CN-116774578-B - Design method of global tracking controller based on integral barrier Lyapunov function

CN116774578BCN 116774578 BCN116774578 BCN 116774578BCN-116774578-B

Abstract

The invention discloses a design method of a global tracking controller based on an integral barrier Lyapunov function, which comprises the steps of constructing a strict feedback system model, setting constraint conditions, dividing global time into one or more time segments according to preset convergence time, mapping each time segment to a corresponding infinite time domain by adopting time scale coordinate translation mapping, respectively generating an improved system model, forming a switching system by all the improved system models, constructing the tracking controller of the improved system model by adopting a back-push method, recursively designing control input by the controller based on the integral barrier Lyapunov function, ensuring global stable tracking control of the controller by adopting a fixed residence time method, solving the convergence of the system after the preset time, and optimizing the self-adaptive tracking effect of the global domain.

Inventors

ZHANG WENQIAN
ZHANG PENG
ZHANG PEIYU
ZHANG HONGMEI
JIANG JUN
WU JIANGNAN

Assignees

中国人民解放军空军工程大学

Dates

Publication Date: 20260512
Application Date: 20230519

Claims (6)

1. The design method of the global tracking controller based on the integral barrier Lyapunov function comprises the following steps: A strict feedback system model is constructed, constraint conditions are set, the global time is divided into one or more time segments according to preset convergence time, a time scale coordinate mapping function is adopted, each time segment is mapped to a corresponding infinite time domain, improved system models are respectively generated, and all the improved system models form a switching system; The improved system model tracking controller is constructed by adopting a back-stepping method, and is based on an integral obstacle Lyapunov function, and virtual control input is recursively designed ,..., ,..., Time-varying gain function ,..., ,..., Adaptive control law ,..., ,..., , wherein, (2≤ ≤ -1), For the vector number of the system model, the actual control input of the improved system model is designed Time-varying gain function Adaptive control rate ; The set time period is as follows: , ,..., ,., wherein The function of the time scale coordinate mapping is set as: Wherein, the For a pre-set convergence time period, , Preset time period Is used for the number of time segments of (a).
2. The method for designing a global tracking controller based on an integral obstacle Lyapunov function according to claim 1, wherein the predetermined convergence time is recorded as The time scale coordinate mapping function is set as: ; Wherein, the For a pre-set convergence time period, , For the time over the infinite domain, 。
3. The method for designing a global tracking controller based on an integral barrier Lyapunov function according to claim 2, wherein the function of the improved system model is set as: ; Wherein, the And Representing a measurable system state vector that is representative of the system state, And Representing the input and output of the system respectively, As a set of real numbers, Representing an unknown differentiable nonlinear system function, , Is the number of vectors of the system model, Representing an unknown differentiable control gain function, Representing an unknown external disturbance and a system uncertainty term, Deriving the time τ over the unconfined domain for a first predetermined function of the time-scale coordinate map of the convergence period, namely: all system states are all constrained to a tight set Wherein, among them, Refers to the designed barrier function.
4. The method for designing a global tracking controller based on an integral barrier Lyapunov function according to claim 1, wherein the function of the improved system model is set as: ; Wherein, the And Representing a measurable system state vector that is representative of the system state, And Representing the system input and output respectively, As a set of real numbers, , Representing an unknown differentiable nonlinear system function, Representing an unknown differentiable control gain function, Representing an unknown external disturbance and a system uncertainty term, The function of the time scale coordinate mapping derives the time τ over the infinite domain, namely: all system states are all constrained to a tight set Wherein, among them, Refers to the designed barrier function; To switch signals, each time-scale coordinate translation map may produce an independent improved system model.
5. The method for designing a global tracking controller based on an integral barrier Lyapunov function according to claim 4, wherein the switching signal is Is fixed in residence time of (2) The conditions are as follows: ; Wherein, the , Wherein Refers to a positive constant.
6. The method of designing a global tracking controller based on an integral barrier Lyapunov function according to claim 3 or 5, wherein an error model of the improved system model tracking controller is as follows: , ; Wherein the method comprises the steps of In order to track the error in the tracking, Virtual control input for the system; actual control input Time-varying gain function Adaptive control rate The design steps of (a) comprise: step 1 tracking error Deriving a time tau on an infinite domain, and selecting an integral type Lyapunov obstacle function as a function; ; Wherein, the In order to achieve a desired trajectory, the track, As a result of the fact that a substitute variable, Is time of An obstacle function designed above; By integrating lyapunov disorder function Deriving time tau on the infinite domain, and knowing the integral type Lyapunov disorder function in the Lobida method by adopting a partial integral method Is bounded within a neighborhood according to Can obtain And (3) with Derivative relation function defining an unknown linear function In the general form of neural networks To approach unknown functions Designing the virtual control input Time-varying gain function Adaptive control law , Is about , , , Is a function of (2); Step (a) Tracking error The time tau over the unconfined domain is derived, wherein, Is about Setting an integral lyapunov barrier function: ; Wherein, the In order to be a virtual control law, Is time of An obstacle function designed above; The integral type Lyapunov obstacle function derives the time tau on the infinite domain, and the integral type Lyapunov obstacle function is verified to be in the infinite domain by adopting a partial integration method and the lobida rule Is bounded within a neighborhood according to Can obtain And (3) with Derivative relation function defining an unknown linear function Virtual control inputs are designed using neural networks to approximate Time-varying gain function Adaptive control law ; Step n tracking error Deriving a time τ over an infinite domain, selecting an integral lyapunov barrier function: ; Wherein, the In order to be a virtual control law, Is time of An obstacle function designed above; The integral type Lyapunov obstacle function derives the time tau on the infinite domain, and the integral type Lyapunov obstacle function is verified to be in the infinite domain by adopting a partial integration method and the lobida rule Is bounded within a neighborhood according to Can obtain And (3) with Derivative relation function defining an unknown linear function The neural network is utilized to approach, the actual control input u is designed, and the time-varying gain function is designed Adaptive control rate 。

