On a Class of Variable-Structure Systems
The purpose of this paper is to investigate the optimal control of a class of discrete, time-invariant, variable-structure systems. Both deterministic and stochastic problems are considered for unbounded control and the cost functional quadratic in state. Solutions are obtained in closed-form.
In the deterministic case, it is seen that the regular path and singular paths satisfying the functional equation of dynamic programming may exist simultaneously. It is shown then that the regular path is optimal. Both additive and multiplicative plant noise are considered in the stochastic problem. It is shown that the presence of noise considerably simplifies the analysis since the cases with singularities are contained in sets of measure zero.
KeywordsOptimal Control Problem Optimal Path Measure Zero Recursive Equation Deterministic Case
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