The problem of optimal control synthesis is formulated and the matrix and vector components in the Riccati system are taken into account. Bellman's dynamic programming method was used to determine the patterns. A specific mathematical model of the oscillatory process is considered and its properties are numerically investigated. Examples of linear and quasi-linear problems are given and the minimum possible value of the quality criterion is determined. The corresponding graphical dependencies are constructed and with the help of optimal control tools, the state of the object is transferred from one point to another. Based on the use of the Zubov power series method, optimal control is revealed. Numerical calculations are carried out and Riccati functions are obtained in a nonlinear system with concentrated parameters.

Keywords: synthesis tasks, optimal control, matrix and vector components, Ricatti system, oscillatory process, quality criteria