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• We construct a chain of two interconnected chemostats, assuming competitive exclusion. • The first chemostat cultivates the unadvantaged competitor. The second cultivates two ones. • The output of the first chemostat is the input of the second one. • We carry out a stability analysis by constructing a Lyapunov functional. We study a nonlinear system of differential delay equations describing a model of a chain of two chemostats, where one contains two microbial species in competition for a single limiting nutrient and receives an external input of the less advantaged competitor, which is cultivated in an external chemostat. We obtain sufficient conditions ensuring coexistence of all the species in competition which consist in upper delay bounds. [ABSTRACT FROM AUTHOR]

A question of ongoing interest for linear Time-delay systems is to determine conditions on the equation parameters that guarantee the exponential stability of solutions. In recent works a new interesting property of time-delay systems was emphasized. As a matter of fact, the multiple spectral values for time-delay systems was characterized by using a Birkhoff/Vandermonde-based approach. Then, a multiplicity induced stability criteria were exhibited for reduced order systems; scalar delay-equations and a special class of second order systems. This work, further explores such a criteria and shows their applicability to the control of a mechanical system. [ABSTRACT FROM AUTHOR]

This paper addresses set invariance properties for linear time-delay systems. More precisely, the first goal of the article is to review known necessary and/or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by linear discrete time-delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the original state space (also called D -invariant sets) by exploiting the forward mappings. The notion of D -invariance is appealing since it provides a region of attraction, which is difficult to obtain for delay systems without taking into account the delayed states in some appropriate extended state space model. The present paper contains a sufficient condition for the existence of ellipsoidal D -contractive sets for dDDEs, and a necessary and sufficient condition for the existence of D -invariant sets in relation to linear time-varying dDDE stability. Another contribution is the clarification of the relationship between convexity (convex hull operation) and D - invariance of linear dDDEs. In short, it is shown that the convex hull of the union of two or more D - invariant sets is not necessarily D - invariant , while the convex hull of a non-convex D - invariant set is D - invariant . [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a process and control simulator for industrial helium cryogenic plants controlled by Programmable Logic Controllers (PLC). This simulator can be used for different purposes such as operator training, test of the PLC programs or the optimization of the plant. The different component models used in the simulator are detailed and explained. Various large scale cryogenic plants used for the particle accelerator LHC (Large Hadron Collider) at CERN have been modeled and simulated. The good agreement between the simulation results and the dynamic behavior of real plants is demonstrated with experimental results. Various discussions complete the presentation. [Copyright &y& Elsevier]

This paper presents a review of past and present results and approaches in the area of motion planning using MIP (Mixed-integer Programming). Although in the early 2000s MIP was still seen with reluctance as method for solving motion planning-related problems, nowadays, due to increases in computational power and theoretical advances, its extensive modeling capabilities and versatility are coming to the fore and enjoy increased application and appreciation. This class of control problems involves, essentially, either a selection from a limited number of alternatives or a constrained optimization problem over a non-convex domain. In both situations, MIP has proven to be an efficient modeling technique as it will be shown in the present review paper. Furthermore, an emphasis is laid on the existing alternatives for implementation and on various experimental validations documented in the literature. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the implementation of a predictive control strategy for Unmanned Air Vehicles in the presence of bounded disturbances. The goal is to prove the feasibility of such a real-time optimization-based control design and to demonstrate its tracking capabilities for the nonlinear dynamics with respect to a reference trajectory which is pre-specified via differential flatness. In order to benefit from the computational advantages of the linear predictive control formulations, an off-line linearization strategy of the nonlinear model of the vehicle along the flat trajectory is employed. The proposed method exhibits effective performance validated through software-in-the-loop simulations and real flight tests on different Unmanned Aerial Vehicles (UAVs). [Copyright &y& Elsevier]

Abstract: In this paper, a PD controller design for haptic systems under delayed feedback is considered. More precisely, a complete stability analysis of a haptic system where local dynamics are described by some second-order mechanical dynamics is presented. Next, using two optimization techniques ( and stability, margin optimization) an optimal choice for the controller gains is proposed. The derived results are tested on a three degree-of-freedom real-time experimental platform to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated. [Copyright &y& Elsevier]