

[0033] Step 301: In the adaptive method, define the adaptive gain μ i The expression is as follows:

[0034]

[0035] Where κ and γ are arbitrary constants greater than 0;

[0036] Step 301: Adopting the adaptive method and finite time theory, according to the observable system proposed in step 2 and the adaptive gain μ defined in step 301 i , the design of unknown parameter adaptive distributed observer is as follows:

[0037]

[0038] in, For i=1,…,N, and They are η i and χ i The estimated value of represents the Kronecker product, sgn{·} is the sign function; in addition, C 1 =P -1 , C 2 =Q -1 , c 3 >0.

[0039] Preferably, the specific method of step 4 is as follows:

[0040] Step 401: Define the dynamic equation of the multi-agent, which can be described by an r-order integrator, and its mathematical expression is as follows:

[0041]

[0042] Where i = 1, ..., N, s = 1, ..., r-1; are the state vector, control input, and output of the agent respectively;

[0043] Step 402: For p=1, ..., r+1, define function f p (·,·)as follows:

[0044]

[0045] Step 403: Design a fast robust tracking controller based on sliding mode algorithm and finite time theory as follows:

[0046]

[0047] where c 4 >0,k i,1 ,…,k i,r >0, and β i,s satisfy β i,r =β,β i,r+1 =1.

[0048] Preferably, the specific steps of step 5 are as follows:

[0049] Step 501: Estimation error analysis of reference signal and its unknown parameters;

[0050] Step 502: Analysis of the agent tracking reference signal.

[0051] Preferably, the step 501 specifically includes the following steps:

[0052] definition are the filter transformation vector η, χ, parameter θ and output signal y in step 2 respectively. N+1 The estimated value of ; for i = 1,…,N, the estimation error is defined as: Define tracking error: The error dynamics of the system is expressed as:

[0053]

[0054]

[0055] make Consider the following Lyapunov function:

[0056]

[0057] in Then, according to Derivative of the above formula (18) yields:

[0058]

[0059] if but Then, define

[0060]

[0061] in make There exists a positive constant μ * Make Then formula (20) can be written as:

[0062]

[0063] when hour, but Therefore, the estimation error In a finite time t 1 Inner convergence; after the estimated error converges, that is, There is a time point t 1 , for all t ≥ t 1 , and All are established;

[0064] Consider, considering the observation system of formula (1), for any initial value and There is a finite time t 1 > 0 makes the estimation error The convergence of is established through the finite-time distributed observer Eq. (4) and Eq. (6)-Eq. (9), where C 1 =P -1 , C 2 =Q -1 , c 3 >0,κ>0 andγ>0.

[0065] Preferably, the specific steps of step 502 are as follows:

[0066] Let e i,1 =x i,1 -y N+1 =x i,1 -f 1 (v,θ)

[0067] and

[0068] According to formula (13), we can get:

[0069]

[0070] Considering system equations (22) and (23), the estimation error will not be outside the neighborhood of 0 in a finite time, and there is a time point, namely t 1 +t 2 , so that for t>t 1 +t 2 , Then considering the controller equation (13), the system equation (22) and the system equation (23) are transformed into:

[0071]

[0072] In the interval [0,t 1 +t 2 ], the closed-loop system is transformed into:

[0073]

[0074] in Furthermore, Δ ei,s and is bounded and in finite time t 1 +t 2 Then it converges to 0; let f(x,d) be the f of the closed-loop system (25) and system (26), where Furthermore, the system is Globally finite-time stable;

[0075] Therefore, considering the observation system (1), (10) and the directed graph For any and Choose any C 1 , C 2 , c 3 and α 1 > 0, and for i = 1, ..., N, μ i Formula (4) is satisfied. Through distributed observers (6)-(9) and robust tracking controllers (12)-(13), each agent can achieve fast estimation and stable tracking of the reference signal within a limited time when only some agents can detect the reference signal.

