Stabilization of systems with changing dynamics by means of switching

We present a framework for designing stable control schemes for systems whose dynamics change. The idea is to develop a controller for each of the regions defined by different dynamic characteristics and design a switching scheme that guarantees the stability of the overall system. We derive sufficient conditions for the stability of the switching scheme for systems evolving on a sequence of embedded manifolds. An important feature of the proposed framework is that if the conditions are satisfied by pairs of controllers adjacent in the hierarchy, the overall system will be stable. This makes the application of our results particularly straight forward. The methodology is applied to stabilization of a shimmying wheel, where changes in the dynamic behaviour are due to switches between sliding and rolling.

[1]  Joel W. Burdick,et al.  A General Method for Motion Planning for Quasi–Static Legged Robotic Locomotion , 1998 .

[2]  Jaydev P. Desai,et al.  Continuous Motion Plans for Robotic Systems with Changing Dynamic Behavior , 1996 .

[3]  M. Branicky.  Stability of switched and hybrid systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[4]  Ling Hou,et al.  Stability analysis of a general class of hybrid dynamical systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Karl Johan Åström,et al.  A Stabilizing Switching Scheme for Multi Controller Systems , 1996 .

[6]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

[7]  M. Branicky,et al.  Algorithms for optimal hybrid control , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  Gábor Stépán,et al.  Controlling Unstable Rolling Phenomena , 2000 .

[9]  Gábor Stépán,et al.  Chaotic Motion of Wheels , 1991 .

[10]  A. Nerode,et al.  Multiple agent hybrid control: carrier manifolds and chattering approximations to optimal control , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[11]  John Lygeros,et al.  A Game-Theoretic Approach to Hybrid System Design , 1996, Hybrid Systems.

[12]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[13]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[14]  A. Puri.  Theory of hybrid systems and discrete event systems , 1996 .

[15]  I. Kolmanovsky,et al.  Hybrid feedback laws for a class of cascade nonlinear control systems , 1996, IEEE Trans. Autom. Control..

[16]  Pravin Varaiya,et al.  Viable Control of Hybrid Systems , 1994, Hybrid Systems.

[17]  A. Vannelli,et al.  THEORY OF PARTIAL STABILITY THEOREMS, CONVERSE THEOREMS, AND MAXIMAL LYAPUNOV FUNCTIONS. , 1980 .