ANALYSIS OF OSCILLATORY CONTROL SYSTEMS

Abstract This paper presents analysis results for control systems subject to oscillatory inputs, i.e., inputs of large amplitude and high frequency. The key results are a series expansion characterizing the averaged system and various Lie-algebraic conditions that guarantee the series can be summed. Some illustrative example systems provide insight into the results; control design applications are discussed in a companion paper.

[1]  Roger W. Brockett.  On the rectification of vibratory motion , 1989 .

[2]  Henry Hermes,et al.  Nilpotent and High-Order Approximations of Vector Field Systems , 1991, SIAM Rev..

[3]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[4]  広瀬 茂男,et al.  Biologically inspired robots : snake-like locomotors and manipulators , 1993 .

[5]  H. Sussmann,et al.  Continuous Dependence with Respect to the Input of Trajectories of Control-Affine Systems , 1999 .

[6]  Herschel Rabitz,et al.  Coherent Control of Quantum Dynamics: The Dream Is Alive , 1993, Science.

[7]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[8]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[9]  A. Seifert,et al.  Oscillatory Control of Separation at High Reynolds Numbers , 1999 .

[10]  John Baillieul,et al.  Stable average motions of mechanical systems subject to periodic forcing , 1993 .

[11]  M. Golubitsky,et al.  Symmetry in locomotor central pattern generators and animal gaits , 1999, Nature.

[12]  J. M. Noworolski,et al.  Generalized averaging method for power conversion circuits , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[13]  Sonia Martínez,et al.  Analysis and design of oscillatory control systems , 2003, IEEE Trans. Autom. Control..

[14]  J. Baillieul,et al.  Scale dependence in the oscillatory control of micromechanisms , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[15]  Mark Levi,et al.  Geometry and physics of averaging with applications , 1999 .

[16]  J. Hale.  Oscillations in Nonlinear Systems , 1963 .

[17]  A. Isidori.  Nonlinear Control Systems , 1985 .

[18]  F. Verhulst,et al.  Averaging Methods in Nonlinear Dynamical Systems , 1985 .

[19]  Jaroslav Kurzweil,et al.  Iterated Lie brackets in limit processes in ordinary differential equations , 1988 .

[20]  P. L. Kapitsa,et al.  Dynamical Stability of a Pendulum when its Point of Suspension Vibrates , 1965 .

[21]  Joel W. Burdick,et al.  The Geometric Mechanics of Undulatory Robotic Locomotion , 1998, Int. J. Robotics Res..

[22]  G. Paramonov.  Coherent control of linear and nonlinear multiphoton excitation of molecular vibrations , 1993 .

[23]  R. Gamkrelidze,et al.  THE EXPONENTIAL REPRESENTATION OF FLOWS AND THE CHRONOLOGICAL CALCULUS , 1979 .

[24]  John Baillieul,et al.  Energy methods for stability of bilinear systems with oscillatory inputs , 1995 .