Robust Adaptive Controllers for Interconnected Mechanical Systems: Influence of Types of Interconnections on Time-Invariant and Time-Varying Systems

Abstract

We investigate robust adaptive controller designs for interconnected systems when no exact knowledge about the structure of the nonlinear interconnections between various subsystems is available. In this study, we concentrate on several different types of systems. We deal with both linear time-invariant (LTI) and linear time-varying (LTV) systems with nonlinear interconnections. For LTI systems, we examine the following types of interconnections: • interconnections that are bounded by first order polynomials in state space; • slowly time varying interconnections; • interconnections bounded by higher-order polynomials in state-space together with input channel interconnections. For LTV systems we deal with interconnections bounded by first-order polynomials in state space. We show that the nature of the nonlinear interactions influences the adaptation laws. We use the direct method of Lyapunov for the design of adaptive controllers for tracking in such systems. We investigate issues such as stability, transient performance and steady-state errors, and derive quantitative estimates and analytical bounds for various different adaptive controllers. For time-varying systems, we analyze the effect of the time variations of parameters and interactions and propose a modified adaptive control scheme with better performance. Simulation results are presented to validate our conclusions. We also investigate these results experimentally on a two-link robot manipulator. Experimental results validate theoretical conclusions and demonstrate the usefulness of such robust adaptive controllers for high-speed motions in uncertain systems.