Practical Optimal Control of Infinite Interval Systems

Abstract

Pontryagin's Maximum Principle was investigated for the finite and infinite time interval cases to assess its usefulness in practical applications. Attention was focused on the analogue control of a second order position control system. The findings demonstrated that the principle was a useful mathematical tool but not satisfactory for direct application for the finite time interval and virtually impossible for the infinite time interval. To produce a method of optimisation for the infinite time interval compatible with that of Dynamic Programming, and yet, preserving the formulated advantages of Pontryagin's Maximum Principle, equations were evolved to replace the characteristic two point boundary value problem. A practical controller was then evolved which would enable optimal control to be obtained without the need for resort to a computer. Optimal control of an actual second order position control system was effected and the results compared with those generally obtained from the application of Dynamic Programming. They were observed to be better. :The evolved method of optimisation was further extended to encompass second and third order systems possessing two time constants, optimal control of an actual third order plant being effected.