Time-optimal control: A continuation approach
Description
This dissertation is concerned primarily with the introduction of the continuation method as a new, uncomplicated, yet efficient process to solve the time-optimal control problem for some classes of systems. A general process for solving the time-optimal control problem of a class of n$\rm\sp{th}$ order linear systems with only denominator dynamics has been developed. All the possible second order cases in this class have been derived. Moreover, the process to preserve the integrity and consistency of the control polarity for higher order systems is explained. The results can be extended to a class of second order nonlinear systems with the time-optimal control law switching at most once from any initial state to the origin. This development provides a new platform for further theoretical research on the closed-loop time-optimal controller as well as developing modified versions of the time-optimal controller for industrial applications Another achievement of this research is that the number of equations describing the switching hypersurface for an undamped flexible structure with a rigid mode and one flexible mode has been reduced from five to three. The switching hypersurface has been graphically derived and has been simulated by a polynomial function. These results have significant value for on-line implementation of the closed-loop, time-optimal controller