Convex Relaxations With Guaranteed Convergence For Control Design Of Takagi-sugeno Fuzzy Systems [relaxações Convexas De Convergência Garantida Para O Projeto De Controladores Para Sistemas Nebulosos De Takagi-sugeno]

dc.creatorMontagner V.F.
dc.creatorOliveira R.C.L.F.
dc.creatorPeres P.L.D.
dc.date2010
dc.date2015-06-26T12:35:33Z
dc.date2015-11-26T15:25:36Z
dc.date2015-06-26T12:35:33Z
dc.date2015-11-26T15:25:36Z
dc.date.accessioned2018-03-28T22:34:22Z
dc.date.available2018-03-28T22:34:22Z
dc.identifier
dc.identifierControle Y Automacao. , v. 21, n. 1, p. 82 - 95, 2010.
dc.identifier1031759
dc.identifier
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-77949931343&partnerID=40&md5=3cef0a74e548382a6736fc34a2a56df1
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/90953
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/90953
dc.identifier2-s2.0-77949931343
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1260941
dc.descriptionThis paper provides convex conditions with certificates of convergence for the design of state feedback controllers that quadratically stabilize and also ensure op- timal H2 and H∞ performances under quadratic sta- bility for Takagi-Sugeno continuous-time fuzzy systems. The proposed conditions are formulated as parameter- dependent linear matrix inequalities (LMIs) that have extra variables from Finsler's lemma and parameters belonging to the unit simplex. The fuzzy control law is written as a state feedback gain that is a homoge- neous polynomial of degree g, encompassing the parallel distributed compensator as a special case when g = 1. Algebraic properties of the system parameters and re- cent results of positive polynomials are used to construct LMI relaxations which, differently from most relaxations in the literature, asymptotically converge to a solution whenever such solution exists. Due to the degree of free- dom obtained with the extra variables, the conditions presented in the paper are an improvement over earlier results based on Pólya's theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms. The numerical efficiency in terms of precision and computational effort is demon- strated by means of comparisons with other methods from the literature.
dc.description21
dc.description1
dc.description82
dc.description95
dc.descriptionAndrea, C.Q., Assunção, E., Pinto, J.O.P., Teixeira, M.C.M., Controle ótimo H∞de sistemas não-lineares com modelos fuzzy Takagi- Sugeno (2008) SBA: Controle & Automação, 19 (3), pp. 256-269
dc.descriptionApkarian, P., Gahinet, P., A convex characterization of gain-scheduled H∞ controllers (1995) IEEE Transactions on Automatic Control, 40 (5), pp. 853-864
dc.descriptionApkarian, P., Gahinet, P., Becker, G., Self-scheduled H∞ control of linear parameter-varying systems: A design example (1995) Automatica, 31 (9), pp. 1251-1261
dc.descriptionArrifano, N.S.D., Oliveira, V.A., Cossi, L.V., Synthesis of an LMI-based fuzzy control system with guaranteed cost performance: A piecewise Lyapunov approach (2006) SBA: Controle & Automação, 17 (2), pp. 213-225
dc.descriptionAvellar, G.S.C., Mozelli, L.A., Palhares, R.M., Condições LMIs alternativas para sistemas Takagi-Sugeno via função de Lyapunov fuzzy (2008) Anais do XVI Congresso Brasileiro de Automática, , Juiz de Fora, MG, Brasil
dc.descriptionBernussou, J., Peres, P.L.D., Geromel, J.C., A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Systems and Control Letters, 13 (1), pp. 65-72
dc.descriptionBliman, P.-A., Oliveira, R.C.L.F., Montagner, V.F., Peres, P.L.D., Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex (2006) Proceedings of the 45th IEEE Conference on Decision and Control, pp. 1486-1491. , San Diego, CA, USA
dc.descriptionBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM Studies in Applied Mathematics,Philadelphia, PA
dc.descriptionCao, Y., Frank, P.M., Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach (2000) IEEE Transactions on Fuzzy Systems, 8 (2), pp. 200-211
dc.descriptionChen, B., Tseng, C., Uang, H., Mixed H2/H∞fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach (2000) IEEE Transactions on Fuzzy Systems, 8 (3), pp. 249-265
dc.descriptionDe Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Perspectives in Robust Control, Lecture Notes in Control and Information Science, 268, pp. 241-257. , S. O. Reza Moheimani (ed.), Springer-Verlag, New York
dc.descriptionDe Souza, C.E., Trofino, A., De Oliveira, J., Parametric Lyapunov function approach to H2 analysis and control of linear parameter-dependent systems (2003) IEE Proceedings-Control Theory and Applications, 150 (5), pp. 501-508
