Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

This paper deals with control of (max,+)-linear systems when a disturbance acts on system state. In a first part we synthesize the greatest control which allows to match the disturbance action. Then, we look for an output feedback which makes the disturbance matching. Formally, this problem is very close to the disturbance decoupling problem for continuous linear systems

Towards geometric control of max-plus linear systems with applications to manufacturing systems

The max-plus linear systems have been studied for almost three decades, however, a well-established system theory on such specific systems is still an on-going research. The geometric control theory in particular was proposed as the future direction for max-plus linear systems by Cohen et al. This paper reports upon recent investigations on the disturbance decoupling problem for max-plus linear systems, which is the standard geometric control problem originated by W. M. Wonham. Different concepts of the disturbance decoupling problem are introduced, as well as the corresponding solvability conditions and controller synthesis procedures. The main results can be used in manufacturing systems, queueing networks, and power system networks for fault detection and system breakdown prevention

Inner and outer approximation of capture basins using interval analysis

Abstract: This paper proposes a new approach to solve the problem of computing the capture basin C of a target T. The capture basin corresponds to the set of initial states such that the target is reached in finite time before possibly leaving of constrained set. We present an algorithm, based on interval analysis, able to characterize an inner and an outer approximation C − ⊂ C ⊂ C+ of the capture basin. The resulting algorithm is illustrated on the Zermelo problem

Capture basin approximation using interval analysis

This paper proposes a new approach for computing the capture basin C of a target T. The capture basin corresponds to the set of initial state vectors such that the target could be reached in finite time via an appropriate control input, before possibly leaving the target. Whereas classical capture basin characterization does not provide any guarantee on the set of state vectors that belong to the capture basin, interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm that is able to provide guaranteed approximation of the inner C− and the outer C+ of the capture basin, such that C−⊆C⊂C+. In order to illustrate the principle and the efficiency of the approach, a testcase on the ‘car on the hill’ problem is provided. Copyright © 2010 John Wiley & Sons, Ltd