Robust adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems with unknown control directions

In this paper, the adaptive fuzzy backstepping control problem is considered for a class of single-input single-output (SISO) unknown uncertain nonaffine nonlinear systems in strict-feedback form. Within this approach, Nussbaum gain functions are introduced to solve the problem of unknown control directions. The unknown nonlinear functions are approximated by employing adaptive fuzzy systems. The stability analysis of the closed-loop system in the sense of Lyapunov guarantees the global boundedness property for all the signals and states, and at the same time, steers the tracking error to a small neighborhood of the origin. The feasibility of the developed control approach is illustrated by numerical simulation.

New Stability Analysis and Design of Discrete Time Delay Control for Nonaffine Nonlinear Systems

Time Delay Control (TDC) for linear and nonlinear systems with uncertain dynamics has been widely discussed in the literature, as it has a very simple and compact form. It uses time-delayed signals for estimating unknown dynamics at an instant, and uses feedback linearization for cancellation of known and estimated unknown dynamics. While the original formulation and most of the analyses have been focused on the continuous version of the controller, its implementation is more natural in digital form. This paper extends the recently improved sufficient Bounded Input - Bounded Output (BIBO) stability conditions for continuous Time Delay Control of nonaffine nonlinear systems to discrete Time Delay Control, including simplified approximate conditions under various assumptions. Additionally. asymptotic stability is established for similar conditions. The derived conditions are contrasted with earlier results for continuous Time Delay Control. Examples are used to illustrate the differences in continuous and discrete TDC, related to performance as well as sufficient and actual conditions for stability.

Characteristic Model-Based Adaptive Control for a Class of MIMO Uncertain Nonaffine Nonlinear Systems Governed by Differential Equations

This paper addresses the difficulty of designing a controller for a class of multi-input multi-output uncertain nonaffine nonlinear systems governed by differential equations. We first derive the first-order characteristic model composed of a linear time-varying uncertain system for such nonaffine systems and then design an adaptive controller based on this first-order characteristic model for position tracking control. The designed controller exhibits a simple structure that can effectively avoid the controller singularity problem. The stability of the closed-loop system is analyzed using the Lyapunov method. The effectiveness of our proposed method is validated with a numerical example.