ALGORITHMS FOR MINIMIZING THE BOUNDARY VALUES OF THE QUADRATIC QUALITY CRITERION BASED ON APPROXIMATION METHODS

This paper considers approximation methods for solving optimization problems while discussing the possibility to reduce the large amount of calculations. Hence, the approximation range is selected in accordance with the optimal value of the quality indicator. To do this, the upper and lower boundaries are being calculated followed by generating the control sequences that minimize the specified boundaries. The next step is to find an approximate solution. An approximate solution to the dual control problem comes from the problem of optimal control of a linear Gaussian system with a quadratic quality criterion and unknown parameters. For the dual control problem, according to the minimization procedure using the dynamic programming method, an optimal loss function VN-k (x(k)/Zk) is determined for a (N-k) -step process with an initial state. The optimal loss function must satisfy the Bellman equation. By solving the equation, it is possible to obtain a quadratic form that does not have the property of reproducibility. To calculate the matrices U or T of quadratic form, the method for obtaining recurrent expressions is unknown. To take into account the required active control, U or T must be calculated at the rate of the real process.