The extended Luenberger observer for nonlinear systems
Systems & Control Letters
Observability and Observers for Nonlinear Systems
SIAM Journal on Control and Optimization
On uniform observation of nonuniformly observable systems
Systems & Control Letters
Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation
Automatica (Journal of IFAC)
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Modern Control System Theory
Nonlinear H2/H-Infinity Constrained Feedback Control: A Practical Design Approach Using Neural Networks (Advances in Industrial Control)
Observer-based adaptive control of robot manipulators: Fuzzy systems approach
Applied Soft Computing
Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators
Automatica (Journal of IFAC)
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In this paper, an observer design is proposed for nonlinear systems. The Hamilton-Jacobi-Bellman (HJB) equation based formulation has been developed. The HJB equation is formulated using a suitable non-quadratic term in the performance functional to tackle magnitude constraints on the observer gain. Utilizing Lyapunov's direct method, observer is proved to be optimal with respect to meaningful cost. In the present algorithm, neural network (NN) is used to approximate value function to find approximate solution of HJB equation using least squares method. With time-varying HJB solution, we proposed a dynamic optimal observer for the nonlinear system. Proposed algorithm has been applied on nonlinear systems with finite-time-horizon and infinite-time-horizon. Necessary theoretical and simulation results are presented to validate proposed algorithm.