Abstract
Algebraic polynomials are used to approximate the constrained optimal cyclic control problem for a system described by differential equations. Optimal control is assumed to be a smooth function within a single cycle, i.e. it is continuously differentiable at least once within this cycle. The set of feasible approximate solutions is made to conform to the smoothness of the basic problem optimal solution. The sufficient conditions are given for the convergence of the approximate solution and the approximation convergence rate is shown to be better than that for non-smooth problems. The usefulness of this approach for non-linear industrial control problems is indicated.
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