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Event-triggered transmission for linear control over communication channels Forni, Fulvio ; ; et al in Automatica (2014), 50(2), 490498 We consider an exponentially stable closed loop interconnection of a continuous linear plant and a continuous linear controller, and we study the problem of interconnecting the plant output to the ... [more ▼] We consider an exponentially stable closed loop interconnection of a continuous linear plant and a continuous linear controller, and we study the problem of interconnecting the plant output to the controller input through a digital channel. We propose a family of "transmission-lazy" sensors whose goal is to transmit the measured plant output information as little as possible while preserving closed-loop stability. In particular, we propose two transmission policies, providing conditions on the transmission parameters. These guarantee global asymptotic stability when the plant state is available or when an estimate of the state is available (provided by a classical continuous linear observer). Moreover, under a specific condition, they guarantee global exponential stability [less ▲] Detailed reference viewed: 22 (1 ULg)Reference mirroring for control with impacts Forni, Fulvio ; ; in Daafouz, Jamal; Tarbouriech, Sophie; Sigalotti, Mario (Eds.) Hybrid Systems with Constraints (2013) We illustrate a peculiar concept of mirrored reference to address reference tracking control systems for plants subject to impacts. The idea is based on the constructions of artiﬁcial references ... [more ▼] We illustrate a peculiar concept of mirrored reference to address reference tracking control systems for plants subject to impacts. The idea is based on the constructions of artiﬁcial references corresponding to suitable reﬂections of the actual reference performed with respect to the impacting surfaces. We illustrate the application of this idea to reference tracking and state observation for a number of examples of control systems subject to impacts: a one-dimensional hammer hitting a surface, a two-dimensional Newton’s cradle, a two-dimensional mass moving in a planar equilateral triangle and a mass moving in an n-dimensional polyhedral region. For each one of these examples, we provide controllers inducing global exponential stability of the error dynamics. Despite the apparently different nature among the examples, we show that the controller/observer design follows the same paradigm based on mirrored references and we highlight the similarities of the different proofs by showing that they are all based on a speciﬁc result about Lyapunov conditions for global exponential stability of hybrid dynamical systems. [less ▲] Detailed reference viewed: 50 (6 ULg)Follow the bouncing ball: global results on tracking and state estimation with impacts Forni, Fulvio ; ; in IEEE Transactions on Automatic Control (2013) In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories ... [more ▼] In this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations. [less ▲] Detailed reference viewed: 55 (5 ULg)Lyapunov-based sufficient conditions for exponential stability in hybrid systems ; Forni, Fulvio ; in IEEE Transactions on Automatic Control (2013) Lyapunov-based sufficient conditions for exponential stability in hybrid systems are presented. The focus is on converting non-strict Lyapunov conditions, having certain observability properties, into ... [more ▼] Lyapunov-based sufficient conditions for exponential stability in hybrid systems are presented. The focus is on converting non-strict Lyapunov conditions, having certain observability properties, into strict Lyapunov conditions for exponential stability. Both local and global results are considered. The utility of the results is illustrated through an example. [less ▲] Detailed reference viewed: 146 (4 ULg)Antiwindup regulation of saturated linear systems Forni, Fulvio ; ; Sepulchre, Rodolphe in 51st IEEE Conference on Decision and Control (2012, December) We consider the output regulation problem for linear systems subject to actuators saturation. A state-feedback unconstrained regulator is transformed into an error-feedback bounded regulator by ... [more ▼] We consider the output regulation problem for linear systems subject to actuators saturation. A state-feedback unconstrained regulator is transformed into an error-feedback bounded regulator by introducing an observer which is then decomposed into the sum of "unconstrained" and "antiwindup" dynamics. The unconstrained dynamics are regulated towards a predefined reference trajectory, by a control signal u which may violate the saturation bounds during transients. The antiwindup dynamics transiently store the mismatch between unconstrained and constrained dynamics. The antiwindup design also applies to a predefined error-feedback dynamic regulator for the unconstrained system, as in standard antiwindup setting. As a particular case of distinct interest, the design provides a new global asymptotic stabilizer for saturated null-controllable systems. [less ▲] Detailed reference viewed: 89 (21 ULg)Model recovery anti-windup for continuous-time rate and magnitude saturated linear plants Forni, Fulvio ; ; in Automatica (2012), 48(8), 15021513 In this paper two approaches are given for anti-windup design for nonlinear control systems with linear plants subject to limitations both in the magnitude and the rate of variation of the control input ... [more ▼] In this paper two approaches are given for anti-windup design for nonlinear control systems with linear plants subject to limitations both in the magnitude and the rate of variation of the control input. Both