Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.

[1]  I. Kanellakopoulos.  Passive adaptive control of non‐linear systems , 1993 .

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

[3]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[4]  I. Kanellakopoulos,et al.  Backstepping to passivity: recursive design of adaptive systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[5]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[6]  A. Castillo-Facuse,et al.  Adaptive Passivity of Nonlinear Systems Using Time-Varying Gains , 2001 .

[7]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[8]  Wei Lin,et al.  Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty , 1999, Autom..

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

[10]  Lihua Xie,et al.  Robust control of nonlinear feedback passive systems , 1996 .

[11]  P. Kokotovic,et al.  A positive real condition for global stabilization of nonlinear systems , 1989 .

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

[13]  Rogelio Lozano,et al.  Passivity and global stabilization of cascaded nonlinear systems , 1992 .

[14]  Wei Lin,et al.  Feedback stabilization of general nonlinear control systems: a passive system approach , 1995 .

[15]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[16]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[17]  D.L. Elliott,et al.  Feedback systems: Input-output properties , 1976, Proceedings of the IEEE.

[18]  David J. Hill,et al.  Exponential Feedback Passivity and Stabilizability of Nonlinear Systems , 1998, Autom..