Dynamic Programming Approach to Solving Continuous-Time Linear Quadratic Regulator Problems

Abstract

This paper investigates and discusses the dynamic programming method as a technic that brakes a complex problem into smaller and sizeable form adopted in solving Bolza’s cost form of Linear Quadratic Regulator Problems (LQRP). The authors of this paper desire to experiment numerically with the solution of this class of problem using dynamic programming to solve for the continuous time linear regulator optimal controls and the trajectories compared with other numerical methods to further improve the results. The method uses the principle of optimality to reduce mathematically the number of calculations required to determine the optimal control law as well as the corresponding optimal cost function.