NONUNIFORM GRIDS FOR REDUCED BASIS DESIGN OF LOW ORDER FEEDBACK CONTROLLERS FOR NONLINEAR CONTINUOUS SYSTEMS

In this paper, we discuss the use of nonuniform grids in reduced basis design for developing low order nonlinear feedback controllers for hybrid distributed parameter systems. The reduced basis approach was presented in an earlier paper by Burns and King; therein, all approximations were based upon uniform grids. In this paper, we explore the effect on control design of using nonuniform grids in the fundamental step of approximating the functional controller gains. We illustrate the process using a weakly nonlinear distributed parameter system.

An existence theorem for an optimal control problem in banach spaces

In this paper we prove the existence of an optimal admissible state-control pair for a nonlinear distributed parameter system, with control constraints of feedback type and with an integral cost criterion. An example is also worked in detail.