View source for Finite-Horizon Optimal Control and Stabilization of Time-Scalable Systems

{{HTDB paper
| authors = Alex Fax and Richard Murray
| title = Finite-Horizon Optimal Control and Stabilization of Time-Scalable Systems
| source = 2000 Conference on Decision and Control
| year = 2000
| type =  Conference 
  Submission
| funding = AFOSR
| url = http://www.cds.caltech.edu/~murray/preprints/fm00a-cdc.pdf
| abstract = 
In this paper, we consider the optimal control of time-scalable systems.
The time-scaling property is shown to convert the  PDE associated
with the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE.  
Solution of this PDE yields the value function at a fixed time, and that solutio
n can be
scaled to find the value function at any point in time.  Furthermore, in certain
 cases the 
unscaled control law stabilizes the system, and the unscaled value function acts
 as a
Lyapunov function for that system.  For the example of the 
nonholonomic integrator, this PDE is solved, and the 
resulting optimal trajectories coincide with the known solution to that problem.

| flags = 
| tag = fm00-cdc
| id = 2000a
}}