Minimum-time control for an inverted pendulum under force constraints

In order to numerically solve the minimum-time control problem of a linear system, the system is usually discretized with a fixed sampling period. Then the minimum count of control steps is searched to meet the constraints of the final state and the input variables. Since the count is a variable, there is no direct way for handling such problems except by exhaustive iteration. In contrast to the traditional methods, a new numerical technique was developed recently to avoid the exhaustive iteration. In this method, the control step is fixed and the sampling period is treated as a variable. Since this method requires only two iterations, it will reduce the computation time significantly. This paper applies this new numerical technique to generate the minimum-time trajectory between two end-points for an inverted pendulum under force constraints. Two main issues are addressed. The first one is the problem formulation in discrete-time domain and the second one is the generation of feasible solutions for the global search. Simulation examples are included for illustration.