The derivation of iterative convergence calculation for a nonlinear MIMO approximate dynamic programming approach

The standard approximate dynamic programming has only one action output. It’s applied to single control variable system, such as inverted pendulum. For multi-input multi-output system, approximate dynamic programming needs a complex scheme. Few papers have derived its iterative convergence calculation, or the presented algorithm lacks rigorous mathematical basis. This paper fist researches matrix analysis foundation for the derivation of multi-input multi-output approximate dynamic programming. The research finds flaws in mathematics of a typical algorithm of its derivation. Hence, we promote approximate dynamic programming to multi-input multi-output form. The detailed iterative convergence calculation of it is derived. An experiment shows its effect. This algorithm is proved to be rigorous in mathematics and not complicated. It is effective for the iterative convergence calculation of multi-input multi-output approximate dynamic programming.