Robust control synthesis for uncertain linear systems with structured unknown inputs


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Résumé / Abstract
A new optimal filtering formula is derived for stochastic linear systems with structured unknown inputs. The main idea consists in finding a robust sub-system of unknown inputs in which the dynamical and output noises are uncorrelated. Thereby the problem is reduced as the sub-state estimation of an unknown inputs-free reduced system, which can be easily dealt with following the well-known Kalman filter theory [12], [22]. After a change of basis we can then rebuild the state of the original system. A straightforward algorithm is developed, and the necessary and sufficient conditions for the convergence and stability of filter are established. The method developed is applied to the lateral control of the vehicle system that is unstable, non linear and has noisy sensors. An integral action is added on the lateral displacement in order to ensure zero steady state error against constant perturbation (road curvature). Thus a state estimation feedback controller is synthesised on the augmented plant using multi-objective linear matrix inequalities (LMI) based method [8], [9], [26].

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