We present a framework for designing stable control schemes for systems with changing dynamics--systems whose dynamics change as the state evolves through di#erent regions in the state space. Systems with changing dynamics (SCD) form a subset of hybrid systems; their stabilization is therefore a problem in hybrid control. It is often di#cult or even impossible to design a single controller that would stabilize a SCD. An appealing alternative are switching control schemes, where a di#erent controller is employed in each dynamic regime and the stability of the overall system is ensured through an appropriate switching scheme. We formulate a set of su#cient conditions for the stability of a switching control scheme. We show that by imposing a hierarchy among the controllers, su#cient conditions can be formulated in a form suitable for the controller design. The hierarchy is formally defined through a partial order. With partial order, the study of the stability of the system is reduced to the study of relationships among the immediate neighbors in the partial order. This significantly simplifies the analysis and design processes. The methodology is applied to stabilization (of a relative equilibrium) of a two-wheel mobile robot of the Hilare type, where the wheels are allowed to slip. The example demonstrates that the approach is easy to use and that the partial order concept naturally leads to modularity in the controller design.
|
300
|
Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems
– Alur, Courcoubetis, et al.
- 1993
|
|
198
|
Introduction to Mechanics and Symmetry
– Ratiu, Marsden
- 1999
|
|
171
|
Nonlinear Systems Analysis
– Vidyasagar
- 2003
|
|
117
|
1967] Stability of Motion
– Hahn
|
|
114
|
Hybrid models for motion control systems
– Brockett
- 1993
|
|
101
|
Computation of piecewise quadratic Lyapunov functions for hybrid systems
– Johansson, Rantzer
- 1998
|
|
89
|
Models for hybrid systems: Automata, topologies, stability
– Nerode, Kohn
- 1993
|
|
85
|
Sequential composition of dynamically dexterous robot behaviors
– Burridge, Rizzi, et al.
- 1999
|
|
83
|
Nonlinear regulation: The piecewise linear approach
– Sontag
- 1981
|
|
73
|
An approach to the description and analysis of hybrid systems
– Nicollin, Olivero, et al.
- 1993
|
|
54
|
Stability of switched and hybrid systems
– Branicky
- 1994
|
|
51
|
Viable control of hybrid systems
– Deshpande, Varaiya
- 1995
|
|
42
|
Stability and robustness for hybrid systems
– Pettersson, Lennartson
- 1996
|
|
41
|
Asymptotic stability of m-switched systems using Lyapunov-like functions
– Peleties, DeCarlo
- 1991
|
|
40
|
A unified framework for hybrid control
– Branicky, Borkar, et al.
- 1994
|
|
40
|
Theory of hybrid systems and discrete event systems
– Puri
- 1995
|
|
39
|
Verified hybrid controllers for automated vehicles
– Lygeros, Godbole, et al.
- 1998
|
|
35
|
A dynamical simulation facility for hybrid systems
– Back, Guckenheimer, et al.
- 1992
|
|
30
|
Stability Theory by Liapunov's Direct Method
– Rouche, Habets, et al.
- 1977
|
|
29
|
Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots
– Sarkar, Yun, et al.
- 1994
|
|
27
|
A game theoretic approach to hybrid system design
– Lygeros, Godbole, et al.
- 1996
|
|
24
|
Algorithms for optimal hybrid control
– Branicky, Mitter
- 1995
|
|
21
|
Nonsmooth control-Lyapunov functions
– Sontag, Sussmann
- 1995
|
|
19
|
Continuous motion plans for robotic systems with changing dynamic behavior
– Zefran, Desai, et al.
- 1996
|
|
12
|
A stabilizing switching scheme for multi-controller systems
– Malmborg, Bernhardsson, et al.
- 1996
|
|
11
|
Multiple agent hybrid control: carrier manifolds and chattering approximations to optimal control
– Kohn, Nerode, et al.
- 1994
|
|
9
|
Hybrid feedback laws for a class of cascade nonlinear control systems
– Kolmanovsky, McClamroch
- 1996
|
|
7
|
Stability analysis of a general class of hybrid dynamical systems
– Hou, Michel
- 1997
|
|
5
|
Con resolution for air trac management: a study in multiagent hybrid systems
– Tomlin, Pappas, et al.
- 1998
|
|
5
|
Lyapunov stability of continuous�valued systems under the supervision of discrete�event transition systems
– He, Lemmon
- 1998
|
|
5
|
Hybrid systems modelling and complementarity problems
– Schaft, Schumacher
- 1997
|
|
4
|
Antsaklis, "Supervisory control of Petri nets with uncontrollable /unobservable transitions
– Moody, J
- 1996
|
|
4
|
Theory of partial stability theorems, converse theorems, and maximal Lyapunov functions
– Vannelli, Vidyasagar
- 1980
|
|
3
|
A general method for motion planning for quasi--static legged robotic locomotion
– Goodwine, Burdick
- 1997
|
|
1
|
Discontinuous stabilizing feedback using partially defined Lyapunov functions
– Laerriere
- 1994
|
|
