Output feedback and adaptive control of uncertain MIMO nonlinear systems with non-symmetric input gain matrix

This Ph.D. dissertation investigates multi-input and multi-output (MIMO) non-linear control systems with structural uncertainty. Specifically, it relaxes the predominant symmetric input gain matrix assumption for MIMO systems from current automatic control literature to cover a non-symmetric scenario. Several control techniques including adaptive control, output feedback control, and modular control are deployed to tackle the nonlinear MIMO systems with structural uncertainty. This dissertation also presents several other control strategies, namely the extremum-seeking control, passive control, and navigation control in human exercise machine and rehabilitation robot applications. A detailed introduction to each of these topics is given in Chapter 1.; Chapter 2 considers a general class of multi-input multi-output nonlinear systems with parametric uncertainty where the matrix pre-multiplying the control input is positive definite but non-symmetric. A new adaptive control law is proposed, exploiting a decomposition of the aforementioned matrix into a symmetric positive definite matrix and a unity upper triangular matrix.; Chapter 3 considers MIMO nonlinear systems with unstructured uncertainty in both the drift vector and the input matrix. With a positive definite restriction on the input matrix that is required for controllability, we are able to construct a continuous state feedback control mechanism that achieves semi-global ultimate bounded tracking.; Continuing the MIMO investigation, Chapter 4 applies a new continuous output feedback control mechanism developed for output tracking for a class of high-order multi-input nonlinear systems with an input gain matrix that is positive definite but non-symmetric. The controller yields nearly semiglobal uniformly ultimately bounded (SGUUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix.; In Chapter 5, a next generation exercise machine controller is developed for a single degree of freedom system to maximize the user's power output and ensure passivity with the user. In an effort to optimize the user's power expenditure, a desired velocity trajectory is developed that seeks the unknown user-dependent optimal velocity setpoint.; Chapter 6 presents a trajectory generation and control strategy for a robotic manipulator to mimic the dynamics of a continuously reconfigurable anisotropic impedance. (Abstract shortened by UMI.)...