Nonlinear and adaptive control of time varying and multivariable systems: New designs and applications

In this dissertation, we introduce several novel nonlinear and adaptive control schemes for certain classes of time varying and multivariable plants as well as presenting a case study on adaptive control of practical time varying and multivariable systems.; We first design a control scheme for linear time varying (LTV) systems with known parameters. In our design, we employ a new parametrization and filter structure that takes into account the plant parameter variations. The control scheme guarantees exponential convergence of the tracking error to zero if the plant parameters are exactly known. This control scheme is modified and supplemented with an update law to be applicable to LTV plants with unknown parameters. In the adaptive control design, the notion of structured parameter variations is used in order to include possible a priori information about the plant parameter variations. With this formulation, only the unstructured plant parameters are estimated and are required to be slowly time varying. We derive performance bounds which can be used to select certain design parameters for performance improvement. We later modify our adaptive design in order to make it applicable to LTV systems with modeling errors.; Next, we design and analyze a switching control scheme for a general multivariable system to overcome some of the traditional parameterization issues. The scheme guarantees stability and convergence of the output to a residual set by output-feedback if the plant parameters are known and by state-feedback if the plant parameters are unknown. The size of the residual set depends on some of the design parameters and can be made arbitrarily small. The proposed scheme has the potential to be extended for output-feedback control of multivariable plants with unknown parameters.; Finally, we present a case study on real time adaptive semiconductor process control. In the case study, single-input single-output and multivariable model based adaptive controllers for the electron cyclotron resonance (ECR) CF4/O2 plasma etching of plasma enhanced chemical vapor deposited (PECVD) silicon nitride thin films are designed and tested in simulation studies and in the laboratory on the actual etching chamber.