R. Ambrosino

Technical communique: Finite-time stability of linear time-varying systems with jumps

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential-difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Some examples illustrate the effectiveness of the proposed approach.

Sufficient Conditions for Finite-Time Stability of Impulsive Dynamical Systems

The finite-time stability problem for state-dependent impulsive dynamical linear systems (SD-IDLS) is addressed in this note. SD-IDLS are a special class of hybrid systems which exhibit jumps when the state trajectory reaches a resetting set. A sufficient condition for finite-time stability of SD-IDLS is provided. S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of Differential Linear Matrix Inequalities. Since such a formulation may be in general more conservative, a procedure which permits to automate its verification, without introduce conservatism, is given both for second order systems, and when the resetting set is ellipsoidal.

Sensor selection strategies for state estimation in energy constrained wireless sensor networks

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central base station. The base station computes an estimate of the process state by means of a Kalman filter. In this paper we assume that, at each time step, only a subset of all sensors are selected to send their observations to the fusion center due to channel capacity constraints or limited energy budget. We propose a multi-step sensor selection strategy to schedule sensors to transmit for the next T steps of time with the goal of minimizing an objective function related to the Kalman filter error covariance matrix. This formulation, in a relaxed convex form, defines an unified framework to solve a large class of optimization problems over energy constrained WSNs. We offer some numerical examples to further illustrate the efficiency of the algorithm.

Advances in the physics basis for the European DEMO design

In the European fusion roadmap, ITER is followed by a demonstration fusion power reactor (DEMO), for which a conceptual design is under development. This paper reports the first results of a coherent effort to develop the relevant physics knowledge for that (DEMO Physics Basis), carried out by European experts. The program currently includes investigations in the areas of scenario modeling, transport, MHD, heating & current drive, fast particles, plasma wall interaction and disruptions.

Finite-Time Stability and Control

Part I: Linear Systems.- Finite-time Stability Analysis of Continuous-Time Linear Systems.- Controller Design for the Finite-Time Stabilization of Continuous-Time Linear Systems.- Robustness Issues.- Finite-time Stability of Discrete-Time Linear Systems.- Finite-time Stability Analysis via PQLFs.- Part II: Hybrid Systems.- Finite-time Stability of Impulsive Dynamical Linear Systems.- Controller Design for the Finite-time Stability of Impulsive Dynamical Linear Systems.- Robustness Issues for Impulsive Dynamical Linear Systems.

Output feedback control of nonlinear quadratic systems

This paper provides some sufficient conditions for the stabilization of nonlinear quadratic systems via output feedback. The main contribution consists of a design procedure which enables to find a dynamic output feedback controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point. This design procedure is formulated in terms of a Linear Matrix Inequalities (LMIs) feasibility problem, which can be efficiently solved via available optimization algorithms. The effectiveness of the proposed methodology is shown through a numerical example.

Input-output finite-time stability of linear systems

In the recent paper “Input-output finite-time stabilization of linear systems,” (F. Amato ) a sufficient condition for input-output finite-time stability (IO-FTS), when the inputs of the system are L2 signals, has been provided; such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). Roughly speaking, a system is said to be input-output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length T, the outputs of the system do not exceed an assigned threshold during such time interval. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. In this context, this paper presents several novel contributions. First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. Amato is actually also a necessary condition for IO-FTS; at the same time we provide an alternative-still necessary and sufficient-condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). We show that the last condition is computationally more efficient; however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples; in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.

Optimal Sensor Scheduling for Remote Estimation over Wireless Sensor Networks

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared lossy channel to a central base station. The base station computes an estimate of the process state. We consider this remote estimation problem for wireless single-hop communication with the widely used IEEE 802.15.4 Media Access Control (MAC) protocol. Using a Markov chain model for the MAC protocol, we derive an expression for the probability of successful packet transmission λ(N). We show that λ(N) is a monotone decreasing function of the number of sensors N attempting to access the channel. State estimation is better served by having data from more sensor nodes, but this results in decreased probability of successful packet transmission. As a consequence, we are faced with a design trade-off in determining how many sensors should attempt to communicate their observations to the base station and which sensors are most informative for the purpose of state estimation. We show that this problem of optimal sensor selection can be cast as an optimization problem which can be solved approximately using convex programming. The optimal selection of sensors is dynamic and leads, in turn, to the problem of optimal sensor scheduling. We offer a synthetic example to illuminate our ideas.

Input to Output Finite-Time Stabilization of Discrete-Time Linear Systems

Abstract Bounded–Input Bounded–Output (BIBO) stability is usually studied when only the input-output behavior of a dynamical system is of interest. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input–Output FTS (IO-FTS). FTS has been already investigated in several papers in terms of state boundedness, whereas in this work we deal with the characterization of the input-output behavior. A system is said to be input-output finite time stable if, assigned a class of input signals and some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. This paper provides some sufficient conditions for the analysis of IO–FTS and for the design of a static state feedback controller guaranteeing IO–FTS of the closed loop system. The effectiveness of the proposed results is eventually illustrated by means of two numerical examples.

Optimal sensor density for remote estimation over Wireless Sensor Networks

Wireless sensor networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense, process and transmit measured information over a lossy wireless network to a central base station, which processes the data and produces an optimal estimate of the state. In order to provide a quantitative design principles on the density of sensor required, we investigate the tradeoff between the estimation performance and the number of communicating nodes with respect to the major MAC protocols used in WSNs. The correlation between packet reception probability and the number of communicating nodes can be studied by selecting a Markov model for the communication protocol. A multi-sensor measurement fusion model is then used to feed a multi-sensor Kalman filtering algorithm to assess the impact of MAC protocols on estimation performance. The proposed approach is placed in the framework of convex optimization problems. A target tracking example illustrates the proposed approach.