Worst-case control of nonlinear systems by minimax programming

Analysis and synthesis of control systems in the presence of model uncertainties have received significant attention in control research over the past few years. Much of the attention has been limited to the robust control of linear uncertain systems. The present work is thus motivated by the issues raised in process control--strong nonlinearities of chemical processes and process model uncertainties. Our approach to robust nonlinear control design is also justified by the increasing power and decreasing cost of computers and the increasing sophistication of nonlinear programming algorithms for solving formidable optimization problems. The proposed robust controller design methodology is based on the worst-case playing strategy of game theory. By taking the worst-case design approach, the controller design problem is formulated as an optimization problem of the minimax structure. The solution of the minimaximization problem produces the desired robust nonlinear controller. While conceptually easy to formulate and understand, minimax problems are difficult to solve and are computationally very intensive. After exploring a variety of optimization methods, it has been concluded that nonsmooth optimization methods are the most efficient for solving practical size worst-case design problems. A special version of a nonsmooth algorithm is implemented in this work. With the problem formulation and method of optimization complete, this work then examines the success of the proposed methodology in several different nonlinear process control problems. The algorithms of our work successfully design robust nonlinear controllers of different structures and varying complexity. The success of the proposed approach and the numerical optimization methods in solving practical nonlinear robust control problems is thus established.