Electrical and Electronic Engineering - Research Publications
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ItemA unifying Lyapunov-based framework for the event-triggered control of nonlinear systems( 2011-08-28)We present a prescriptive framework for the event-triggered control of nonlinear systems. Rather than closing the loop periodically, as traditionally done in digital control, in event-triggered implementations the loop is closed according to a state-dependent criterion. Event-triggered 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 event-triggered implementations as hybrid systems, we provide Lyapunov-based conditions to guarantee the stability of the resulting closed-loop system and explain how they can be utilized to synthesize event-triggering rules. We illustrate the generality of the approach by showing how it encompasses several existing event-triggering policies and by developing new strategies which further reduce the resources needed for control.
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ItemEvent-triggered and self-triggered stabilization of distributed networked control systems( 2011-08-28)Event-triggered and self-triggered 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 multiple-feedback 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 event-triggered control of nonlinear systems to develop novel policies suitable for the considered distributed scenario. Afterwards, we explain how self-triggering rules can be deduced from the developed event-triggered strategies.
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ItemMaximum-Hands-Off Control and L1 Optimality( 2013-07-31)In this article, we propose a new paradigm of control, called a maximum-hands-off control. A hands-off control is defined as a control that has a much shorter support than the horizon length. The maximum-hands-off control is the minimum-support (or sparsest) control among all admissible controls. We first prove that a solution to an L 1 -optimal control problem gives a maximum-handsoff control, and vice versa. This result rationalizes the use of L 1 optimality in computing a maximum-hands-off control. The solution has in general the ”bang-off-bang” property, and hence the control may be discontinuous. We then propose an L 1 /L 2 -optimal control to obtain a continuous hands-off control. Examples are shown to illustrate the effectiveness of the proposed control method.
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ItemEvent-triggered transmission for linear control over communication channels( 2013-10-03)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.
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ItemA Local Characterization of Lyapunov Functions and Robust Stability of Perturbed Systems on Riemannian Manifolds( 2013-10-31)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.
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ItemAveraging for nonlinear systems evolving on Riemannian manifolds( 2013-11-11)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 time-varying 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.
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ItemParameter and state estimation of nonlinear systems using a multi-observer under the supervisory framework( 2014-03-18)We present a hybrid scheme for the parameter and state estimation of nonlinear continuous-time 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 zoom-in 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.
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ItemHands-Off Control as Green Control( 2014-07-09)In this article, we introduce a new paradigm of control, called hands-off control, which can save energy and reduce CO2 emissions in control systems. A hands-off control is defined as a control that has a much shorter support than the horizon length. The maximum hands-off control is the minimum support (or sparsest) control among all admissible controls. With maximum hands-off control, actuators in the feedback control system can be stopped during time intervals over which the control values are zero. We show the maximum hands-off control is given by L 1 optimal control, for which we also show numerical computation formulas.
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ItemMaximum Hands-Off Control: A Paradigm of Control Effort Minimization( 2014-08-13)In this paper, we propose a paradigm of control, called a maximum hands-off control. A hands-off control is defined as a control that has a short support per unit time. The maximum hands-off control is the minimum support (or sparsest) per unit time among all controls that achieve control objectives. For finite horizon continuous-time control, we show the equivalence between the maximum hands-off 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 hands-off control. The same result is obtained for discrete-time hands-off control. We also propose an L 1 / L 2 -optimal control to obtain a smooth hands-off control. Furthermore, we give a self-triggered feedback control algorithm for linear time-invariant 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.
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ItemStabilization of nonlinear systems using event-triggered output feedback controllers( 2014-08-25)The objective is to design output feedback event-triggered 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 event-triggered and time-triggered control. The idea is to turn on the event-triggering 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 time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.