Constructive methods for nonlinear control of finite and infinite-dimensional systems

This dissertation develops novel constructive methods for nonlinear control of finite and infinite dimensional systems. We present four control design methods that are applicable to finite dimensional systems and one that is applicable to infinite dimensional systems.; The first method for finite dimensional systems is the nonlinear optimal control design, which uses dynamic programming and power series methods to minimize non-quadratic cost functions subject to linear dynamics. The second method, nonlinear optimal control with preview of the disturbance uses the minimum principle to minimize non-quadratic cost functions with linear dynamics, but with preview of the disturbance. The third method is the nonlinear H_∞ control design which uses game theory and power series methods to minimize the L₂ gain from the disturbance to nonlinear outputs. The fourth method can deal with hard constraints. It applies to systems in strict feedback form and uses backstepping techniques to design a controller that renders the closed loop system nonlinear in the domain where the uncontrolled system itself is linear. This allows for an increased stiffness of the closed loop system as the state approaches its hard constraint. The design methodologies are applied to an active suspension system, and it is demonstrated that each of them improves the performance of the suspension dramatically when compared to conventional designs.; The design method for infinite dimensional systems computes the distributed control that minimizes a non-quadratic cost function when the distributed dynamic system is linear. Using power series methods and tensor theory, we derive a recursive procedure to obtain the successive power series terms of the controller. The design is illustrated on the optimal nonlinear distributed temperature control of a bimorph cantilever beam.; All design algorithms except the one based on backstepping result in recursive schemes, where the linear component of the controller is computed from the solution of a Riccati equation, and where each one of the higher order nonlinear terms is obtained by solving a linear Lyapunov equation. The algorithm using backstepping techniques; however, offers a systematic tuning of the parameters in the controller.