Feedback limitations in nonlinear systems: from Bode integrals to cheap control

This paper links the Bode integral characterization of performance limitations in linear control systems with the limiting cost of a particular linear cheap control. This link allows us to establish analogous feedback limitations in nonlinear systems. We show how unstable zero dynamics impose unavoidable obstructions to the closed-loop performance.

[1]  Li Qiu,et al.  Limitations on maximal tracking accuracy. I. Tracking step signals , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[2]  J. Freudenberg,et al.  Right half plane poles and zeros and design tradeoffs in feedback systems , 1985 .

[3]  B. Francis.  The optimal linear-quadratic time-invariant regulator with cheap control , 1979 .

[4]  Edward J. Davison,et al.  Performance limitations of non-minimum phase systems in the servomechanism problem, , 1993, Autom..

[5]  Vadim I. Utkin,et al.  A singular perturbation analysis of high-gain feedback systems , 1977 .

[6]  Michael J. Grimble,et al.  Optimal Control and Stochastic Estimation: Theory and Applications , 1988 .

[7]  Brian D. O. Anderson,et al.  Optimal control problems over large time intervals , 1987, Autom..

[8]  Edward J. Davison,et al.  The optimal LQ regulator with cheap control for not strictly proper systems , 1983 .

[9]  G. Zames,et al.  On H ∞ -optimal sensitivity theory for SISO feedback systems , 1984 .

[10]  T. J. Tarn,et al.  Performance bounds for disturbance attenuation in nonlinear non-minimum-phase systems , 1997, 1997 European Control Conference (ECC).

[11]  Rick H. Middleton,et al.  Trade-offs in linear control system design , 1991, Autom..

[12]  Mathukumalli Vidyasagar,et al.  Control System Synthesis , 1985 .

[13]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[14]  Sheldon S. L. Chang,et al.  Synthesis of Optimum Control Systems , 1961 .

[15]  H. Kwakernaak,et al.  The maximally achievable accuracy of linear optimal regulators and linear optimal filters , 1972 .

[16]  A. Saberi,et al.  Cheap and singular controls for linear quadratic regulators , 1985, 1985 24th IEEE Conference on Decision and Control.

[17]  M. J. Grimble,et al.  An H/sub infinity / indentification algorithm and its use in adaptive control , 1991 .

[18]  Jeff S. Shamma,et al.  Performance limitations in sensitivity reduction for nonlinear plants , 1991 .

[19]  Graham C. Goodwin,et al.  Sensitivity limitations in nonlinear feedback control , 1996 .

[20]  David Q. Mayne,et al.  Feedback limitations in nonlinear systems: from Bode integrals to cheap control , 1999, IEEE Trans. Autom. Control..

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

[22]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .

[23]  R. E. Kalman,et al.  When Is a Linear Control System Optimal , 1964 .

[24]  A. Jameson,et al.  Cheap control of the time-invariant regulator , 1975 .