| Scope and method of study. Adaptive output feedback control of classes of nonlinear systems and related problems are investigated. The classes of systems that are studied include Lipschitz nonlinear systems, large-scale interconnected nonlinear systems with quadratically bounded interconnections, nonlinear systems containing product terms of unmeasured states and unknown parameters, and mechanical systems with unknown time-varying parameters and disturbances. Solutions and their bounds of relevant algebraic and differential matrix equations in systems and control theory are also studied. For analysis and synthesis of controllers, methods from Lyapunov theory, Algebraic Riccati Equations (AREs), Linear Matrix Inequalities (LMIs), and local polynomial approximations are extensively used.; Findings and conclusions. A stable output feedback controller can be designed for Lipschitz nonlinear systems if sufficient conditions related to distances to uncontrollability and unobservability of pairs of system matrices are satisfied. Stable linear decentralized output feedback controllers can be designed for large-scale systems if certain sufficient conditions are satisfied; these conditions can be formulated either as existence of positive definite solutions to AREs or as a feasibility problem of an LMI. By casting the dynamics of a nonlinear system, which contains products of unmeasurable states and unknown parameters, into a modified form, a stable adaptive output feedback controller can be constructed using a parameter dependent Lyapunov function; the procedure for casting the system dynamics into a modified form is constructive and is always possible. A stable adaptive controller for mechanical systems with unknown time-varying parameters and disturbances can be designed using local polynomial approximation; the time-varying parameters and disturbances are estimated by a modified least-squares algorithm using a new resetting strategy, which is a consequence of keeping the estimates continuous at the beginning of each time interval of local polynomial approximation. For all the problems that are investigated, simulation and experimental results are given to verify and validate the proposed methods. |
