Solution of Inverse Problems for Control Systems with Large Control Parameter Dimension

The a posteriori analysis of the realized motions (in other words, trajectories and controls) is an important part of the theory of optimal control and decision making. This paper is devoted to solving inverse problems of reconstruction of realized controls for control systems using known inaccurate measurements of the realized trajectories. A new method for solving inverse problems is suggested for a class of control systems with dynamics linear in controls and non-linear in state coordinates where the dimension of the control parameter is greater than or equal to the dimension of the state variable. This method relies on necessary optimality conditions in auxiliary variational problems. An illustrating example is exposed. © 2018 Russian Foundation for Basic Research, RFBR Russian Foundation for Basic Research, RFBR: 17-01-00074 Ural Branch, Russian Academy of Sciences, UB RAS: 18-1-1-10.