Design of control laws for adaptive signal tracking systems

This dissertation develops and analyzes a novel approach to the synthesis of adaptive controllers for single-input single-output systems with uncertain parameters operating in a stochastic disturbance environment. The proposed algorithm, formulated in discrete time domain, is based on the certainty-equivalence principle. It combines a recursive extended least squares parameter estimation algorithm with an optimal feedback regulator/feedforward signal tracking controller in an indirect model reference adaptive scheme. The control law synthesis is based on the discrete version of generalized singular linear quadratic control theory. In this approach, only the signal error is penalized in the controller performance index and naturally leads to the feedback/feedforward control structure. The stability and performance characteristics of the proposed algorithm are analyzed both analytically and via selected simulations. It is shown that the algorithm performs acceptably in situations where many current algorithms are known to fail. An instability mechanism for indirect adaptive schemes is identified and analyzed. As a result, an approach is suggested that could lead to improved robustness of this algorithm without impacting the performance of the system.