Method for Searching the Gradient of the Functional by the Matrix of a Feedback Circuit on Solving the Problem of the Synthesis of the Optimal Stabilization System by Output

摘要

We consider the stationary problem of the synthesis of a stabilization system by output. On solving this problem we use optimization methods, for which realization calculation of the gradient of the functional by the matrix of a feedback circuit is necessary. Calculation of the gradient of the functional with respect to scalar variables meets certain difficulties, which are caused by the necessity of calculation of the gradient with respect to every element of the feedback matrix. By means of the Kronecker product we suggest analytical expressions for calculation of the gradient by the feedback matrix. These expressions make it possible to solve problems of the synthesis of the optimal stabilization system by output for both continuous and discrete time.