Numerical Method for Solving a Nonlinear Time-Optimal Control Problem

G.V. Shevchenko (Russia)


Optimal control, attainability domain, conjugate system, simplex, adjacent simplex, covering


Nonlinear systems of ordinary autonomous differential equations are considered. An iterative method is pro posed for solving time-optimal control problems for such systems. This method is efficient and has a global convergence under an enough common conditions of controllability. The method is based on constructing finite sequences of adjacent simplexes with their vertices lying on the boundaries of attainability domains. For a controllable system, it is proved that the minimizing sequence converges to an ε-optimal solution in a finite number of iterations. A pair {T, u(·)} is called an ε-optimal solution if |TTopt| ≤ ε, Topt is a minimum time of moving the system from the initial state to the origin, u is an admissible control under which the system moves from the initial state to an ε-neighbourhood of the origin.

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