1,721,054 research outputs found
Dual chemical reaction networks and implications for Lyapunov-based structural stability
No full textGiven a class of (bio)Chemical Reaction Networks (CRNs) identified by a stoichiometric matrix S, we define as dual reaction network, CRN*, the class of (bio)Chemical Reaction Networks identified by the transpose stoichiometric matrix S. We consider both the dynamical systems describing the time evolution of the species concentrations and of the reaction rates. First, based on the analysis of the Jacobian matrix, we show that the structural (i.e., parameter-independent) local stability properties are equivalent for a CRN and its dual CRN*. We also assess the structural global stability properties of the two dual networks, analysing both concentration and rate representations. We prove that the existence of a polyhedral (or piecewise-linear) Lyapunov function in concentrations for a CRN is equivalent to the existence of a piecewise-linear in rates Lyapunov function for the dual CRN*; in fact, if V is a polyhedral Lyapunov function for a CRN, the dual polyhedral function V* is a piecewise-linear in rates Lyapunov function for the dual network. We finally show how duality can be exploited to gain additional insight into biochemical reaction networks
Spiking Systems in Population-Infection Dynamics
Full text linkMotivated by a class of models in population dynamics, we introduce the concept of spiking dynamical systems. A spiking system admits an asymptotically stable equilibrium but, under proper perturbations on the initial conditions in a compact region including the equilibrium, its output exhibits a spike of arbitrarily large magnitude before the state returns within the region. We consider a model that describes a well-documented phenomenon in caterpillar-virus dynamics: a sudden increase of the caterpillar population occurs, due to a temporary reduction of the viral population, and is then followed by a sudden decrease. We prove that the caterpillar-virus system is spiking according to our proposed mathematical definition: the model can yield arbitrarily large population densities for caterpillars, and then the original conditions are suddenly restored. When the model also takes into account environmental constraints that keep the caterpillar population bounded, the spike cannot be arbitrarily large, but the population density can get arbitrarily close to the maximal one that can be achieved in the absence of virus
Minimum waiting time scheduling of power supply assignation to variable rate requests
Full text linkThe paper deals with a novel scheduling strategy for the assignation of a power resource. More precisely, a set of tasks, characterized by power requests with variable power rate, such as in the domestic electric appliances, is considered and the strategy aims at minimizing the average waiting time. The main result is that to determine the assignation strategy only the information on the maximum needed power and on the duration of the tasks is required. During the implementation of the strategy, the scheduler needs to periodically obtain, from the appliances, information on the maximum power needed to complete the task. In the case of two tasks, the strategy is shown, both analytically and with simulations, to perform better than a non-interruptible strategy
Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular
No full textFor a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate Lyapunov function
Average flow constraints and stabilizability in uncertain production-distribution systems
No full textConsider multi-inventory systems in presence of uncertain demand and assume that demand is unknown but bounded in an assigned compact set and the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we are interested in a control strategy that satisfies just one of the two requirements: i) meeting at each time all possible current demands (worst case stability) or ii) achieving a pre-defined nominal flow in the average (average flow constraints). We show that if we retain the average constraints and relax worst case stability requirement we can achieve stochastic stability. On the contrary, if we retain the worst case stability and relax the average flow constraints we can optimize the average linear flow cost. In the latter case we provide a tight bound for the cost
Decentralized control of continuous-time production-distribution systems with unknown inputs
No full textSimultaneous performance achievement via compensator blending
No full textIn this paper we consider the problem of designing a state-feedback controller that simultaneously achieves different optimality criteria defined on different input–output pairs. Precisely, if r “optimal” target transfer functions are given (as the result of local “optimal” controllers), it is shown that (under mild assumptions) there exists a unique controller capable of replicating these transfer functions in the closed-loop system,
so simultaneously achieving the performances inherited by the chosen local transfer functions. An explicit and constructive procedure (we refer to such procedure as “compensator blending”) is provided. The possibility of designing a stable blending compensator or the generalization to
dynamic local controllers or time varying systems are also discussed. We finally consider the dual version of the problem, precisely, we show how to achieve simultaneous optimality by filter blending
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