Online Optimal Control of Affine Nonlinear Discrete-Time Systems With Unknown Internal Dynamics by Using Time-Based Policy Update


During this paper, the Hamilton–Jacobi–Bellman equation is solved forward-in-time for the optimal control of a class of general affine nonlinear discrete-time systems without using price and policy iterations. The proposed approach, known as adaptive dynamic programming, uses 2 neural networks (NNs), to unravel the infinite horizon optimal regulation management of affine nonlinear discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the price function and is known as the critic NN, while the second NN generates the management input and is called the action NN. The cost perform and policy are updated once at the sampling instant and so the proposed approach can be referred to as time-based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to indicate that all signals are uniformly ultimately bounded and that the approximated management signal approaches the optimal management input with little bounded error over time. Within the absence of disturbances, an optimal management is demonstrated. Simulation results are included to show the effectiveness of the approach. The finish result's the systematic design of an optimal controller with guaranteed convergence that is appropriate for hardware implementation.

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