Rejection of bounded exogenous disturbances by the method of invariant ellipsoids

Rejection of the bounded exogenous disturbances was first studied by the l1-optimization theory. A new approach to this problem was proposed in the present paper on the basis of the method of invariant ellipsoids where the technique of linear matrix inequalities was the main tool. Consideration was given to the continuous and discrete variants of the problem. Control of the “double pendulum” was studied by way of example.

[1]  B.T. Polyak,et al.  Rejection of Bounded Disturbances via Invariant Ellipsoids Technique , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  S. Gusev,et al.  Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay , 2006 .

[3]  M. Dahleh,et al.  Does star norm capture l/sub 1/ norm? , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[4]  M. Sznaier,et al.  Persistent disturbance rejection via static-state feedback , 1995, IEEE Trans. Autom. Control..

[5]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[6]  D. Bertsekas,et al.  On the minimax reachability of target sets and target tubes , 1971 .

[7]  Boris T. Polyak,et al.  On Convergence of External Ellipsoidal Approximations of the Reachability Domains of Discrete Dynamic Linear Systems , 2004 .

[8]  Boris T. Polyak,et al.  Hard Problems in Linear Control Theory: Possible Approaches to Solution , 2005 .

[9]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[10]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[11]  Boris Polyak.  Convexity of Quadratic Transformations and Its Use in Control and Optimization , 1998 .

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[13]  Munther A. Dahleh,et al.  Minimization of the worst case peak-to-peak gain via dynamic programming: state feedback case , 2000, IEEE Trans. Autom. Control..

[14]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

[15]  D. Bertsekas,et al.  Recursive state estimation for a set-membership description of uncertainty , 1971 .

[16]  K. Poolla,et al.  A linear matrix inequality approach to peak‐to‐peak gain minimization , 1996 .

[17]  F. Schweppe,et al.  Control of linear dynamic systems with set constrained disturbances , 1971 .

[18]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .