Analytical synthesis of time-optimal control in a third-order system

A time-optimal control that steers the phase point for a third-order linear system to the origin is constructed in an explicit analytical form. It is assumed that the characteristic exponents are zero, and the constraints on the control function are non-symmetric. The system simulates the dynamics of a point mass driven by a force whose rate of change can be regulated. An optimal control is constructed both in the feedback and open-loop forms. In the latter case, the optimal control is a function of time. Relations are derived for the switching curve and surface and for the time intervals of the motion; optimal phase trajectories are constructed; the feedback control portrait is investigated. The influence of a parameter characterizing the degree of asymmetry of the constraints is studied. "Near-optimal" control modes, which are much simpler to implement, are constructed. (C) 2000 Elsevier Science Ltd. All rights reserved.