A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs. (27th July 2017) - Garcia Tirado, Jose Fernando
Summary: This paper addresses the problem of estimating the state for a class of uncertain discrete‐time linear systems with constraints by using an optimization‐based approach. The proposed scheme uses the moving horizon estimation philosophy together with the game theoretical approach to the H ∞ filtering to obtain a robust filter with constraint handling. The used approach is constructive since the proposed moving horizon estimator (MHE) results from an approximation of a type of full information estimator for uncertain discrete‐time linear systems, named in short H ∞ ‐MHE and H ∞ –full information estimator, respectively. Sufficient conditions for the stability of the H ∞ ‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the H ∞ ‐MHE needs the solution of a complex minimax optimization problem at each sampling time, we propose an approximation to relax the optimization problem and hence to obtain a feasible numerical solution of the proposed filter. Simulation results show the effectiveness of the robust filter proposed.