Approximate solution of feedback optimal control problems for distributed parameter systems

Suboptimal approximate feedback solutions to optimal control problems of systems described by partial differential equations are investigated. The approximation consists in constraining the control functions to take on a fixed structure, where a finite number of free parameters is inserted. The original functional optimization problem is then reduced to a mathematical programming problem, in which the values of the parameters have to be optimized. More specifically, linear combinations of fixed and parameterized basis functions are used as fixed structure for the control functions, thus giving rise to two different approximation schemes. The proposed approach is quite general since it can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations. Moreover, it provides a constructive way of finding approximate solutions with a moderate computational burden. Simulation results are presented to show the potentials of the proposed approach in comparison with dynamic programming.