The Synthesis of the Proportional-Differential Regulators for the Systems with Fixed Ends of Trajectories Under Two-Sided Constraints on Control Values

The problem of optimal control for time‐varying linear systems with fixed ends of the trajectories is considered. A correspondent quadratic functional depends on the control, the state of the object and on its derivative. A constructive method of synthesis of the proportional‐differential type regulators is proposed based on the feedback principle taking into account the bilateral constraints on control values. The problem is solved with using of a special type Lagrange multipliers.