A new approach to constrained state estimation for discrete‐time linear systems with unknown inputs |
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| Authors: | Jose Fernando Garcia Tirado Alejandro Marquez‐Ruiz Hector Botero Castro Fabiola Angulo |
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| Affiliation: | 1. Instituto Tecnológico Metropolitano, Facultad de Ciencias Económicas y Administrativas, Grupo Calidad, Metrología y Producción, Medellín, Colombia;2. Universidad Nacional de Colombia Sede Medellín, Facultad de Minas, Departamento de Energía Eléctrica y Automática, Medellín, Colombia;3. Eindhoven University of Technology, Department of Electrical Engineering, Control Systems Group, Eindhoven, the Netherlands;4. Universidad Nacional de Colombia Sede Medellín, Facultad de Minas, Departamento de Energía Eléctrica y Automática, Grupo KALMAN, Medellín, Colombia;5. Universidad Nacional de Colombia Sede Manizales, Facultad de Ingeniería y Arquitectura, Departamento de Ingeniería Eléctrica, Electrónica y Computación, Grupo Percepción y Control Inteligente, Manizales, Colombia |
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| Abstract: | 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  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  ‐MHE and  –full information estimator, respectively. Sufficient conditions for the stability of the  ‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the  ‐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. |
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| Keywords: | constrained estimation moving horizon estimation optimization robust estimation uncertain linear systems |
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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 
‐MHE and 
–full information estimator, respectively. Sufficient conditions for the stability of the 
‐MHE are discussed for a class of uncertain discrete‐time linear systems with constraints. Finally, since the 
‐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.