An Adaptive Cross Approximation-based Method for Robust Nonlinear Feedback Control Problems

In this paper, an adaptive cross approximation-based method is proposed for nonlinear robust control problems. Firstly, taking advantage of the underlying relationship between robustness property and nonlinear optimality, the robust control problem for the original system is transformed into an infinite-horizon optimal control problem for the nominal system. Secondly, to realize online implementation, an adaptive cross approximation-based method is proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation for the infinite-horizon optimal control problem. The proposed adaptive cross approximation-based method can reconstruct the value function tensor by only solving the optimal control problems on a small subset of the grids. Simulation results show that the proposed method can achieve a speed of about 200 Hz for the four-dimensional nonlinear robust control problem.

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