Explicit construction of H∞ control law for a class of nonminimum phase nonlinear multivariable systems

This paper addresses a nonlinear Hinfin control problem for a class of nonminimum phase nonlinear multivariable systems. To avoid the complicated recursive design procedure, the asymptotic time-scale and eigenstructure assignment method is adopted to construct the control law for the nonlinear Hinfin control problem. A sufficient solvability condition is established on the unstable zero-dynamics of the system for the nonlinear Hinfin control problem. Moreover, based on the sufficient solvability condition, an upper bound of the achievable L2 gain is estimated for the nonlinear Hinfin control problem.

[1]  Jie Huang,et al.  Numerical approach to computing nonlinear H-infinity control laws , 1995 .

[2]  C. Scherer.  H∞ -control by state-feedback for plants with zeros on the imaginary axis , 1992 .

[3]  Ali Saberi,et al.  Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling , 1987 .

[4]  Ben M. Chen,et al.  Explicit construction of Hinfinity control law for a class of nonminimum phase nonlinear systems , 2008, Autom..

[5]  Ben M. Chen,et al.  Explicit Constructions of Global Stabilization Control Laws for a Class of Nonminimum Phase Nonlinear Systems , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[6]  Ali Saberi,et al.  Time-scale structure assignment in linear multivariable systems using high-gain feedback , 1989 .

[7]  A. Isidori.  Global almost disturbance decoupling with stability for non minimum-phase single-input single-output , 1996 .

[8]  Zhengtao Ding.  Adaptive estimation and rejection of unknown sinusoidal disturbances in a class of non-minimum-phase nonlinear systems , 2006 .

[9]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[10]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

[11]  Zhengtao Ding.  Backstepping stabilization of nonlinear systems with a nonminimum phase zero , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[12]  Wei-Bing Gao,et al.  Nonlinear H ∞ -control and estimation of optimal H ∞ -gain , 1995 .

[13]  Anders Robertsson,et al.  Observer backstepping for a class of nonminimum-phase systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[14]  Ben M. Chen,et al.  Linear Systems Theory: A Structural Decomposition Approach , 2004 .

[15]  C. Mead,et al.  Linear Systems Theory , 2004 .

[16]  Tzyh Jong Tarn,et al.  Semiglobal L2 performance bounds for disturbance attenuation in nonlinear systems , 1999, IEEE Trans. Autom. Control..

[17]  Ben M. Chen.  Robust and H[∞] control , 2000 .

[18]  P. Sannuti,et al.  A special coordinate basis of multivariable linear systems- Finite and infinite zero structure , 1986, 1986 25th IEEE Conference on Decision and Control.

[19]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[20]  Zhengtao Ding,et al.  Adaptive estimation and rejection of unknown disturbances through measurement feedback for a class of nonminimum phase nonlinear MIMO systems , 2005, 2005 International Conference on Control and Automation.

[21]  Zongli Lin,et al.  Almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance-affected unstable zero dynamics , 1998 .

[22]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[23]  Weiyao Lan,et al.  Explicit Construction of H Control Law for a Class of Nonminimum Phase Nonlinear Systems , 2007, 2007 American Control Conference.

[24]  F. Lewis,et al.  Hamilton-Jacobi-Isaacs formulation for constrained input nonlinear systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[25]  I. Petersen.  Disturbance attenuation and H^{∞} optimization: A design method based on the algebraic Riccati equation , 1987 .

[26]  Alberto Isidori,et al.  A note on almost disturbance decoupling for nonlinear minimum phase systems , 1996 .

[27]  A. Schaft.  On a state space approach to nonlinear H ∞ control , 1991 .

[28]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[29]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.