Neuro-Adaptive Control With Given Performance Specifications for Strict Feedback Systems Under Full-State Constraints

Abstract

In this paper, we investigate the tracking control problem for a class of strict feedback systems with pregiven performance specifications as well as full-state constraints. Our focus is on developing a feasible neural network (NN)-based control method that is able to, under full-state constraints, force the tracking error to converge into a prescribed region within preset finite time and further reduce the error to a smaller and adjustable residual set, while confining the overshoot within predefined small level. Based on two consecutive error transformations governed by two auxiliary functions, named with behavior-shaping function and asymmetric scaling function, respectively, a novel approach to achieve given performance specifications is developed under certain bound condition on the transformed error, such condition, along with the full-stated constraints, is guaranteed by imbedding barrier Lyapunov function (BLF) into the back-stepping design. Furthermore, asymmetric output constraints are maintained with a single symmetric BLF, simplifying the procedure of stability analysis. All internal signals including the stimulating inputs to the NN unit are ensured to be bounded. Both theoretical analysis and numerical simulation verify the effectiveness and the benefits of the design.

Broad learning control of a two-link flexible manipulator with prescribed performance and actuator faults

“…[49] The behavior-shaping function shown in (8) possesses the following properties: ; and for all ; , is a positive integer. …”

“…Inspired by neural adaptive PPC proposed in ref. [49], an asymmetric scaling function and a behavior-shaping function are introduced to constraint overshoot and steady-state errors, respectively. The unknown model dynamics of flexible robotic manipulator is approximated by the improved RBFNNs.…”

Neuroadaptive tracking control for uncertain pure‐feedback systems under dynamic constraints

“…In this paper, we will use radial basis function NN 39‐42 to approximate some (lumped) unknown nonlinear functions as long as the NN structure is sufficiently complex and the number of neurons is larger enough. According to universal approximation theorem, for any given continuous function $$$ {F}_i\left({X}_i\right):{R}^n\to R $$$ on a compact set $$$ {D}_i\subset {R}^n $$$, there exists a NN such that $$$ {F}_i\left({X}_i\right) $$$ can be approximated with sufficient accuracy by choosing an ideal NN as follows: $$$$ {F}_i\left({X}_i\right)={W}_i^{\ast T}{S}_i\left({X}_i\right)+{\xi}_i\left({X}_i\right), $$$$ where $$$ {W}_i^{\ast } $$$ denotes the ideal constant neural weight vector, $$$ {X}_i\in {R}^n $$$ is the NN input vector and $$$ {\xi}_i\left({X}_i\right) $$$ is the approximation error.…”

Non-Parametric Neuro-Adaptive Control Subject to Task Specifications

“…A large variety of previous works considers neural-network-based adaptive control (neuro-adaptive control) with stability guarantees, focusing on the optimal control problem [2,11,12,10,13,14,15,16,17,18,19,5]. Nevertheless, the related works draw motivation from the neural network density property (see, e.g., [20]) 2 and assume sufficiently small approximation errors and linear parameterizations of the unknown terms (dynamics, optimal controllers, or value functions), which is also the case with standard adaptive control methodologies [1,21,22,8].…”