Description

Design method of global tracking controller based on integral barrier Lyapunov function Technical Field The invention relates to the field of control, in particular to a design method of a global tracking controller based on an integral barrier Lyapunov function. Background In robot control, vehicle control, and other physical systems, there is a stringent requirement for achieving state convergence within a predetermined time. Since the preset time control method can not only stabilize the system within a fixed time, but also design the convergence time independent of the initial conditions in advance according to the system demand, in recent years, the preset time is controlled to be a control theory of one leading edge. In the prior study, krishnamurthy and the like adopt a dynamic scaling form with a time forcing term, the preset time stability of the system is realized based on a dynamic high-gain scaling technology, besides the single system, the preset time stability has a large number of research achievements in the multi-agent system, wang and the like establish a new scale function to realize the preset time distributed control of the network multi-agent system, in addition, ning and the like propose a time base generator method, solve the problem of the actual fixed time consistency of no leader and leader-follower in the integral multi-agent system, and Chen and the like construct the event triggering control of the multi-agent system to realize the bisection consistency of the preset time. Liu et al define the concept of preassigned finite time performance functions for time-lapse feedback nonlinear systems with quantized inputs. Cao et al construct a finite time performance function to ensure convergence time and consistency of the high-order nonlinear multi-agent system under mismatched uncertainty and external disturbance conditions. Ning et al introduce an auxiliary quantity based on a time-varying function to ensure that a second-order multi-agent system realizes bipartite consistency tracking within preset time. The prior art has the following problems: 1) The above results are all based on solving the tracking control problem of the preset time, and most of the preset time control methods are used for solving the calm problem, so that the convergence of the system after the preset time is not considered. 2) The above-mentioned preset time tracking control method is implemented by controlling the gain angle, the designed function is generally defined as a normal number after the preset time, and the design method cannot meet the adaptive requirement. 3) And aiming at the possible jump behavior of the time mapping switching point of each period, generating independent Lyapunov functions of each subsystem through time scale coordinate translation mapping, and adopting a Fixed Dwell time Method (FDT) to ensure global stable tracking control. 4) In order to break through the conservative limitation of the traditional barrier lyapunov function, an integral BLF is introduced to ensure the full state constraint, instead of converting the state constraint into a known error constraint. Disclosure of Invention The invention provides a design method of a global tracking controller based on an integral barrier Lyapunov function aiming at the problems. The technical scheme adopted by the invention is as follows: the design method of the global tracking controller based on the integral barrier Lyapunov function comprises the following steps: A strict feedback system model is constructed, constraint conditions are set, the global time is divided into one or more time segments according to preset convergence time, a time scale coordinate mapping function is adopted, each time segment is mapped to a corresponding infinite time domain, improved system models are respectively generated, and all the improved system models form a switching system; the improved system model tracking controller is constructed by adopting a back-push method, and is based on an integral obstacle Lyapunov function, and virtual control input alpha 1,...,αi,...,αn-1 and a time-varying gain function are recursively designed Adaptive control lawWherein i (i is more than or equal to 2 and less than or equal to n-1), n is the number of vectors of the system model, and the actual control input u of the improved system model is designed, and a time-varying gain function is designedAdaptive control rate Further, the preset convergence time is recorded as T P, and the time scale coordinate mapping function is set as follows: wherein T P is a preset convergence time, T ε [0, T P), τ is the time over the infinite domain and, τ is one of the values of e 0, +++). Further, the function of the improved system model is set as follows: Wherein, the And χ= [ χ 1,χ2,...,χn]T∈Rn ] represents a measurable system state vector, u e R and y e R represent system input and output, respectively, R is a real set,Representing an unknown differentiable nonlin