Nonlinear impulsive optimal control synthesis with optimal impulse timing: A pseudo-spectral approach

Following the philosophy of pseudo-spectral approach, a nonlinear variable-time impulsive optimal control system design approach is presented in this paper for a class of problem with hard terminal constraint. In this approach the impulse application time instants are also take as 'decision variables' and are fixed through an optimization process in addition to the magnitudes of control at those instants. This gives additional freedom for optimization and hence leads to better performance than the fixed timing approach. Three benchmark problems which include a scalar linear problem, the Van-der Pol's oscillator problem and an inverted pendulum problem are solved to demonstrate the effectiveness of the new technique. The proposed approach is also computationally efficient owing to the usage of the pseudo-spectral philosophy.