[0076] The technical effects achieved by the present invention are:

[0077] The multi-agent reference signal fast adaptive distributed tracking system model constructed by the present invention takes into account the unknown parameters in the reference signal, as well as the influence of external interference such as wind, interference signals, and sound waves on intelligent systems such as drones and unmanned vehicles, and improves the convergence speed of the system based on the finite time theory. It provides a new modeling idea for the autonomous estimation and fast tracking control of unknown reference signals by multi-agents, enriches the research methods in this field, and the designed distributed observer and fast robust tracking controller significantly improve the practicality and reliability of multi-agent tracking systems in this field.

[0078] The distributed observer and tracking controller proposed in the present invention enable multiple agents to quickly estimate and stably track reference signals when only some agents can detect the reference signals, thereby improving the flexibility and applicability of the system.

[0079] The present invention takes into account the impact of external interferences such as wind, interference signals and sound waves on the multi-agent tracking system. The designed robust controller based on the sliding mode algorithm shows better anti-interference characteristics, especially in uncertain and disturbed environments, and can effectively suppress the impact of external interference.

[0080] The robust tracking controller designed by the present invention based on finite time theory realizes finite time convergence and significantly improves the convergence speed. The convergence speed and estimation accuracy are improved through distributed computing and finite time theory, showing higher operation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 The flowchart of the method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller provided by the present invention is

[0082] Figure 2is the estimation error diagram of the unknown reference signal by the five agents in the embodiment of the present invention

[0083] Figure 3 is a graph showing the tracking errors of the five agents for the unknown reference signal in the embodiment of the present invention.

[0084] Figure 4 is a graph showing the estimation of the unknown parameters of the reference signal by the five agents in the embodiment of the present invention.

[0085] Figure 5 is a graph showing the estimation errors of the unknown parameters of the reference signal by the five agents in the embodiment of the present invention.

[0086] Figure 6 is a graph of the estimation of unknown frequencies in the reference signal by five agents in an embodiment of the present invention

[0087] Figure 7 It is the adaptive gain diagram of 5 agents in the embodiment of the present invention. DETAILED DESCRIPTION

[0088] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0089] like Figure 1 As shown, a reference signal fast adaptive distributed tracking method based on adaptive estimation and robust controller is characterized by comprising the following steps:

[0090] Step 1: Construct a multi-agent reference signal fast adaptive distributed tracking system based on unknown parameter observer and robust controller. The multi-agent reference signal fast adaptive distributed tracking system based on unknown parameter observer and robust controller includes: reference signal unknown parameter model construction module, reference signal unknown parameter fast distributed estimation module, reference signal fast robust tracking control module and closed-loop system stability analysis module;

[0091] Step 2: In the reference signal unknown parameter model construction module, establish an observable model of the reference signal containing unknown parameters;

[0092] Step 3: In the fast distributed estimation module of unknown parameters of the reference signal, for the observable model generated in step 2, an unknown parameter adaptive distributed observer is designed based on the adaptive method and finite time theory. When only some agents can detect the reference signal, each agent can use only limited communication information to realize autonomous estimation of the reference signal and its unknown parameters within a limited time.

[0093] Step 4: In the reference signal fast robust tracking control module, for example, considering the influence of external interference factors such as wind, interference signals, and sound waves on intelligent systems such as drones and unmanned vehicles, the reference signal information estimated in step 3 is used to design a fast robust tracking controller based on the sliding mode algorithm and finite time theory, so that the output signal of each intelligent agent can quickly track the reference signal containing unknown parameters within a limited time;

[0094] Step 5: In the closed-loop system stability analysis module, a proof of finite-time convergence of the multi-agent reference signal fast adaptive distributed tracking system is provided; based on steps 1 to 4, by designing the Lyapunov function, it is proved that the multi-agent reference signal fast adaptive distributed tracking system based on the unknown parameter observer and the robust controller can achieve fast estimation and stably tracking of the reference signal in a finite time under the action of the distributed observer designed in step 3 and the robust tracking controller designed in step 4 when only some of the agents can detect the reference signal.

