Feature Learning for Optimal Control with B-spline Representations

The paper develops a feature learning-based method to solve optimal control problems using B-splines to approximate the optimal solutions. The feature learning-based optimal control method can quickly generate near-optimal trajectories for general optimal control problems subject to system dynamics and constraints. The steps in the proposed method are as follows: Firstly, by representing the state and control variables with B-spline functions, the optimal control problem is converted into an approximate nonlinear programming (NLP) problem, where parameters of the B-splines are identified as features of the optimal solution. Secondly, for a specific problem with designated inputs, a dataset of the optimal trajectories under varying inputs is generated by solving the corresponding NLP problem offline. Finally, the neural network is applied to map the relationship between the designated inputs and identified features, represented by the parameters of B-splines and time variables. To show the effectiveness and efficiency of the proposed method for solving the optimal control problems, extensive simulation cases are presented and analyzed.