We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generali...

Hybrid dynamic systems are analyzed through linear hybrid automaton. In this paper, we propose a mapping algorithm to deal with a new Continuous elementary HPN. The method shown enables us to analyze some system properties using a linear hybrid automaton generated by a mapping process. The application involves a water system of three tanks, which is analyzed by a PHAVer (Polyhedral Hybrid Autom...

This paper addresses questions regarding the decidability of hybrid automata that may be constructed hierarchically and in a modular way, as is the case in many exemplar systems, be it natural or engineered. Since an important step in such constructions is a product operation, which constructs a new product hybrid automaton by combining two simpler component hybrid automata, an essential proper...

The purpose of this report is to present research results on control of piecewise-linear hybrid systems of an investigation carried out as part of the project Verification of Hybrid Systems (VHS). Many engineering systems can in a first approximation be described by a piecewise-linear hybrid system. Moreover, the computational and complexity issues of this class of systems seems comparatively s...

This paper gives a short overview of a model checking tool for Cottbus Timed Automata, which is a modular modeling language based on timed and hybrid automata. For timed automata, the current version of the tool provides BDD-based verification using an integer semantics. Reachability analysis as well as refinement checking is possible. To find good variable orderings it uses the component struc...

The learning automata operate in unknown random environments and progressively improve their performance via a learning process. The learning automata are very useful for optimization of multi-modal functions when the function is unknown and only noise-corrupted evaluations are available. In this paper we propose a new hybrid algorithm for noisy optimization. This model is obtained by combining...

Hybrid systems are dynamical systems with the ability to describe mixed discretecontinuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete...

We extend the concept of manifold with boundary to weight and boundary weight functions. With the new concept, we obtained the double reciprocity laws for simplicial complexes, cubical complexes, and lattice polyhedra with weight functions. For a polyhedral manifold with boundary, if the weight function has the constant value 1, then the boundary weight function has the constant value 1 on the ...

In this paper, an off-line synthesis approach to robust constrained model predictive control is presented. Most of the computational burdens are reduced by computing off-line a sequence of state feedback control laws that corresponds to a sequence of polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant set containing the currently measured state is determined and ...

We present a novel ultimate bound and invariant set computation method for continuous-time switched linear systems with disturbances and arbitrary switching. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds and invariant sets in the form ...