dc.descriptionFang, C.-H., Liu, Y.-S., Kau, S.-W., Hong, L., Lee, C.-H., A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems (2006) IEEE Transactions on Fuzzy Systems, 14 (3), pp. 386-397
dc.descriptionFeng, G., A survey on analysis and design of model-based fuzzy control systems (2006) IEEE Transactions on Fuzzy Systems, 14 (5), pp. 676-697
dc.descriptionGreen, M., Limebeer, D.J.N., (1995) Linear Robust Control, , Prentice-Hall, Englewood Cliffs, NJ
dc.descriptionHardy, G.H., Littlewood, J.E., Pólya, G., (1952) Ine-qualities, , 2 edn, Cambridge University Press, Cambridge, UK
dc.descriptionJohansson, M., Rantzer, A., Arzen, K.E., Piecewise quadratic stability of fuzzy systems (1999) IEEE Transactions on Fuzzy Systems, 7 (6), pp. 713-722
dc.descriptionKau, S.-W., Liu, Y.-S., Hong, L., Lee, C.-H., Fang, C.-H., Lee, L., A new LMI condition for robust stability of discrete-time uncertain systems (2005) Systems & Control Letters, 54 (12), pp. 1195-1203
dc.descriptionKim, E., Lee, H., New approaches to relaxed quadratic stability condition of fuzzy control systems (2000) IEEE Transactions on Fuzzy Systems, 8 (5), pp. 523-534
dc.descriptionKumar, P.P., Kar, I., Behera, L., Variable gain controllers for nonlinear systems using the T-S fuzzy model (2006) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 36 (6), pp. 1442-1449
dc.descriptionLam, H.K., Leung, F.H.F., LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form (2007) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 37 (5), pp. 1396-1406
dc.descriptionLian, K., Chiang, T., Chiu, C., Liu, P., Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems (2001) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 31 (1), pp. 66-83
dc.descriptionLin, C., Wang, Q.-G., Lee, T.H., Less conservative D-stability test for polytopic systems using linearly parameter-dependent Lyapunov functions (2006) IEE Proceedings-Control Theory and Applications, 153 (6), pp. 665-670
dc.descriptionLiu, X., Zhang, Q., New approaches to H∞controller designs based on fuzzy observers for T-S fuzzy systems via LMI (2003) Automatica, 39 (5), pp. 1571-1582
dc.descriptionLöfberg, J., YALMIP: A toolbox for modeling and optimization in MATLAB (2004) Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, pp. 284-289. , http://control.ee.ethz.ch/~joloef/yalmip.php, Taipei, Taiwan
dc.descriptionMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Necessary and sufficient LMI conditions to compute quadratically stabilizing state feedback controllers for Takagi-Sugeno systems (2007) Proceedings of the 2007 American Control Conference, pp. 4059-4064. , New York, NY, USA
dc.descriptionMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Relaxações LMI para o projeto convexo de controladores H∞ para sistemas nebulosos de Takagi-Sugeno (2008) Anais do XVI Congresso Brasileiro de Automática, , Juiz de Fora, MG, Brasil
dc.descriptionMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Convergent LMI relaxations for quadratic stabilizability and H∞ control of Takagi-Sugeno fuzzy systems (2009) IEEE Transactions on Fuzzy Systems, , to appear
dc.descriptionMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Bliman, P.-A., Linear matrix inequality characterisation for H∞ and H2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems (2007) IET Control Theory & Applications, 1 (6), pp. 1726-1735
dc.descriptionMontagner, V.F., Peres, P.L.D., (2006) Journal of Dynamic Systems, Measurement and Control-Transactions of ASME, 128 (2), pp. 365-370
dc.descriptionMozelli, L.A., Palhares, R.M., Avellar, G.S.C., Novas condições de estabilidade e de estabilizaç ão para sistemas Takagi-Sugeno baseadas na função de Lyapunov fuzzy (2008) Anais do XVI Congresso Bra-sileiro de Automática, , Juiz de Fora, MG, Brasil
dc.descriptionMozelli, L.A., Palhares, R.M., Avellar, G.S.C., A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems (2009) Information Sciences, 179 (8), pp. 1149-1162
dc.descriptionMozelli, L.A., Palhares, R.M., Souza, F.O., Mendes, E.M.A.M., Reducing conservativeness in recent stability conditions of TS fuzzy systems (2009) Automatica, 45 (6), pp. 1580-1583
dc.descriptionNguang, S.K., Shi, P., H∞ fuzzy output feedback control design for nonlinear systems: An LMI approach (2003) IEEE Transactions on Fuzzy Systems, 11 (3), pp. 331-340
dc.descriptionOliveira, R.C.L.F., Peres, P.L.D., Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions (2005) Linear Algebra and Its Applications, 405, pp. 209-228