[0095] In summary, the multi-agent reference signal fast adaptive distributed tracking system model constructed by the present invention takes into account the unknown parameters in the reference signal, as well as the influence of external interference such as wind, interference signals, and sound waves on intelligent systems such as drones and unmanned vehicles, and at the same time improves the convergence speed of the system based on the finite time theory. It provides a new modeling idea for the autonomous estimation and fast tracking control of unknown reference signals by multi-agents, enriches the research methods in this field, and the designed distributed observer and fast robust tracking controller significantly improve the practicality and reliability of multi-agent tracking systems in this field.

[0096] Among them, in step 1: the reference signal unknown parameter model construction module is mainly used to establish an observable model for the reference signal containing unknown parameters;

[0097] The module for fast distributed estimation of unknown parameters of reference signals enables each agent to autonomously estimate the unknown parameters of reference signals based on the state information obtained from sensors and communication networks;

[0098] The reference signal fast robust tracking control module enables the intelligent agent to track the reference signal safely and stably under the influence of external disturbances;

[0099] The closed-loop system stability analysis module is mainly used to provide finite-time convergence proof for multi-agent reference signal fast adaptive distributed tracking systems.

[0100] Among them, in step 2, since sinusoidal signals can be composed of various periodic signals, the reference signal to be tracked is specifically represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase; through the parameter transformation method, the reference signal containing unknown parameters is re-parameterized, and converted into an observable system that is easier to control and observe through filtering transformation technology.

[0101] The specific steps in step 2 are as follows:

[0102] Step 201: The reference signal to be tracked is represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase:

[0103]

[0104] in, ω k and ψ k Respectively represent the amplitude, frequency and phase of the sinusoidal signal, y N+1 is the output signal of the system to be tracked;

[0105] Step 202: Based on the mathematical expression of the reference signal to be tracked proposed in step 201, the reference signal containing unknown parameters is re-parameterized through parameter transformation, that is, the reference sinusoidal signal (1) to be tracked can be regarded as the output of the following virtual linear system:

[0106]

[0107] Among them, and in And θ=[θ 1 ,θ 2 ,…,θ l ] T is based on l unknown parameters Reversible reparameterization of ;

[0108] Step 203: Based on the virtual linear system (2) proposed in step 2.2), (2) is converted into an observable system through filtering transformation:

[0109]

[0110] in, is the filter transformation vector,

[0111]

[0112]

[0113]

[0114]

[0115] The specific method in step 3 is as follows:

[0116] Step 301: In the adaptive method, define the adaptive gain μ i The expression is as follows:

[0117]

[0118] Where κ and γ are arbitrary constants greater than 0;

[0119] Step 301: Adopting the adaptive method and finite time theory, according to the observable system proposed in step 2 and the adaptive gain μ defined in step 301 i , the design of unknown parameter adaptive distributed observer is as follows:

[0120]

[0121] in, For i=1,…,N, and They are η i and χ i The estimated value of represents the Kronecker product, sgn{·} is the sign function; in addition, C 1 =P -1 , C 2 =Q -1 , c 3 >0.

[0122] The specific method of step 4 is as follows:

[0123] Step 401: Define the dynamic equation of the multi-agent, which can be described by an r-order integrator, and its mathematical expression is as follows:

[0124]

[0125] Where i = 1, ..., N, s = 1, ..., r-1; are the state vector, control input, and output of the agent respectively;

[0126] Step 402: For p=1, ..., r+1, define function f p (·,·)as follows:

[0127]

[0128] Step 403: Design a fast robust tracking controller based on sliding mode algorithm and finite time theory as follows:

[0129]

[0130] where c 4 >0,k i,1 ,…,k i,r >0, and β i,s satisfy β i,r =β,β i,r+1 =1.

