Output feedback control of linear fractional transformation systems subject to actuator saturation

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.     

Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.     

Tuples of Disjoint $\mathsf{NP}$ -Sets

Disjoint gif" alt="$\mathsf{NP}$" align="middle" border="0"> -pairs are a well studied complexity-theoretic concept with important applications in cryptography and propositional proof complexity. In this paper we introduce a natural generalization of the notion of disjoint gif" alt="$\mathsf{NP}$" align="middle" border="0"> -pairs to disjoint k-tuples of gif" alt="$\mathsf{NP}$" align="middle" border="0"> -sets for k≥2. We define subclasses of the class of all disjoint k-tuples of gif" alt="$\mathsf{NP}$" align="middle" border="0"> -sets. These subclasses are associated with a propositional proof system and possess complete tuples which are defined from the proof system. In our main result we show that complete disjoint gif" alt="$\mathsf{NP}$" align="middle" border="0"> -pairs exist if and only if complete disjoint k-tuples of gif" alt="$\mathsf{NP}$" align="middle" border="0"> -sets exist for all k≥2. Further, this is equivalent to the existence of a propositional proof system in which the disjointness of all k-tuples is shortly provable. We also show that a strengthening of this conditions characterizes the existence of optimal proof systems. An extended abstract of this paper appeared in the proceedings of the conference CSR 2006 (Lecture Notes in Computer Science 3967, 80–91, 2006). Supported by DFG grant KO 1053/5-1.     

Convergence analysis of geometrical multigrid methods for solving data-sparse boundary element equations

The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometrical multigrid methods for solving large-scale, data-sparse boundary element equations. In particular, we investigate multigrid methods for \(\mathcal{H}\)-matrices arising from the adaptive cross approximation to the single layer potential operator.     

Separation of synchronous and asynchronous communication via testing

One of the early results concerning the asynchronous π-calculus which significantly contributed to its popularity is the capability of encoding the output prefix of the (choiceless) π-calculus in a natural and elegant way. Encodings of this kind were proposed by Honda and Tokoro, by Nestmann and (independently) by Boudol. We investigate whether the above encodings preserve De Nicola and Hennessy’s testing semantics. In this sense, it turns out that, under some general conditions, no encoding of the output prefix is able to preserve the must testing. This negative result is due to (a) the non-atomicity of the sequences of steps which are necessary in the asynchronous π-calculus to mimic synchronous communication, and (b) testing semantics’ sensitivity to divergence.     

A reactive GRASP and path relinking for a combined production–distribution problem

An NP-hard production–distribution problem for one product over a multi-period horizon is investigated. The aim is to minimize total cost taking production setups, inventory levels and distribution into account. An integer linear model is proposed as a compact problem specification but it cannot be solved to optimality for large instances. Instead of using a classical two-phase approach (production planning and then route construction for each day), metaheuristics that simultaneously tackle production and routing decisions are developed: a GRASP (greedy randomized adaptive search procedure) and two improved versions using either a reactive mechanism or a path-relinking process. These algorithms are evaluated on 90 randomly generated instances with 50, 100 and 200 customers and 20 periods. The results confirm the interest of integrating production and distribution decisions, compared to classical two-phase methods. Moreover, reaction and path-relinking give better results than the GRASP alone.     

Simplifying the weft hierarchy

We give simple, self-contained proofs of the basic hardness results for the classes W[t] of the weft hierarchy. We extend these proofs to higher levels of the hierarchy and illuminate the distinctions among its classes. The anti-monotone collapse at W[1,s] and the normalization of weft-t formulas arise as by-products of the proofs.