GLOBAL CONTROLLABILITY AND COMPUTATION OF CONTROLS IN NONLINEAR SYSTEMS

摘要

The authors consider the problem of constructing an admissible open-loop control of bounded energy steering a nonlinear system from a given initial state to a given final state under the condition that the first-approximation system is completely controllable. The convergent iterative procedure for computing an admissible control is verified. It is shown that a nonlinear system locally controllable with respect to the first approximation becomes globally completely controllable for any boundary conditions from the stability region if the initial nonlinear system is stabilizable up to the asymptotic stability in the large and in the whole and the nonlinear terms either satisfy the global Cauchy-Lipschitz condition or are polynomials of a certain degree in state coordinates with arbitrary coefficients. The nonlinear system of algebraic equations to computation of whose solutions the problem of constructing the admissible control reduces is indicated.