2,043 research outputs found
Minimally Constrained Stable Switched Systems and Application to Co-simulation
We propose an algorithm to restrict the switching signals of a constrained
switched system in order to guarantee its stability, while at the same time
attempting to keep the largest possible set of allowed switching signals. Our
work is motivated by applications to (co-)simulation, where numerical stability
is a hard constraint, but should be attained by restricting as little as
possible the allowed behaviours of the simulators. We apply our results to
certify the stability of an adaptive co-simulation orchestration algorithm,
which selects the optimal switching signal at run-time, as a function of
(varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication:
Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe.
"Minimally Constrained Stable Switched Systems and Application to
Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL,
USA, 201
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control
This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods
On stability of randomly switched nonlinear systems
This article is concerned with stability analysis and stabilization of
randomly switched nonlinear systems. These systems may be regarded as piecewise
deterministic stochastic systems: the discrete switches are triggered by a
stochastic process which is independent of the state of the system, and between
two consecutive switching instants the dynamics are deterministic. Our results
provide sufficient conditions for almost sure global asymptotic stability using
Lyapunov-based methods when individual subsystems are stable and a certain
``slow switching'' condition holds. This slow switching condition takes the
form of an asymptotic upper bound on the probability mass function of the
number of switches that occur between the initial and current time instants.
This condition is shown to hold for switching signals coming from the states of
finite-dimensional continuous-time Markov chains; our results therefore hold
for Markov jump systems in particular. For systems with control inputs we
provide explicit control schemes for feedback stabilization using the universal
formula for stabilization of nonlinear systems.Comment: 13 pages, no figures. A slightly modified version is scheduled to
appear in IEEE Transactions on Automatic Control, Dec 200
Towards a Global Controller Design for Guaranteed Synchronization of Switched Chaotic Systems
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a sufficient condition for synchronization of identical master-slave switched nonlinear chaotic systems and are expressed in the form of bilinear matrix inequalities (BMIs). The nonlinear controller design problem is then recast in the form of linear matrix inequalities (LMIs) to facilitate numerical computation by standard LMI solvers and is illustrated by appropriate examples
Online Data-Driven Stabilization of Switched Linear Systems
We consider the stabilization problem of a discrete-time system that switches among a finite set of un-known linear subsystems under unknown switching signal. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees exponential stability of the closed-loop switched system under sufficiently slow switching. The effectiveness of the approach is illustrated via a numerical example
Discrete Time Systems
Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area
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