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| Abstract: | We propose a symbolic algorithm for the analysis of the robustness of timed automata, that is the correctness of the model in presence of small drifts on the clocks or imprecision in testing guards. This problem is known to be decidable with an algorithm based on detecting strongly connected components on the region graph, which, for complexity reasons, is not effective in practice. Our symbolic algorithm is based on the standard algorithm for symbolic reachability analysis using zones to represent symbolic states and can then be easily integrated within tools for the verification of timed automata models. It relies on the computation of the stable zone of each cycle in a timed automaton. The stable zone is the largest set of states that can reach and be reached from itself through the cycle. To compute the robust reachable set, each stable zone that intersects the set of explored states has to be added to the set of states to be explored. |
| Abstract: | This paper focuses on the control of a team of agents designated either as leaders or followers and exchanging information over a directed communication network. The goal is to drive each follower to a target position that depends on its neighbors. To this purpose, we propose a decentralized control scheme based on sliding--mode techniques and study the position error propagation within the network using the notion of Input--to--State Stability (ISS). In particular, we derive sufficient conditions on the control parameters for guaranteeing that the error dynamics is ISS with respect to the leaders'velocities. Moreover, we show that, under suitable assumptions, the sliding--mode part of the control law is capable of steering the position errors to zero in finite time. The theoretical results are backed up by numerical simulations. |
| Abstract: | In this paper we address the problem of driving a group of agents towards a consensus point when agents have a discrete-time integrator dynamics and the communication graph is time-varying. We propose two decentralized Model Predictive Control (MPC) schemes that take into account constraints on the agents'inputs and show that they guarantee consensus under mild assumptions. Since the global cost does not decrease monotonically, it cannot be used as a Lyapunov function for proving convergence to consensus. Rather, our proofs exploit geometric properties of the optimal path followed by individual agents. |
| Abstract: | Optimizing energy transfer from an ac source to a load is a classical problem in electrical engineering. The design of power apparatus is such that the bulk of the transfer occurs at the fundamental frequency of the source. In practice, the efficiency of this transfer is typically reduced due to the phase shift between voltage and current at the fundamental frequency. The phase shift arises largely due to energy flows characterizing electric motors that dominate the aggregate load. The power factor, defined as the ratio between the real or active power (average of the instantaneous power) and the apparent power (the product of rms values of the voltage and current), then captures the energy-transmission efficiency for a given load. The main contribution of this article is the identification of the key role played by cyclodissipativity [15], [16] in power-factor compensation. We prove that a necessary and sufficient condition for a parallel (shunt) lossless compensator to improve the power factor is that the overall system satisfy a cyclodissipativity property. In the spirit of standard passivation [17], this result leads naturally to a formulation of the power-factor-compensation problem as one of rendering the load cyclodissipative. Consequently, we show that cyclodissipativity provides a rigorous mathematical framework for analyzing and designing powerfactor compensators for general nonlinear loads operating in nonsinusoidal regimes. |
| Abstract: | We investigate the resource allocation problem for large-scale server clusters with quality-of-service objectives, where key functions are decentralized. Specifically, the optimal service selection is posed as a discrete utility maximization problem that reflects management objectives and resource constraints. We develop an efficient centralized algorithm that solves this problem, and we propose three suboptimal schemes that operate with local information. The performance of the suboptimal schemes is evaluated in simulations, both under idealized conditions and in a full-scale system simulator. |
| Abstract: | The logic-dynamical hybrid system given by a set of subsystems which are linear differential-difference equations with constant coefficients and constant delay is investigated in the paper. The estimations of disturbances of such system are obtained. We consider the cases of stable and unstable subsystems. Besides the estimations of solutions of hybrid system given by a set of scalar subsystems are obtained. |
| Abstract: | This tutorial paper is concerned with the identification of hybrid models, i.e. dynamical models whose behavior is determined by interacting continuous and discrete dynamics. Methods specifically aimed at the identification of models with a hybrid structure are of very recent date. After discussing the main issues and difficulties connected with hybrid system identification, and giving an overview of the related literature, this paper focuses on four different approaches for the identification of switched affine and piecewise affine models, namely an algebraic procedure, a Bayesian procedure, a clustering-based procedure, and a bounded-error procedure. The main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested. |
| Abstract: | A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input?output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied. |
| Abstract: | We consider the problem of joint end-to-end bandwidth allocation and radio resource management in WiMax single-carrier wireless networks. The design problem is posed as a utility maximization problem subject to link rate constraints which involve transmission scheduling and power allocation. Inspired by a centralized algorithm for solving the associated optimization problem, we proceed systematically in our development of distributed resource allocation mechanisms. Contrary to the centralized algorithm, the proposed solution is distributed and of low computational complexity, generates schedules of finite length and with fixed time-slot durations, and acts on local neighborhood information only. Although the final scheme is suboptimal, we isolate and quantify the performance losses incurred and demonstrate strong performance in examples. |
| Abstract: | The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models. |
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