Abstract
As an effort to establish a stability and performance metric for adaptive control systems and an attempt to expand nonlinear system operating range with linearization-based designs in the presence of uncertainties, this dissertation focuses on the gain margin (GM) of adaptive control systems and the development of novel adaptive control schemes for piecewise linear systems. The contributions are a systematic gain margin analysis for a variety of adaptive control systems, and a framework of solutions to the open problems in adaptive control of uncertain piecewise linear systems.
The gain margin of adaptive control systems is defined as the specification of the parameter range of a control gain matrix in a designed adaptive control system for maintaining the desired closed-loop signal boundedness and asymptotic tracking performance. A systematic gain margin analysis is conducted for continuous- and discrete-time, direct and indirect model reference adaptive control (MRAC) systems, adaptive state feedback control systems, and sampled-data adaptive control systems. The derived gain margin results are applicable to systems with adaptive nonlinear or pole placement control designs. Methods for enlarging the GM by proper choices of design parameters are presented. This gain margin study has established guidelines for designing control systems with stability and tracking guarantees in the presence of uncertain control gain variations. Furthermore, the derived gain margin results are applied to solve the problem of system performance robustness with respect to reduced actuator effectiveness.
The adaptive control approach to piecewise linear systems is largely unexploited, despite the tremendous growth of research interest in stability analysis and control design for such systems over the past two decades. This dissertation focuses on the development of model reference adaptive control designs for piecewise linear systems to achieve closed-loop stability (signal boundedness) and system state or output tracking as close as possible, in the presence of structural and parametric uncertainties and repetitive system mode switches. State feedback for state tracking (SFST), state feedback for output tracking (SFOT), and output feedback for output tracking (OFOT) MRAC designs are presented. It is shown that under a slow system mode switching condition, closed-loop stability and a small tracking error in the mean-square sense are achieved. For the SFST design, asymptotic state tracking performance is restored under certain persistency of excitation (P.E.) condition, and the slow switching condition can be relaxed to arbitrary system mode switches, when a common Lyapunov function exists for the constituent system modes. For the SFOT design, asymptotic tracking performance is ensured for arbitrary system mode switches, in addition to closed-loop stability, under an additional plant-model matching condition. Effectiveness of the proposed adaptive control schemes are demonstrated by simulation studies on linearized and nonlinear aircraft models (NASA generic transport model (GTM)).
