 Electrical and Electronic Engineering  Research Publications
Electrical and Electronic Engineering  Research Publications
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ItemA unifying Lyapunovbased framework for the eventtriggered control of nonlinear systemsPostoyan, R ; Anta, A ; Nesic, D ; Tabuada, P ( 20110828)We present a prescriptive framework for the eventtriggered control of nonlinear systems. Rather than closing the loop periodically, as traditionally done in digital control, in eventtriggered implementations the loop is closed according to a statedependent criterion. Eventtriggered control is especially well suited for embedded systems and networked control systems since it reduces the amount of resources needed for control such as communication bandwidth. By modeling the eventtriggered implementations as hybrid systems, we provide Lyapunovbased conditions to guarantee the stability of the resulting closedloop system and explain how they can be utilized to synthesize eventtriggering rules. We illustrate the generality of the approach by showing how it encompasses several existing eventtriggering policies and by developing new strategies which further reduce the resources needed for control.

ItemEventtriggered and selftriggered stabilization of distributed networked control systemsPostoyan, R ; Tabuada, P ; Nesic, D ; Anta, A ( 20110828)Eventtriggered and selftriggered control have recently been proposed as implementation strategies that considerably reduce the resources required for control. Although most of the work so far has focused on closing a single control loop, some researchers have started to investigate how these new implementation strategies can be applied when closing multiplefeedback loops in the presence of physically distributed sensors and actuators. In this paper, we consider a scenario where the distributed sensors, actuators, and controllers communicate via a shared wired channel. We use our recent prescriptive framework for the eventtriggered control of nonlinear systems to develop novel policies suitable for the considered distributed scenario. Afterwards, we explain how selftriggering rules can be deduced from the developed eventtriggered strategies.

ItemMaximumHandsOff Control and L1 OptimalityNagahara, M ; Quevedo, DE ; Nesic, D ( 20130731)In this article, we propose a new paradigm of control, called a maximumhandsoff control. A handsoff control is defined as a control that has a much shorter support than the horizon length. The maximumhandsoff control is the minimumsupport (or sparsest) control among all admissible controls. We first prove that a solution to an L 1 optimal control problem gives a maximumhandsoff control, and vice versa. This result rationalizes the use of L 1 optimality in computing a maximumhandsoff control. The solution has in general the ”bangoffbang” property, and hence the control may be discontinuous. We then propose an L 1 /L 2 optimal control to obtain a continuous handsoff control. Examples are shown to illustrate the effectiveness of the proposed control method.

ItemEventtriggered transmission for linear control over communication channelsForni, F ; Galeani, S ; Nesic, D ; Zaccarian, L ( 20131003)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 “transmissionlazy” sensors whose goal is to transmit the measured plant output information as little as possible while preserving closedloop 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.

ItemA Local Characterization of Lyapunov Functions and Robust Stability of Perturbed Systems on Riemannian ManifoldsTaringoo, F ; Dower, PM ; Nešić, D ; Tan, Y ( 20131031)This paper proposes converse Lyapunov theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of Lyapunov functions with respect to the Riemannian distance function. We extend classical Lyapunov converse theorems for dynamical systems in R n to dynamical systems evolving on Riemannian manifolds. This is performed by restricting our analysis to the so called normal neighborhoods of equilibriums on Riemannian manifolds. By employing the derived properties of Lyapunov functions, we obtain the stability of perturbed dynamical systems on Riemannian manifolds.

ItemAveraging for nonlinear systems evolving on Riemannian manifoldsTaringoo, F ; Nešić, D ; Tan, Y ; Dower, PM ( 20131111)This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on R n to dynamical systems defined on Riemannian manifolds by employing differential geometry. A generalization of closeness of solutions for periodic dynamical systems on compact time intervals is derived for dynamical systems evolving on compact Riemannian manifolds. Under local asymptotic (exponential) stability of the average vector field, we further relax the compactness of the ambient Riemannian manifold and obtain the closeness of solutions on the infinite time interval by employing the notion of uniform normal neighborhoods of an equilibrium point of a vector field. These results are also presented for timevarying dynamical systems where their averaged systems are almost globally asymptotically or exponentially stable on compact manifolds. The main results of the paper are illustrated by several examples.

ItemParameter and state estimation of nonlinear systems using a multiobserver under the supervisory frameworkChong, MS ; Nešić, D ; Postoyan, R ; Kuhlmann, L ( 20140318)We present a hybrid scheme for the parameter and state estimation of nonlinear continuoustime systems, which is inspired by the supervisory setup used for control. State observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant, which provides state and parameter estimates. Assuming that a persistency of excitation condition holds, the convergence of the parameter and state estimation errors to zero is ensured up to a margin, which can be made as small as desired by increasing the number of observers. To reduce the potential computational complexity of the scheme, we explain how the sampling of the parameter set can be dynamically updated using a zoomin procedure. This strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy. The results are shown to be applicable to linear systems and to a class of nonlinear systems. We illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model.

ItemHandsOff Control as Green ControlNagahara, M ; Quevedo, DE ; Nesic, D ( 20140709)In this article, we introduce a new paradigm of control, called handsoff control, which can save energy and reduce CO2 emissions in control systems. A handsoff control is defined as a control that has a much shorter support than the horizon length. The maximum handsoff control is the minimum support (or sparsest) control among all admissible controls. With maximum handsoff control, actuators in the feedback control system can be stopped during time intervals over which the control values are zero. We show the maximum handsoff control is given by L 1 optimal control, for which we also show numerical computation formulas.

ItemMaximum HandsOff Control: A Paradigm of Control Effort MinimizationNagahara, M ; Quevedo, DE ; Nesic, D ( 20140813)In this paper, we propose a paradigm of control, called a maximum handsoff control. A handsoff control is defined as a control that has a short support per unit time. The maximum handsoff control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon continuoustime control, we show the equivalence between the maximum handsoff control and L 1 optimal control under a uniqueness assumption called normality. This result rationalizes the use of L 1 optimality in computing a maximum handsoff control. The same result is obtained for discretetime handsoff control. We also propose an L 1 / L 2 optimal control to obtain a smooth handsoff control. Furthermore, we give a selftriggered feedback control algorithm for linear timeinvariant systems, which achieves a given sparsity rate and practical stability in the case of plant disturbances. An example is included to illustrate the effectiveness of the proposed control.

ItemStabilization of nonlinear systems using eventtriggered output feedback controllersAbdelrahim, M ; Postoyan, R ; Daafouz, J ; Nešić, D ( 20140825)The objective is to design output feedback eventtriggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from eventtriggered and timetriggered control. The idea is to turn on the eventtriggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of timedriven sampleddata systems. The overall strategy ensures an asymptotic stability property for the closedloop system. The results are proved to be applicable to linear timeinvariant (LTI) systems as a particular case.
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