B-Splines Based Optimal Control Solution

A fast convergent optimization algorithm is proposed in this paper to calculate sequential optimal trajectories for pursuing a moving target or under dynamically changing environments. The changing boundary conditions or perturbations in such problems require an efficient algorithm to update the optimal trajectories with appropriate time steps. Concepts of a uniform B-spline and differentially flat system are introduced to map the system equations to a lower dimensional space with least number of variables as necessary. The initial trajectory starts from quadratic uniform B-splines and then is refined by increasing the spline degree level to generate smooth trajectories with higher accuracy. Solution of all levels is transformed to a unit time interval. The whole procedure is schemed to be applicable to most of the classical Bolza problems. Finally, simulation results are compared to those solved by trapezoidal and pseudospectral discretization methods.