Abstract
In this paper, we study a class of optimization problems,which are of certain interest for control theory. These problemsare of global constrained optimization and may be nonconvex ingeneral. A simple approach to their solution is presented. Aspecial attention is paid to the case when the objective andconstraints functions are quadratic functionals on a Hilbertspace. As an example of an application of the general approach,a methodology is presented by which an optimal controller canbe synthesized for a finite-horizon linear-quadratic controlproblem with quadratic constraints. Both inequality and equalityconstraints are considered. The objective and constraints functionalsmay be nonconvex and may contain both integral and terminal summands.It is shown that, under certain assumptions, the optimal controlexists, is unique, and has feedback structure. Furthermore, theoptimal controller can be computed by the methods of classiclinear-quadratic control theory coupled with those of finitedimensional convex programming.
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Matveev, A., Yakubovich, V. Nonconvex Problems of Global Optimization: Linear-Quadratic Control Problems with Quadratic Constraints. Dynamics and Control 7, 99–134 (1997). https://doi.org/10.1023/A:1008236815189
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DOI: https://doi.org/10.1023/A:1008236815189