Robust observer-based controller design for state constrained uncertain systems: attractive ellipsoid method. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Mera, Manuel; Salgado, Ivan; Chairez, Isaac
• Is Part Of: International journal of control. Volume 93:Issue 6(2020)
• Page Start: 1397
• Page End: 1407
• Publication Date: 2020-06-02
• Subjects: Constrained linear systems -- Barrier Lyapunov functions -- attractive ellipsoid method; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2018.1508853
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.