dc.descriptionOliveira, R.C.L.F., Peres, P.L.D., Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations (2007) IEEE Transactions on Automatic Control, 52 (7), pp. 1334-1340
dc.descriptionPowers, V., Reznick, B., A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra (2001) Journal of Pure and Applied Algebra, 164, pp. 221-229
dc.descriptionPrajna, S., Papachristodoulou, A., Seiler, P., Parrilo, P.A., (2004) SOSTOOLS: Sum of squares optimization toolbox for MATLAB
dc.descriptionRhee, B.-J., Won, S., A new fuzzy Lyapu-nov function approach for a Takagi-Sugeno fuzzy control system design, Fuzzy Sets and Systems (2006) Fuzzy Sets and Systems, 157 (9), pp. 1211-1228
dc.descriptionSala, A., Arinõ, C., (2007) Asymptotically Necessary and Sufficient Conditions for Stability and Performance in Fuzzy Control: Applications of Polya's Theorem, 158 (24), pp. 2671-2686
dc.descriptionScherer, C.W., LPV control and full block multipliers (2001) Automatica, 37 (3), pp. 361-375
dc.descriptionScherer, C.W., Higher-order relaxations for robust LMI problems with verifications for exactness (2003) Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 4652-4657. , Maui, HI, USA
dc.descriptionScherer, C.W., Relaxations for robust linear matrix inequality problems with verifications for exactness (2005) SIAM Journal on Matrix Analysis and Applications, 27 (2), pp. 365-395
dc.descriptionScherer, C.W., Hol, C.W.J., (2006) Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs, 107 (1-2), pp. 189-211
dc.descriptionSturm, J.F., A MATLAB toolbox for optimization over symmetric cones (1999) Optimization Methods and Software, pp. 625-653. , http://sedumi.mcmaster.ca/, Using SeDuMi 1.02
dc.descriptionTanaka, K., Ikeda, T., Wang, H.O., Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs (1998) IEEE Transactions on Fuzzy Systems, 6 (2), pp. 250-265
dc.descriptionTanaka, K., Ikeda, T., Wang, H.O., A unified approach to controlling chaos via an LMI-based fuzzy control system design (1998) IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications, 45 (10), pp. 1021-1040
dc.descriptionTanaka, K., Ohtake, H., Wang, H.O., A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions (2007) IEEE Transactions on Fuzzy Systems, 15 (3), pp. 333-341
dc.descriptionTanaka, K., Ohtake, H., Wang, H.O., Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach (2009) IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 39 (2), pp. 561-567
dc.descriptionTanaka, K., Wang, H., (2001) Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, , John Wiley & Sons, Inc., New York
dc.descriptionTeixeira, M.C.M., Assunção, E., Avellar, R.G., On relaxed LMI-based designs for fuzzy regulators and fuzzy observers (2003) IEEE Transactions on Fuzzy Systems, 11 (5), pp. 613-623
dc.descriptionTeixeira, M.C.M., Pietrobom, H.C., Assunção, E., Novos resultados sobre a estabilidade e controle de sistemas não-lineares utilizando mo- delos fuzzy e LMI (2000) SBA: Controle & Automação, 11 (2), pp. 37-48
dc.descriptionTeixeira, M.C.M., Zak, S.H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models (1999) IEEE Transactions on Fuzzy Systems, 7 (2), pp. 133-142
dc.descriptionTuan, H.D., Apkarian, P., Narikiyo, T., Yamamoto, Y., Parameterized linear matrix inequality techniques in fuzzy control system design (2001) IEEE Transactions on Fuzzy Systems, 9 (2), pp. 324-332
dc.descriptionWang, F., Balakrishnan, V., Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems (2002) IEEE Transactions on Automatic Control, 47 (5), pp. 720-734
dc.descriptionWang, H.O., Tanaka, K., Griffin, M.F., An approach to fuzzy control of nonlinear systems: Stability and design issues (1996) IEEE Transactions on Fuzzy Systems, 4 (1), pp. 14-23
dc.descriptionXu, S., Lam, J., Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers (2005) IEEE Transactions on Fuzzy Systems, 13 (2), pp. 82-93
dc.descriptionRobust stability of polytopic systems via affine parameter-dependent Lyapunov functions (2008) SIAM Journal on Control and Optimization, 47 (5), pp. 2642-2662
dc.languagept
dc.publisher
dc.relationControle y Automacao
dc.rightsaberto
dc.sourceScopus
dc.titleConvex Relaxations With Guaranteed Convergence For Control Design Of Takagi-sugeno Fuzzy Systems [relaxações Convexas De Convergência Garantida Para O Projeto De Controladores Para Sistemas Nebulosos De Takagi-sugeno]
dc.typeArtículos de revistas


Este ítem pertenece a la siguiente institución