Two Topics in Nonlinear Control: Real-Time Optimization and General System Structure

Toshiyuki Ohtsuka, University of Tsukuba, Tsukuba, Japan

The talk will present recent results on two different problems: how to realize real-time nonlinear optimal feedback control and how to express the input-output relation of nonlinear systems using state equations of a fixed structure. Those problems are essential to establish a general framework of feedback control design. For the first problem, a real-time algorithm is derived without any approximations for a class of nonlinear optimal state feedback control problems. The same technique is also applicable to a class of nonlinear optimal state estimation problems. For the second problem, a constructive proof of a necessary and sufficient condition is shown for existence of a quadratic-in-the-state representation for a given nonlinear system. Most practical nonlinear systems satisfy the condition and, consequently, can be expressed by a state equation that is at most quadratic with respect to state variables.