State observer design for nonlinear systems using neural network

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.

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. In the present algorithm, neural network (NN) is used to approximate value function to find approximate solution of HJB equation. A dynamic optimal observer for the nonlinear system is proposed. Results show application of proposed observer design for estimation of bioreactor dynamics [13].Figure optionsDownload as PowerPoint slideHighlights
► An observer design is proposed for nonlinear systems.
► The Hamilton–Jacobi–Bellman (HJB) equation is formulated using a suitable non-quadratic term in the performance functional to tackle magnitude constraints on the observer gain.
► In the present algorithm, neural network (NN) is used to approximate value function to find approximate solution of HJB equation.
► The proposed optimal observer has been validated using simulation experiment of estimation of bioreactor dynamics