Robust control of linear systems with bounded state dependent additive disturbances

This paper examines attractiveness and minimality of invariant sets for linear systems subject to additive disturbances bounded in a state-dependent set. Existence of a minimal attractor is proved under the assumption that the state-dependent set, to which the disturbance is confined, is upper-semi-continuous. In many practical applications, the disturbance may be an output of a dynamic process. The results for systems subject to general state dependent disturbances are applied to this case to prove existence of a minimal robust invariant attractor (MRIA). The MRIA set can be employed for the design of an MPC strategy to achieve the robust stability. Moreover, in case constraint sets are polytopes, a computational method is provided to approximate the MRIA.

[1]  Zvi Artstein,et al.  Feedback and invariance under uncertainty via set-iterates , 2008, Autom..

[2]  Mirko Fiacchini,et al.  Invariant Approximations of the Maximal Invariant Set or "Encircling the Square" , 2008 .

[3]  Sasa V. Rakovic,et al.  Minkowski algebra and Banach Contraction Principle in set invariance for linear discrete time systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[4]  E. Gilbert,et al.  Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints , 1987 .

[5]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[6]  Ilya V. Kolmanovsky,et al.  Robust control of ship fin stabilizers subject to disturbances and constraints , 2009, 2009 American Control Conference.

[7]  Graham C. Goodwin,et al.  Constrained predictive control of ship fin stabilizers to prevent dynamic stall , 2008 .

[8]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[9]  Reza Ghaemi,et al.  Robust Model Based Control of Constrained Systems. , 2010 .

[10]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[11]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[12]  Ilya Kolmanovsky,et al.  Toward less conservative designs of multimode controllers for systems with state and control constraints , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[13]  Luigi Chisci,et al.  Systems with persistent disturbances: predictive control with restricted constraints , 2001, Autom..

[14]  Ilya Kolmanovsky,et al.  Fast reference governors for systems with state and control constraints and disturbance inputs , 1999 .

[15]  T. Alamo,et al.  Stability analysis of systems with bounded additive uncertainties based on invariant sets: Stability and feasibility of MPC , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[16]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[17]  A. C. Thompson,et al.  Theory of correspondences : including applications to mathematical economics , 1984 .

[18]  E. Mosca,et al.  Nonlinear control of constrained linear systems via predictive reference management , 1997, IEEE Trans. Autom. Control..