Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Abstract

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding-based technique. As an attractive alternative of the adaptive backstepping method, this bottom-up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower-order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results. KEYWORDS adaptive control, filters, input saturation, mapping filtered forwarding control, uncertain nonlinear systems 248 ;32:248-264. ZHANG ET AL. 249error as z =θ − θ + β(x), where β(x) is a continuous term, and utilizing the uncertainty equivalence principle to design parameter update laws for lower triangular systems. Although researchers used this method to design parameter update laws in some practical systems, the achievements strictly depend on an assumption satisfying the partial differential inequality to obtain β(x). 20,21 In essence, the solvability of this inequality strongly relies on the structure of the regressor, and as system order increases, the implementation will be limited. Therefore, it could not be feasible to achieve I&I adaptive stabilization for high-order nonlinear systems with extended matching uncertainties. 22,23 Furthermore, control input saturation severely limits system performance in many physical systems, giving rise to undesirable properties or leading instability. 24,25 The hyperbolic tangent function is used to approximate the saturated nonlinearity, 12 where the approximated error is considered as an augmented external disturbance. Although this algorithm is easy to be carried out, the problem of the definition domain of artanh(·) is encountered while tuning controller gains. It can be shown that the bound of the nonlinear function we derive must be restricted to (−1, 1). 26 The problem of the controller design for the nonlinear systems with input saturation and parametric uncertainties has not been addressed adequately under a mapping filtered forwarding-based framework.In this paper, we will study the robust adaptive control design for nonlinear systems subject to input saturation and uncertainties under the mapping filtered forwarding-based framework. A new bottom-up control scheme from a manifold's perspective, namely, mapping filtered adaptive forwarding, which consists of virtual control laws and parameter updated laws, will be presented. With the proposed controller architecture, manifolds are guaranteed to be insensitive to uncertainties, and the iss...

Adaptive Trajectory Tracking Control of a Cable-Driven Underwater Vehicle on a Tension Leg Platform

“…Another technical challenge for cable-driven vehicle control is the input saturation caused by physical actuator [40]. The undesirable input saturation will influence the stability of the control system and even make the entire system unstable.…”