[0131] The specific steps of step 5 are as follows:

[0132] Step 501: Estimation error analysis of reference signal and its unknown parameters;

[0133] Step 502: Analysis of the agent tracking reference signal.

[0134] Wherein, step 501 specifically includes the following steps:

[0135] definition are the filter transformation vector η, χ, parameter θ and output signal y in step 2 respectively. N+1 The estimated value of ; for i = 1,…,N, the estimation error is defined as: Define tracking error: The error dynamics of the system is expressed as:

[0136]

[0137] make Consider the following Lyapunov function:

[0138]

[0139] in Then, according to Derivative of the above formula (18) yields:

[0140]

[0141] if but Then, define

[0142]

[0143] in make There exists a positive constant μ * Make Then formula (20) can be written as:

[0144]

[0145] when hour, but Therefore, the estimation error In a finite time t 1 Inner convergence; after the estimated error converges, that is, There is a time point t 1 , for all t ≥ t 1 , and All are established;

[0146] Consider, considering the observation system of formula (1), for any initial value and There is a finite time t 1 > 0 makes the estimation error The convergence of is established through the finite-time distributed observer Eq. (4) and Eq. (6)-Eq. (9), where C 1 =P -1 , C 2 =Q -1 , c 3 >0,κ>0 andγ>0.

[0147] The specific steps of step 502 are as follows:

[0148] Let e i,1 =x i,1 -y N+1 =x i,1 -f 1 (v,θ)

[0149] and

[0150] According to formula (13), we can get:

[0151]

[0152] Considering system equations (22) and (23), the estimation error will not be outside the neighborhood of 0 in a finite time, and there is a time point, namely t 1 +t 2 , so that for t>t 1 +t 2 , Then considering the controller equation (13), the system equation (22) and the system equation (23) are transformed into:

[0153]

[0154] In the interval [0,t 1 +t 2 ], the closed-loop system is transformed into:

[0155]

[0156] in Furthermore, Δ ei,s and is bounded and in finite time t 1 +t 2 Then it converges to 0; let f(x,d) be the f of the closed-loop system (25) and system (26), where Furthermore, the system is Globally finite-time stable;

[0157] Therefore, considering the observation system (1), (10) and the directed graph For any and Choose any C 1 , C 2 , c 3 and α 1 > 0, and for i = 1, ..., N, μ i Formula (4) is satisfied. Through distributed observers (6)-(9) and robust tracking controllers (12)-(13), each agent can achieve fast estimation and stable tracking of the reference signal within a limited time when only some agents can detect the reference signal.

[0158] In actual use, this embodiment takes five agents as an example to simulate and construct a multi-agent reference signal fast adaptive distributed tracking system model, taking into account the unknown parameters in the reference signal, as well as the impact of external interference such as wind, interference signals, and sound waves on intelligent systems such as drones and unmanned vehicles. Figure 2-7 The experimental results in Figure 2 is a graph of estimation errors of the five agents for an unknown reference signal in an embodiment of the present invention; Figure 3 is a graph of tracking errors of five agents for an unknown reference signal in an embodiment of the present invention; Figure 4 is a diagram of the estimation of unknown parameters of the reference signal by five agents in an embodiment of the present invention; Figure 5 is a graph of the estimation errors of the unknown parameters of the reference signal by the five agents in the embodiment of the present invention; Figure 6 is a graph of the estimation of unknown frequencies in the reference signal by five agents in an embodiment of the present invention; Figure 7It is the adaptive gain diagram of the five intelligent agents in the embodiment of the present invention. It can be seen from the figure that the finite time theory improves the convergence speed of the system, improves the convergence speed and estimation accuracy, and shows higher operating efficiency; when only some intelligent agents can detect the reference signal, the multi-agent fast estimation and stable tracking of the reference signal are realized; the flexibility and scope of application of the system are improved, and better anti-interference characteristics are shown, especially in uncertain and interfered environments, and the impact of external interference can be effectively suppressed.

