Computation of optimal controls for non-linear distributed-parameter systems using multivariate spline functions†

Abstract

A computational technique is developed for the solution of optimal control problems for distributed-parameter systems. The method involves an expansion of the state variables in terms of multivariate spline basis functions. The optimal control problem is thereby reduced to a finite-dimensional constrained minimization problem that may be solved numerically using standard algorithms. Unlike in previous approaches, the system partial differential equations are satisfied exactly at every stage of the computation without, however, explicitly solving them. This feature results in both a decreased computational load and an increased solution accuracy. A numerical example is presented.

Notes

† This research was supported in part by the University Grants Committee of New Zealand.