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Error bounds in nonlinear control design via approximate policy iteration

We consider the optimal nonlinear control problem and evaluate a computational design procedure which produces suboptimal controllers (policies), an approximate policy iteration. The method uses an approximation of the cost (cost-to-go) function of a given closed loop system in order to produce an updated controller of (hopefully) improved performance. We develop bounds on the approximation error such that the resulting controllers are stabilizing and bounds on the approximation error such that the resulting controllers are of improved performance.