Probabilistic Robust Control

A novel approach based on probability and randomization recently emerged to synergize with the standard deterministic methods for robust control. This philosophy and body of techniques, known under the generic name of "probabilistic robust control," is here introduced and reviewed in a tutorial perspective, with focus on design techniques based on the interaction of uncertainty randomization and convex optimization.

[1]  Giuseppe Carlo Calafiore,et al.  Randomized algorithms for probabilistic robustness with real and complex structured uncertainty , 2000, IEEE Trans. Autom. Control..

[2]  András Prékopa,et al.  ON PROBABILISTIC CONSTRAINED PROGRAMMING , 2015 .

[3]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[4]  G. Calafiore,et al.  On Distributionally Robust Chance-Constrained Linear Programs , 2006 .

[5]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[6]  Peter Kall,et al.  Stochastic Programming , 1995 .

[7]  Tamer Basar,et al.  Randomized algorithms for synthesis of switching rules for multimodal systems , 2005, IEEE Transactions on Automatic Control.

[8]  Yurii Nesterov,et al.  Complexity estimates of some cutting plane methods based on the analytic barrier , 1995, Math. Program..

[9]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[10]  Giuseppe Carlo Calafiore.  Cutting plane methods for probabilistically-robust feasibility problems , 2006 .

[11]  Tansu Alpcan,et al.  Randomized algorithms for stability and robustness analysis of high-speed communication networks , 2005, IEEE Transactions on Neural Networks.

[12]  B. Ross Barmish,et al.  The uniform distribution: A rigorous justification for its use in robustness analysis , 1996, Math. Control. Signals Syst..

[13]  Roberto Tempo,et al.  Probabilistic design of LPV control systems , 2003, Autom..

[14]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[15]  Jean-Philippe Vial,et al.  Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method , 2002, Optim. Methods Softw..

[16]  Giuseppe Carlo Calafiore,et al.  Radial and Uniform Distributions in Vector and Matrix Spaces for Probabilistic Robustness , 1999 .

[17]  F. Dabbene,et al.  An Iterative Localization Method for Probabilistic Feasibility of Uncertain LMIs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[18]  Robert F. Stengel,et al.  Some Effects of Parameter Variations on the Lateral-Directional Stability of Aircraft , 1980 .

[19]  Yasumasa Fujisaki,et al.  Guaranteed cost regulator design: A probabilistic solution and a randomized algorithm , 2007, Autom..

[20]  Fabrizio Dabbene,et al.  Control design with hard/soft performance specifications: a Q-parameter randomization approach , 2004 .

[21]  Pramod P. Khargonekar,et al.  Randomized algorithms for robust control analysis and synthesis have polynomial complexity , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[22]  Giuseppe Carlo Calafiore,et al.  A probabilistic framework for problems with real structured uncertainty in systems and control , 2002, Autom..

[23]  Giuseppe Carlo Calafiore,et al.  Distributionally Robust Chance-Constrained Linear Programs with Applications , 2006 .

[24]  Yasuaki Oishi,et al.  Polynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities , 2007, Autom..

[25]  Dmitry Panchenko,et al.  Improved sample complexity estimates for statistical learning control of uncertain systems , 2000, IEEE Trans. Autom. Control..

[26]  Andreas Griewank,et al.  On constrained optimization by adjoint based quasi-Newton methods , 2002, Optim. Methods Softw..

[27]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[28]  John E. Mitchell,et al.  Polynomial Interior Point Cutting Plane Methods , 2003, Optim. Methods Softw..

[29]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

[30]  Giuseppe Carlo Calafiore,et al.  Stochastic algorithms for exact and approximate feasibility of robust LMIs , 2001, IEEE Trans. Autom. Control..

[31]  Vincent D. Blondel,et al.  Probabilistic solutions to some NP-hard matrix problems , 2001, Autom..

[32]  Michel Verhaegen,et al.  An ellipsoid algorithm for probabilistic robust controller design , 2003, Syst. Control. Lett..

[33]  Pravin M. Vaidya,et al.  A cutting plane algorithm for convex programming that uses analytic centers , 1995, Math. Program..

[34]  R. Stengel.  Stochastic Optimal Control: Theory and Application , 1986 .

[35]  Thomas D. Sandry,et al.  Probabilistic and Randomized Methods for Design Under Uncertainty , 2007, Technometrics.

[36]  Daniel Liberzon,et al.  Common Lyapunov functions and gradient algorithms , 2004, IEEE Transactions on Automatic Control.

[37]  R. Tempo,et al.  Probabilistic robustness analysis: explicit bounds for the minimum number of samples , 1997 .

[38]  Giuseppe Carlo Calafiore,et al.  Sampled Convex Programs and Probabilistically Robust Design , 2006 .

[39]  A. Nemirovski.  On tractable approximations of randomly perturbed convex constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[40]  L. Lorefice,et al.  Robust and Randomized Control Design of Mini-UAVs: The MH1000 Platform , 2007, 2007 American Control Conference.

[41]  M. Sznaier,et al.  An algorithm for sampling subsets of H/sub /spl infin// with applications to risk-adjusted performance analysis and model (in)validation , 2005, IEEE Transactions on Automatic Control.

[42]  A. Nemirovski,et al.  Scenario Approximations of Chance Constraints , 2006 .

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

[44]  Mathukumalli Vidyasagar,et al.  Statistical learning theory and randomized algorithms for control , 1998 .

[45]  R. Tempo,et al.  Probabilistic robust design of LPV control systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[46]  Roberto Tempo,et al.  Probabilistic robust design with linear quadratic regulators , 2001, Syst. Control. Lett..

[47]  Pierre Apkarian,et al.  Parameterized LMIs in Control Theory , 2000, SIAM J. Control. Optim..

[48]  Mathukumalli Vidyasagar,et al.  Learning and Generalization: With Applications to Neural Networks , 2002 .

[49]  Robert F. Stengel,et al.  Probabilistic Control of Nonlinear Uncertain Systems , 2006 .

[50]  Olivier Péton.  The homogeneous analytic center cutting plane method , 2002 .

[51]  Minyue Fu,et al.  Worst-case properties of the uniform distribution and randomized algorithms for robustness analysis , 1998, Math. Control. Signals Syst..

[52]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[53]  Mathukumalli Vidyasagar,et al.  Randomized algorithms for robust controller synthesis using statistical learning theory , 2001, Autom..