Reference
B. De Schutter, "Optimal control of a class of linear hybrid systems with
saturation,"
SIAM Journal on Control and Optimization,
vol. 39, no. 3, pp. 835-851, 2000.
Abstract
We consider a class of first order linear hybrid systems with saturation. A
system that belongs to this class can operate in several modes or phases; in
each phase each state variable of the system exhibits a linear growth until a
specified upper or lower saturation level is reached, and after that the state
variable stays at that saturation level until the end of the phase. A typical
example of such a system is a traffic signal controlled intersection. We
develop methods to determine optimal switching time sequences for first order
linear hybrid systems with saturation that minimize criteria such as average
queue length, worst case queue length, average waiting time, and so on. First
we show how the Extended Linear Complementarity Problem (ELCP), which is a
mathematical programming problem, can be used to describe the set of system
trajectories of a first order linear hybrid systems with saturation.
Optimization over the solution set of the ELCP then yields an optimal switching
time sequence. Although this method yields globally optimal switching time
sequences, it is not feasible in practice due to its computational complexity.
Therefore, we also present some methods to compute suboptimal switching time
sequences. Furthermore, we show that if there is no upper saturation then for
some objective functions the globally optimal switching time sequence can be
computed very efficiently. We also discuss some approximations that lead to
suboptimal switching time sequences that can be computed very efficiently.
Finally, we use these results to design optimal switching time sequences for
traffic signal controlled intersections.
Publisher page
Downloads
Addendum
- B. De Schutter, "Optimal control of a class of linear hybrid systems with saturation: Addendum," Tech. report bds:99-03a, Control Systems Engineering, Fac. of Information Technology and Systems, Delft University of Technology, Delft, The Netherlands, 8 pp., Oct. 1999. (abstract, bibtex, report (pdf))
BibTeX
@article{DeS:99-03,
author = {De Schutter, Bart},
title = {Optimal Control of a Class of Linear Hybrid Systems with
Saturation},
journal = {SIAM Journal on Control and Optimization},
volume = {39},
number = {3},
pages = {835--851},
year = {2000}
}