Citation
M'Closkey, Robert Thomas (1995) Exponential stabilization of driftless nonlinear control systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10172007104556
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form,
[...].
Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a nonstandard dilation. Even though the approximation can be given a coordinatefree interpretation, the homogeneous structure is useful to exploit. Since implementing a controller requires choosing a coordinate system, there are extra benefits to be gained by choosing coordinates in which the approximation is homogeneous. The feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closedloop system. The stability achieved is called pexponential stability. This extended notion of exponential stability is required since the feedback, and hence the closedloop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closedloop driftless system cannot be bounded by an exponential envelope.
The synthesis methods generate feedbacks which are not smooth on [...]. The solutions of the closedloop system are proven to be unique in this case. In addition, for many driftless systems the control inputs are often velocities. A more appropriate formulation of the stabilization problem has the control law specifying forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still pexponentially stabilize the system.
Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the pexponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods and problems in this thesis bring the practical control of strongly nonlinear systems one step closer.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Mechanical Engineering 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  6 December 1994 
Record Number:  CaltechETD:etd10172007104556 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10172007104556 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4139 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  26 Oct 2007 
Last Modified:  26 Dec 2012 03:05 
Thesis Files
PDF (M'Closkey_rt_1995.pdf)
 Final Version
Restricted to Caltech community only See Usage Policy. 6Mb 
Repository Staff Only: item control page