The suboptimal control of nonlinear systems using liapunov‐like functions

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Abstract
A technique which calculates approximate solutions to optimal control problems is developed in this work. The technique, which uses an empirically found weighted quadratic Liapunov function to transform the original n‐dimensional optimization problem into a scalar optimization problem, is applied to a number of optimal control problems typical of those encountered in chemical engineering practice. The problems considered include both linear and nonlinear, lumped and distributed systems with minimum time, and quadratic and final value type performance indices. The solutions of these control problems show that the Liapunov‐like suboptimal method, in general, requires less computer time and storage than that required by iterative and noniterative optimal methods currently used to solve optimal control problems. The reduction in computer storage and time enables the Liapunov‐like technique to handle large dimensional control problems with relatively little effort.