Dissipativity-based switching adaptive control

This paper presents a new switching adaptive control strategy for nonlinear systems with uncertainties on discrete finite sets. Differently to multiple model supervisory control, switching adaptive control needs no estimators for switching decisions. The switching logic is designed based on the relationship between passivity (or more generally dissipativity) and the adaptive systems, such that in the process of switching control, the transient boundary can be guaranteed by appropriately switching the parameter estimate. This makes it possible to apply the strategy in nonlinear systems modelled in local regions in the state space. Simulation will be employed to show the effectiveness of the approach.

[1]  Brian D. O. Anderson,et al.  Challenges of adaptive control-past, permanent and future , 2008, Annu. Rev. Control..

[2]  Michael G. Safonov,et al.  The unfalsified control concept and learning , 1997 .

[3]  Brian D. O. Anderson,et al.  Stability of adaptive systems: passivity and averaging analysis , 1986 .

[4]  F A Mussa-Ivaldi,et al.  Adaptive representation of dynamics during learning of a motor task , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[5]  João Pedro Hespanha,et al.  Overcoming the limitations of adaptive control by means of logic-based switching , 2003, Syst. Control. Lett..

[6]  Ji-Feng Zhang,et al.  Adaptive sampled-data based linear quadratic optimal control of stochastic systems , 2007, Int. J. Control.

[7]  Cong Wang,et al.  Learning from neural control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[8]  Elias B. Kosmatopoulos,et al.  A switching adaptive controller for feedback linearizable systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[9]  P. R. Kumar,et al.  Optimal Adaptive Control of Linear-Quadratic-Gaussian Systems , 1983 .

[10]  Rogelio Lozano,et al.  On the passivity of linear delay systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[11]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[12]  D. Mayne,et al.  Design issues in adaptive control , 1988 .

[13]  B. Anderson,et al.  Multiple model adaptive control. Part 1: Finite controller coverings , 2000 .

[14]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[15]  A. Morse,et al.  A cyclic switching strategy for parameter-adaptive control , 1994, IEEE Trans. Autom. Control..

[16]  Romeo Ortega,et al.  Passivity properties for stabilization of cascaded nonlinear systems , 1991, Autom..

[17]  Kumpati S. Narendra,et al.  Adaptive control using multiple models , 1997, IEEE Trans. Autom. Control..

[18]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[19]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[20]  Domenico D'Alessandro.  On passivity and adaptive stabilization of nonlinear systems , 1996, IEEE Trans. Autom. Control..

[21]  G. Goodwin,et al.  Hysteresis switching adaptive control of linear multivariable systems , 1994, IEEE Trans. Autom. Control..

[22]  Wai-Kai Chen,et al.  Visions of Nonlinear Science in the 21st Century: Festschrift Dedicated to Leon O. Chua on the Occasion of His 60th Birthday , 1999 .

[23]  Torsten Bohlin,et al.  Interactive System Identification: Prospects and Pitfalls , 1991 .

[24]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[25]  A. L. Fradkov.  Quadratic Lyapunov functions in the adaptive stability problem of a linear dynamic target , 1976 .

[26]  B. Barmish,et al.  Adaptive stabilization of linear systems via switching control , 1986, 1986 25th IEEE Conference on Decision and Control.

[27]  David J. Hill,et al.  Nonlinear adaptive control of feedback passive systems , 1995, Autom..

[28]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .