Robust adaptive control and filtering

This thesis examines the robustness properties of various adaptive systems for control, filtering, and identification. These include the uniform boundedness or mean-square boundedness of all closed-loop signals (robust boundedness, robust ultimate boundedness), the closed-loop system tracking error performance in the presence (robust performance), and absence (nominal performance) of unmodelled dynamics, disturbances, and parameter time variations.The thesis is divided into three main parts. The first part considers the robustness of continuous-time adaptive control, the second part is concerned with robust adaptive control of discrete-time plants with time-varying parameters, and the third part deals with the robustness of stochastic adaptive algorithms that include parallel model adaptation problems such as output error identification, adaptive IIR filtering, adaptive feedforward control, and adaptive noise cancelling, and ELS (Extended Least Squares)-based adaptive control.In the first part, a continuous-time direct model reference adaptive controller (MRAC) using a gradient adaptation law based on parameter projection and "extended regressor" normalization is proposed. Based on this, boundedness of all closed-loop signals is established for a continuous-time plant of arbitrary positive relative degree, in the presence of persistent bounded disturbances and small unmodelled dynamics that depend on both input and output, in possibly nonlinear or time-varying fashion. The deterioration of output tracking error performance is shown to be a continuous function of the sizes of the disturbance and unmodelled dynamics.In the second part, a discrete-time indirect adaptive pole-zero placement controller using a gradient adaptation law based on parameter projection and "extended regressor" normalization is proposed for adaptive control of a discrete-time plant with time-varying parameters. Based on this, closed-loop boundedness and performance are established in the presence of disturbances, small unmodelled dynamics, and slow-in-the-mean parameter variations.In the third part, we consider the robustness of parameter projection-based parallel adaptation (output error-based) problems such as output error identification, adaptive IIR filtering, adaptive feedforward control, and adaptive noise cancelling, to unmodelled dynamics and to violation of statistical assumptions on the noise. We analyze vanishing gain algorithms. In the case of output error identification/adaptive IIR filtering, we also consider nonvanishing gain algorithms. It is found that the commonly imposed strict positive realness (SPR) condition can be relaxed in certain cases. We also consider the robustness of ELS-based adaptive control, which is an equation error-based approach. (Abstract shortened by UMI.)U of I OnlyETDs are only available to UIUC Users without author permissio