By Topic

A comparison principle for state-constrained differential inequalities and its application to time-optimal control

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Seung-Jean Kim ; Inf. Syst. Lab., Stanford Univ., CA, USA ; Dong-Soo Choi ; In-Joong Ha

In this paper, we present a comparison principle that characterizes the maximal solutions of state-constrained differential inequalities in terms of solutions of certain differential equations with discontinuous right-hand sides. For the sake of completeness, we show through some set-valued analysis that the differential equations determining the maximal solutions have the unique solutions in the Carathe´odory sense, in spite of discontinuity of their right-hand sides. We apply our comparison principle to the explicit characterization of the solution to a time-optimal control problem for a class of state-constrained second-order systems which includes the dynamic equations of robotic manipulators with geometric path constraints as well as single-degree-of-freedom mechanical systems with friction. Specifically, we show that the time-optimal trajectory is uniquely determined by two curves that can be constructed by solving two scalar ordinary differential equations with continuous right-hand sides. Hence, the time-optimal trajectory can be found in a computationally efficient way through the direct use of the well-known Euler or Runge-Kutta methods. Another interesting feature is that our method to solve the time-optimal control problem works even when there exist an infinite number of switching points. Finally, some simulation results using a two-degrees-of-freedom (DOF) robotic manipulator are presented to demonstrate the practical use of our complete characterization of the time-optimal solution.

Published in:

IEEE Transactions on Automatic Control  (Volume:50 ,  Issue: 7 )