Synthesizing suboptimal controls in non-linear dynamical systems

Abstract

A non-linear dynamical system whose motion is described by second-order Lagrangian equations is considered. The following problem is investigated. It is required to construct a control in the form of a synthesis, i.e. in the form of a function of the current values of the phase coordinates and time, that takes the system in a given time from an arbitrary initial phase state to a given final phase state. A method for solving this problem is presented based on the use of first integrals of the equations of free motion of the system and local connection of the values of the required control forces in a small neighbourhood of the final moment of the control process. Here the control processes are synthesized analytically and are optimal in the sense of minimizing a functional of mixed type [1]over almost the entire time interval of the control process. The efficiency of the proposed method of control synthesis is illustrated by examples.