approaches are based on the so-called Model Recovery Anti-windup (MRAW) framework. The ﬁrst approach is built by treating the rate+magnitude saturation as a single dynamic nonlinearity, while in the second one, the dynamic compensator dynamics is extended with extra states to treat the two saturations separately. Both approaches lead to global stability with exponentially stable plants and local stability in all other cases. For both approaches, stability and performance guarantees are proven, numerical recipes are given and the relative merits are comparatively highlighted on a simulation example. [less ▲] Detailed reference viewed: 72 (40 ULg)Global tracking and state estimation with non- smooth impacts for a mass confined to an n-dimensional half-space Forni, Fulvio ; ; in IFAC Conference on Analysis and Design of Hybrid Systems (ADHS 12) (2012) We formulate tracking and state-estimation problems of a translating mass moving in an n-dimensional space and impacting on a hyperplane. Due to the discontinuous trajectories arising from the nonsmooth ... [more ▼] We formulate tracking and state-estimation problems of a translating mass moving in an n-dimensional space and impacting on a hyperplane. Due to the discontinuous trajectories arising from the nonsmooth impacts, we use hybrid systems stability analysis tools to establish that 1) a tracking control algorithm and 2) an observer algorithm guarantee global exponential stability. Then, based on a separation principle, we combine the two constructions above to design a dynamic output feedback controller ensuring asymptotic tracking. [less ▲] Detailed reference viewed: 56 (19 ULg)Tracking Control in Billiards Using Mirrors without Smoke, Part I: Lyapunov-Based Local Tracking in Polyhedral Regions Forni, Fulvio ; ; in 50th IEEE Conference on Decision and Control (cdc 2011) (2011) In this paper we formulate the tracking problem of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous dynamics arising from nonsmooth ... [more ▼] In this paper we formulate the tracking problem of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous dynamics arising from nonsmooth impacts, the tracking problem is formulated within a hybrid systems framework and a Lyapunov function is given, which decreases during flow (continuous motion) and remains constant across jumps (impacts of the masses). To guarantee non-increase of the Lyapunov function at jumps, we introduce a novel concept of mirrored images of the target mass and prove that, with this concept, local tracking is achieved. Several simulations illustrate the effectiveness of the proposed approach as compared to alternative solutions. In a companion paper [6] we address global results and generalize the local approach to curved billiards. [less ▲] Detailed reference viewed: 14 (5 ULg)Reset passivation of nonlinear controllers via a suitable time-regular reset map Forni, Fulvio ; ; in Automatica (2011), 47(9), 2099-2106 For a class of square continuous-time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule ... [more ▼] For a class of square continuous-time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous-time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant. [less ▲] Detailed reference viewed: 43 (12 ULg)A Family of Global Stabilizers for Quasi-Optimal Control of Planar Linear Saturated Systems Forni, Fulvio ; ; in IEEE Transactions on Automatic Control (2010), 55(5), 1175-1180 We propose a family of nonlinear state feedback global stabilizers for all planar linear systems which are globally stabilizable by bounded inputs (namely, all non exponentially unstable linear systems ... [more ▼] We propose a family of nonlinear state feedback global stabilizers for all planar linear systems which are globally stabilizable by bounded inputs (namely, all non exponentially unstable linear systems). This family is parametrized by a nonlinear function whose selection can yield quasi time-optimal responses, where the "quasi" is required to achieve local exponential stability of the closed loop. The arising trajectories are quasi-time-optimal for arbitrarily large initial conditions; so, we expect the very simple proposed nonlinear control law to be very useful for embedded control applications with strong computational constraints. [less ▲] Detailed reference viewed: 32 (11 ULg)Results on Passification of Nonlinear Controllers Via a Suitable Time-Regular Reset Map Forni, Fulvio ; ; in 8th IFAC Symposium on nonlinear control systems (2010) For a class of square continuous time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule ... [more ▼] For a class of square continuous time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant. [less ▲] Detailed reference viewed: 16 (5 ULg)Model Recovery Anti-Windup for plants with rate and magnitude saturation Forni, Fulvio ; ; in European Control Conference (2009) (2009) In this paper two alternative approaches are provided to design an anti-windup compensator for control systems subject to limitations both in the magnitude and the rate of variation of the plant input ... [more ▼] In this paper two alternative approaches are provided to design an anti-windup compensator for control systems subject to limitations both in the magnitude and the rate of variation of the plant input. For both approaches, constructive numerical recipes are given and the relative merits are highlighted. [less ▲] Detailed reference viewed: 51 (8 ULg)Globally stabilizing quasi time-optimal control of planar saturated linear systems Forni, Fulvio ; ; in 16th Mediterranean Conference on Control and Automation (2008) (2008) Detailed reference viewed: 8 (3 ULg) |
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