A unified adaptive control approach of nonlinear continuous non‐parameterized systems with asymmetric control gains for trajectory tracking in different domains

Abstract

In this article, for nonlinear continuous non-parameterized (NCNP) systems, an adaptive iterative learning control (ILC) algorithm, which can adjust the adaptive parameters in both iteration-domain and time-domain, is first proposed to track different reference trajectories repetitively over a finite time interval. As the NCNP system is required to asymptotically track reference trajectory in infinite time-domain, by virtue of partitioning the reference trajectory and system signals with a fixed time interval, the proposed adaptive ILC controller is then extended to handle the asymptotic tracking issue in infinite time-domain. Therefore, a unified adaptive control approach is practically presented for NCNP systems to track reference trajectories in different domains (the infinite iteration-domain and the infinite time-domain). A prominent feature of the unified adaptive control approach is that the unknown control gain matrices in the NCNP systems are assumed to be invertible only. As a result, the general requirement in conventional adaptive control and adaptive ILC that the control gain matrices of plants are real symmetric and positive-definite (or negative-definite) is greatly relaxed. In addition, only three adaptive variables are designed for adjusting or updating in the proposed unified adaptive control approach such that the structure of controller is very simple and the memory space for computing is saved.

High-Order Modeling, Zeroing Dynamics Control, and Perturbations Rejection for Non-Linear Double-Holding Water Tank

“…Therefore, the robustness of a given system must be investigated, as it is the key to survival in the event of abnormal and dangerous situations. Many researchers have studied numerous methods to enhance the robustness of systems [11][12][13][14][15][16][17][18][19]; for example, a discrete time-zeroing neural algorithm has been proposed for the solution of a system of linear equations with the aid of control techniques. To lay a foundation for theoretical analyses, this proposed algorithm with non-linearity was converted into a second-order linear system plus a residual term [12].…”