13,470 research outputs found

    Co-design of aperiodic sampled-data min-jumping rules for linear impulsive, switched impulsive and sampled-data systems

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    Co-design conditions for the design of a jumping-rule and a sampled-data control law for impulsive and impulsive switched systems subject to aperiodic sampled-data measurements are provided. Semi-infinite discrete-time Lyapunov-Metzler conditions are first obtained. As these conditions are difficult to check and generalize to more complex systems, an equivalent formulation is provided in terms of clock-dependent (infinite-dimensional) matrix inequalities. These conditions are then, in turn, approximated by a finite-dimensional optimization problem using a sum of squares based relaxation. It is proven that the sum of squares relaxation is non conservative provided that the degree of the polynomials is sufficiently large. It is emphasized that acceptable results are obtained for low polynomial degrees in the considered examples.Comment: 27 pages; 5 figure

    Cooperative Global Robust Stabilization for a Class of Nonlinear Multi-Agent Systems and its Application

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    This paper studies the cooperative global robust stabilization problem for a class of nonlinear multi-agent systems. The problem is motivated from the study of the cooperative global robust output regulation problem for the class of nonlinear multi-agent systems in normal form with unity relative degree which was studied recently under the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition. We first solve the stabilization problem by using the multiple Lyapunov functions approach and the average dwell time method. Then, we apply this result to the cooperative global robust output regulation problem for the class of nonlinear systems in normal form with unity relative degree under directed switching network, and have removed the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition.Comment: 9 pages, 1 figure. This paper was submitted to the journal "Automatica

    Stabilization Based Networked Predictive Controller Design for Switched Plants

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    Stabilizing state feedback controller has been designed in this paper for a switched DC motor plant, controlled over communication network. The switched system formulation for the networked control system (NCS) with additional switching in a plant parameter along with the switching due to random packet losses, have been formulated as few set of non-strict Linear Matrix Inequalities (LMIs). In order to solve non-strict LMIs using standard LMI solver and to design the stabilizing state feedback controller, the Cone Complementary Linearization (CCL) technique has been adopted. Simulation studies have been carried out for a DC motor plant, operating at two different sampling times with random switching in the moment of inertia, representing sudden jerks.Comment: 6 pages, 4 figure

    Convex lifted conditions for robust stability analysis and stabilization of linear discrete-time switched systems

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    Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed by Geromel and Colaneri. The convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables. The convexity of the conditions can be exploited to extend the results to uncertain systems, control design and â„“2\ell_2-gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.Comment: 9 pages, 3 figure

    A para-model agent for dynamical systems

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    Consider a dynamical system u↦x,x˙=fnl(x,u)u \mapsto x, \dot{x} = f_{nl}(x,u) where fnlf_{nl} is a nonlinear (convex or nonconvex) function, or a combination of nonlinear functions that can eventually switch. We present, in this preliminary work, a generalization of the standard model-free control, that can either control the dynamical system, given an output reference trajectory, or optimize the dynamical system as a derivative-free optimization based "extremum-seeking" procedure. Multiple applications are presented and the robustness of the proposed method is studied in simulation.Comment: 41 pages, 38 figures, partially presented at the French Symposium of Electrical Engineering in Grenoble, Jun. 2016 and at the Sparse days in St Girons III, Jul. 201

    Stability analysis of positive semi-Markovian jump linear systems with state resets

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    This paper studies the mean stability of positive semi-Markovian jump linear systems. We show that their mean stability is characterized by the spectral radius of a matrix that is easy to compute. In deriving the condition we use a certain discretization of a semi-Markovian jump linear system that preserves stability. Also we show a characterization for the exponential mean stability of continuous-time positive Markovian jump linear systems. Numerical examples are given to illustrate the results

    Input-Output Finite-Time Stability

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    This paper introduces the extension of Finite-Time Stability (FTS) to the input-output case, namely the Input-Output FTS (IO-FTS). The main differences between classic IO stability and IO-FTS are that the latter involves signals defined over a finite time interval, does not necessarily require the inputs and outputs to belong to the same class of signals, and that quantitative bounds on both inputs and outputs must be specified. This paper revises some recent results on IO-FTS, both in the context of linear systems and in the context of switching systems. In the final example the proposed methodology is used to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.Comment: 14 pages, 9 figures, 2 tables. This paper has been accepted for presentation at AUTOMATICA.IT, Convegno Annuale dei Docenti e Ricercatori Italiani in Automatica, Pisa, Italy, September 201

    Model Predictive Control for Regular Linear Systems

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    The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modelled by partial differential equations. The structure-preserving Cayley-Tustin transformation is utilized to approximate the continuous-time system by a discrete-time model representation without using any spatial discretization or model reduction. The discrete-time model is utilized in the design of model predictive controller accounting for optimality, stabilization, and input and output/state constraints in an explicit way. The proposed model predictive controller is dual-mode in the sense that predictive controller steers the state to a set where exponentially stabilizing unconstrained feedback can be utilized without violating the constraints. The construction of the model predictive controller leads to a finite-dimensional constrained quadratic optimization problem easily solvable by standard numerical methods. Two representative examples of partial differential equations are considered.Comment: 19 pages, 4 figure

    Robust stability and stabilization of uncertain linear positive systems via Integral Linear Constraints: L1- and Linfinity-gains characterization

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    Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for robustness and performance analysis using L1- and Linfinity-gains. Robust stability analysis is performed using Integral Linear Constraints (ILCs) for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's Theorem. Several examples are provided for illustration.Comment: Accepted in the International Journal of Robust and Nonlinear Contro

    Fractional-order Generalized Principle of Self-Support (FOG PSS) in Control Systems Design

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    This paper reviews research that studies the principle of self-support (PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time. The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics, high precision linear motor system, multi-axis high precision positioning system with unmeasurable variables, imprecise sensor information, uncertain parameters and external disturbances. More generally, by formulating the fractional PSS concept as a new generalized framework, we will focus in the possible fields on the fractional-order control problems such as practical tracking, λ\lambda-tracking, etc. of robot systems, multiple mobile agents, discrete dynamical systems, time delay systems and other uncertain nonlinear systems. Finally, the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support (FOGPSS) control strategy
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