A Computationally Fast Iterative Dynamic Programming Method for Optimal Control of Loosely Coupled Dynamical Systems with Different Time Scales

摘要

Iterative dynamic programming is a powerful method that is often used to solve finite-dimensional nonlinear constrained global optimal control problems. However, multidimensional problems are often computationally complex, and in some cases an infeasible result is generated despite the existence of a feasible solution. A new iterative multi-pass method is presented that reduces the execution time of multi-dimensional, loosely-coupled, dynamic programming problems, where some state variables exhibit dynamic behavior with time scales significantly smaller than the others. One potential application is the optimal control of a hybrid electrical vehicle, where the computational burden can be reduced by a factor on the order of 100 - 10000. Furthermore, new regularization terms are introduced that typically improve the likelihood of generating a feasible optimal trajectory. Though the regularization terms may generate suboptimal solutions in the interim, with successive iterations the generated solution typically asymptotically approaches the true optimal solution. Note: Full source code is freely available online with an implementation of the solver, some usage examples, and the test cases used to generate the results shown in this paper.