Sequential Synthesis of Time-Optimal Control for Dynamic Systems

V.M. Aleksandrov (Russia)


Optimal control, dynamic system, disturbance, phase trajectory, switching time, adjoint system, duration of computation, variation, iteration.


A method of sequential synthesis of time-optimal control for a linear system with disturbances is considered. A system of linear algebraic equations is obtained which relates the increments of phase coordinates to the increments of initial conditions of a normalized adjoint system and to the increment of control completion time. Evaluations consist in solving repeatedly a system of linear algebraic equations and integrating a matrix differ ential equation on the displacement intervals of control switching times and on the displacement interval of final control time. A procedure of correcting the switching times and the completion time in moving along the phase trajectory of a controllable object is examined. Simple and constructive conditions are specified for a discontinuous mode to occur, for a representation point to move along the switching manifolds, and for the optimal control structure to transform in moving along the phase trajectory of a system. A computational algorithm is presented.

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