Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
Automatica (Journal of IFAC)
Linear Quadratic Control: An Introduction
Linear Quadratic Control: An Introduction
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Brief Paper: An EKF-Based Nonlinear Observer with a Prescribed Degree of Stability
Automatica (Journal of IFAC)
Statistical optimal control using neural networks
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part II
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This paper presents a nonlinear optimal control technique based on approximating the solution to the Hamilton-Jacobi-Bellman (HJB) equation. The HJB solution (value function) is approximated as the output of a radial basis function neural network (RBFNN) with unknown parameters (weights, centers, and widths) whose inputs are the system's states. The problem of solving the HJB equation is therefore converted to estimating the parameters of the RBFNN. The RBFNN's parameters estimation is then recognized as an associated state estimation problem. An adaptive extended Kalman filter (AEKF) algorithm is developed for estimating the associated states (parameters) of the RBFNN. Numerical examples illustrate the merits of the proposed approach.