Application of numerical hill‐climbing in control of systems via Liapunov's direct method

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Abstract
The procedure of determining the control effort which minimizes the forward difference of the quadratic function x(k)TQx(k) combined with improving Q by numerical hill‐climbing is investigated to determine the feasibility of establishing time sub‐optimal control policies for both linear and nonlinear systems.For linear systems, Rosenbrock's hill‐climbing procedure is more efficient for improving Q than the method of Hooke and Jeeves; moreover it yields policies closer to the optimum when the number of state variables exceeds six. The “best” value of Q obtained by hill‐climbing depends on the initial choice of Q and the initial state of the system x(0).The evaluation, carried out with a linear gas absorber and a nonlinear continuous stirred tank reactor, shows that the combined sub‐optimal procedure yields results close to time‐optimal control with little computational effort.