[0159] In summary, the present invention improves the convergence speed of the system based on the finite time theory at the same time; provides a new modeling idea for the autonomous estimation and rapid tracking control of unknown reference signals by multi-agents, enriches the research methods in this field, and the designed distributed observer and fast robust tracking controller significantly improve the practicality and reliability of the multi-agent tracking system in this field; the distributed observer and tracking controller proposed in the present invention enable the multi-agent to quickly estimate and stably track the reference signal when only some of the agents can detect the reference signal, thereby improving the flexibility and scope of application of the system; the present invention considers the influence of external interferences such as wind, interference signals and sound waves on the multi-agent tracking system, and the designed robust controller based on the sliding mode algorithm shows better anti-interference characteristics, especially in uncertain and disturbed environments, it can effectively suppress the influence of external interference; the present invention is based on the finite time theory, and the designed robust tracking controller realizes finite time convergence, significantly improving the convergence speed. The convergence speed and estimation accuracy are improved through distributed computing and finite time theory, showing higher operating efficiency.

[0160] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A fast adaptive distributed tracking method of reference signals based on adaptive estimation and robust controller, characterized in that: The following steps are involved: Step 1: construct a multi-agent reference signal fast adaptive distributed tracking system based on an unknown parameter observer and a robust controller, wherein the multi-agent reference signal fast adaptive distributed tracking system based on an unknown parameter observer and a robust controller comprises: a reference signal unknown parameter model construction module, a reference signal unknown parameter fast distributed estimation module, a reference signal fast robust tracking control module, and a closed-loop system stability analysis module; Step 2: In the reference signal unknown parameter model construction module, establish an observable model of the reference signal containing unknown parameters; Step 3: In the reference signal unknown parameter fast distributed estimation module, for the observable model generated in step 2, an unknown parameter adaptive distributed observer is designed based on an adaptive method and finite time theory, so that when only some agents can detect the reference signal, each agent can use only limited communication information to achieve autonomous estimation of the reference signal and its unknown parameters within a limited time; Step 4: In the reference signal fast robust tracking control module, the reference signal information estimated in step 3 is used to design a fast robust tracking controller based on a sliding mode algorithm and finite time theory, so that the output signal of each intelligent agent can track the reference signal containing unknown parameters within a finite time; Step 5: In the closed-loop system stability analysis module, a proof of finite-time convergence of the multi-agent reference signal fast adaptive distributed tracking system is provided; on the basis of steps 1 to 4, by designing the Lyapunov function, it is proved that the multi-agent reference signal fast adaptive distributed tracking system based on the unknown parameter observer and the robust controller, under the action of the distributed observer designed in step 3 and the robust tracking controller designed in step 4, enables each agent to estimate and track the reference signal within a finite time when only some agents can detect the reference signal.

2. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 1, characterized in that: In the step 1: the reference signal unknown parameter model building module is mainly used to establish an observable model for the reference signal containing unknown parameters; The reference signal unknown parameter fast distributed estimation module enables each intelligent agent to autonomously estimate the unknown parameters of the reference signal based on the state information obtained by the sensor and the communication network; The reference signal fast robust tracking control module enables the intelligent agent to achieve safe and stable tracking of the reference signal under the influence of external disturbances; The closed-loop system stability analysis module is mainly used to provide a finite-time convergence proof for a multi-agent reference signal fast adaptive distributed tracking system.

3. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 1, characterized in that: In step 2, since sinusoidal signals can form various periodic signals, the reference signal to be tracked is specifically represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase; the reference signal containing unknown parameters is re-parameterized through the parameter transformation method, and converted into an observable system that is easier to control and observe through filtering transformation technology.

4. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 3, characterized in that: The specific steps in step 2 are as follows: Step 201: The reference signal to be tracked is represented as the sum of sinusoidal signals with unknown frequency, amplitude and initial phase: in, ω k and ψ k Respectively represent the amplitude, frequency and phase of the sinusoidal signal, y N+1 is the output signal of the system to be tracked; Step 202: Based on the mathematical expression of the reference signal to be tracked proposed in step 201, the reference signal containing unknown parameters is re-parameterized through parameter transformation, that is, the reference sinusoidal signal (1) to be tracked can be regarded as the output of the following virtual linear system: Among them, and in And θ=[θ1,θ2,...,θ l ] T is based on l unknown parameters Reversible reparameterization of ; Step 203: Based on the virtual linear system (2) proposed in step 2.2), (2) is converted into an observable system through filtering transformation: in, is the filter transformation vector, 5. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 1, characterized in that: The specific method in step 3 is as follows: Step 301: In the adaptive method, define the adaptive gain μ i The expression is as follows: Where κ and γ are arbitrary constants greater than 0; Step 301: Adopting the adaptive method and finite time theory, according to the observable system proposed in step 2 and the adaptive gain μ defined in step 301 i , the design of unknown parameter adaptive distributed observer is as follows: in, For i=1,...,N, and They are η i and χ i The estimated value of represents the Kronecker product, sgn{·} is the sign function; in addition, C1=P -1 , C2=Q -1 , c3>0.

6. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 1, characterized in that: The specific method of step 4 is as follows: Step 401: Define the dynamic equation of the multi-agent, which can be described by an r-order integrator, and its mathematical expression is as follows: Where i=1,...,N,s=1,...,r-1; are the state vector, control input, and output of the agent respectively; Step 402: For p=1, ..., r+1, define function f p (·,·)as follows: Step 403: Design a fast robust tracking controller based on sliding mode algorithm and finite time theory as follows: Where c4>0, k i,1 ,…,k i,r >0, and β i,s satisfy 7. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 1, characterized in that: The specific steps of step 5 are as follows: Step 501: Estimation error analysis of reference signal and its unknown parameters; Step 502: Analysis of the agent tracking reference signal.

8. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 7, characterized in that: The step 501 specifically includes the following steps: definition are the filter transformation vector η, χ, parameter θ and output signal y in step 2 respectively. N+1 The estimated value of ; for i = 1,…,N, the estimation error is defined as: Define tracking error: The error dynamics of the system is expressed as: make Consider the following Lyapunov function: in Then, according to Derivative of the above formula (18) yields: if but Then, define in make There exists a positive constant μ * Make Then formula (20) can be written as: when hour, but Therefore, the estimation error Converges within a finite time t1; after the estimation error converges, that is, There exists a time point t1 such that for all t≥t1, and All are established; Consider, considering the observation system of formula (1), for any initial value and There exists a finite time t1>0 such that the estimation error The convergence of is established by the finite-time distributed observer Eq. (4) and Eq. (6)-Eq. (9), where C1 = P -1 , C2=Q -1 , c3>0, κ>0 and γ>0.

9. The method for fast adaptive distributed tracking of reference signals based on adaptive estimation and robust controller according to claim 8, characterized in that: The specific steps of step 502 are as follows: Let e i,1 = x i,1 - y N+1 = x i,1 - f1(v,θ) and According to formula (13), we can get: Considering system equations (22) and (23), the estimation error will not be outside the neighborhood of 0 in a finite time, and there is a time point, namely t1+t2, such that for t>t1+t2, Then considering the controller equation (13), the system equation (22) and the system equation (23) are transformed into: In the interval [0, t1+t2], the closed-loop system is transformed into: in Furthermore, Δ ei,s and is bounded and converges to 0 after a finite time t1+t2; let f(x,d) be the f of the closed-loop system (25) and the system (26), where Furthermore, the system is Globally finite-time stable; Therefore, considering the observation system (1), (10) and the directed graph For any and Choose any C1, C2, c3 and α1>0, and for i=1,…,N, μ i Formula (4) is satisfied. Through distributed observers (6)-(9) and robust tracking controllers (12)-(13), each agent can estimate and track the reference signal within a limited time when only some agents can detect the reference signal.

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