Generalized Z Trajectory and Synthesis of Time-Optimal Control Systems with Nonlinear Restoring Force

概要

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In this paper, the maximum principle is applied to a time-optimal control problem of control systems with nonlinear restoring force.In order to find the initial values of an adjoint system relating to the control system, L.W. Neustadt's method concerning linear control systems is extended to this class of nonlinear control systems.A generalized Z trajectory, which has the same physical meaning as a Z trajectory in Neustadt's method has, is defined, and two noteworthy pronerties of the generalized Z trajectory are clarified from the analysis of the behavior of the trajectory in the state plane. By using the properties, it is proved that the initial values of the adjoint system can be calculated by an iterative procedure using the generalized Z trajectory.For illustrating the method proposed here, a control system with particular nonlinear restoring force is considered in the main part of this paper. The application of the similar method to other control systems with general nonlinear restoring force are also discussed.
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