**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.

Online version of the paper

Corresponding technical report: pdf file (294 KB)

@article{DeS:99-03,

author={B. {D}e Schutter},

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},

doi={10.1137/S0363012999354648}

}

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