Gradient generation for parametric control models

Abstract This paper presents a numerical method for approximating the solution of complex optimal control problems by a constrained function minimization problem in a finite dimensional space. This end is achieved by approximating only the control functions by a finite set of parameters. The computation of gradients with respect to the parameters modeling the control is explored in depth. A hybrid technique combining the rapid gradient generation capability of the method of gradients with the rapid convergence characteristics of finite-dimensional, variable-metric function minimization algorithms is presented. An algorithm for mapping the impulsive response gradient trajectory generated by the method of gradients into a gradient vector of the performance index with respect to the parameters modeling the control function is presented. The class of local parameterizations is shown to have a distinct computational advantage, from a gradient generation point of view, over the class of continuous polynomial approximations. Detailed results are presented for piecewise linear parametric control models. An algebraic transformation is presented for improving inaccurate gradients generated by a widespread computer implementation of the method of gradients.

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