New Algorithms for Determining Optimal Control: A Differential Dynamic Programming Approach
Differential Dynamic Programming is a successive approximation technique, based on Dynamic Programming rather than the Calculus of Variations, for determining optimal control of non-linear systems. In each iteration, the system equations are integrated in forward time using the current nominal control, and accessory equations which yield the coefficients of a linear or quadratic expansion of the cost function in the neighbourhood of the nominal trajectory are integrated in reverse time, yielding an improved control law. This control law is applied to the system equations, producing a new, improved trajectory. By continued iteration, the procedure produces control functions which successively approximate to the optimal control function.
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