MINIMUM-TIME CONTROL FOR AN INVERTED PENDULUM UNDER FORCE CONSTRAINTS

In order to numerically solve the minimum-time control problem of a li near system, the system is usually discretized with a fixed sampling p eriod. Then the minimum count of control steps is searched to meet the constraints of the final state and the input variables. Since the cou nt is a variable, there is no direct way for handling such problems ex cept by exhaustive iteration. In contrast to the traditional methods, a new numerical technique was developed recently to avoid the exhausti ve iteration. In this method, the control step is fixed and the sampli ng period is treated as a variable. Since this method requires only tw o iterations, it will reduce the computation time significantly. This paper applies this new numerical technique to generate the minimum-tim e trajectory between two end-points for an inverted pendulum under for ce constraints. Two main issues are addressed. The first one is the pr oblem formulation in discrete-time domain and the second one is the ge neration of feasible solutions for the global search. Simulation examp les are included for illustration.