To enable inference in hybrid Bayesian networks containing nonlinear deterministic conditional distributions using mixtures of polynomials or mixtures of truncated exponentials, Cobb and Shenoy in 2005 propose approximating nonlinear deterministic functions by piecewise linear ones. In this paper, we describe a method for finding piecewise linear approximations of nonlinear functions based on t...

In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the fa...

A “hybrid method”, dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux’s method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions—this, even in the case when the unit circle is a natural boundary. A prime ap...

In this note, a practical way to compute limit cycles in context of hybrid systems is investigated. As in many hybrid applications the steady state is depicted by a limit cycle, control design and stability analysis of such hybrid systems require the knowledge of this periodic motion. Analytical expression of this cycle is generally an impossible task due to the complexity of the dynamic. A fas...

time, cost and quality are considered as the main components in managing each project. previous researches have mainly focused on the time-cost trade-off problems. recently quality is considered as the most important factor in project�s success, which is influenced by time acceleration that is the less time is spent the more success is gained. in time-cost-quality trade-off problems, each act...

We construct hybrid loops that augment continuous-time control systems. We consider a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time state feedback controller. The arising hybrid closed loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the close...

Many different bases functions have been used to estimate the solution to differential equations, such as orthogonal bases [3, 4, 14, 15], wavelets [7–8] and hybrid [2, 13, 16–17]. The various systems of orthogonal functions may be classified into two categories. The first is piecewise continuous function (PCBF) to which the orthogonal systems of Walsh functions [5], Block-pulse functions [4, 1...

The verification of hybrid systems, encompassing both discrete-time and continuoustime behavior, is a problem of rising importance. Hybrid behavior occurs wherever a digital system, operating in discrete time, interacts with a real-world environment, which evolves in continuous time. One desired property of hybrid systems is global asymptotic stability. A globally asymptotically stable system c...

The hybrid dynamics of the genetic regulatory networks (GRNs) have attracted much research attention in recent years. This paper is concerned with the stability analysis of piecewise GRNs. Depending on whether the state partitions and mode transitions are known or unknown as a priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, b...