Tracking control of nonlinear systems with improved performance via transformational approach

Abstract

Summary In this work, we present a transformation‐based adaptive control design, for uncertain strict‐feedback nonlinear systems, to achieve given performance specifications in terms of convergence rate/time, overshoot, steady‐state (zero‐error) precision, in addition to the primary stability requirement. For the case with no uncertainty and known control coefficient, by introducing a time‐varying scaling function and an error‐dependent transformation, we develop a control strategy that is able to achieve exponential and uniform convergence of the tracking error and at the same time maintain the output tracking overshoot to be as small as desired without the need for trajectory initialization resetting. For the case with nonparametric uncertainties and unknown control directions, by employing an additional time‐varying scaling function together with a self‐tuning Nussbaum function, we develop a control scheme that not only secures asymptotic tracking but also guarantees finite time transient process in that the tracking error, prior to converging to zero, is regulated into a prespecified residual set within a prescribed time. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

Prescribed‐time control of uncertain strict‐feedback‐like systems

“…(1) Aiming at a more general yet more complex class of nonlinear systems, we establish a method for prescribed-time regulation. Different from the finite/fixed-time control that is based on fractional power of state feedback, our result provides a solution with settling time being fully independent of initial conditions; (2) Unlike the prescribed performance control method, [18][19][20] our method makes all the system states converge to the origin precisely within a preset time without the need for barrier Lyapunov function or any other state transformation; (3) In contrast to most existing results 13,14,16,17 that are only valid for t ∈ [0, t f ), our control scheme, featured with simplicity and elegance, is fully functional for t ∈ [0, + ∞) in that it makes each system state converge to zero (within user-chosen settling time) and remain zero thereafter, allowing for nonstop running of the system beyond the settling time t f .…”

Global practical tracking for nonlinear systems with unknown input powers using dual high‐gain‐based adaptive feedback

“…Second, the transient performance, such as the arrival time and maximum overshoot, is excluded in this article. Actually, in works of Zhao et al 27,28 and Li and Liu, 13 prescribed performance tracking control is investigated for nonlinear systems, and particularly, the tracking error can be driven to a prescribed compact set after a prescribed time and its maximum overshoot can be prespecified. How to achieve prescribed performance tracking control in the case with unknown input powers deserves further investigation.…”

Adaptive dynamic surface asymptotic tracking control of uncertain strict‐feedback systems with guaranteed transient performance and accurate parameter estimation

“…On the other hand, the asymptotic tracking control is the same significant in many high precision applications such as spacecraft proximity operations, 31 electrohydraulic servomechanisms, 32 hypersonic flight vehicles, 33 Euler–Lagrange systems, 34 and so on. In References 35‐37, the asymptotic tracking control of fault‐tolerant systems and strict‐feedback systems (SFSs) with unknown control directions is achieved with guaranteed transient performance. The employment of the traditional backstepping design method in References 35‐37 is inevitable to bring about the “differential explosion” problem, and thus, it is natural to adopt the DSC method for further studies.…”

“…In References 35‐37, the asymptotic tracking control of fault‐tolerant systems and strict‐feedback systems (SFSs) with unknown control directions is achieved with guaranteed transient performance. The employment of the traditional backstepping design method in References 35‐37 is inevitable to bring about the “differential explosion” problem, and thus, it is natural to adopt the DSC method for further studies.…”