Electrical and Electronic Engineering - Research Publications
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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.
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ItemCo-design of output feedback laws and event-triggering conditions for linear systems( 2014-08-26)We present a procedure to simultaneously design the output feedback law and the event-triggering condition to stabilize linear systems. The closed-loop system is shown to satisfy a global asymptotic stability property and the existence of a strictly positive minimum amount of time between two transmissions is guaranteed. The event-triggered controller is obtained by solving linear matrix inequalities (LMIs). We then exploit the flexibility of the method to maximize the guaranteed minimum amount of time between two transmissions. Finally, we provide a (heuristic) method to reduce the amount of transmissions, which is supported by numerical simulations.
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ItemOptimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms( 2014-12-09)This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization of cost functions defined on smooth Riemannian manifolds. This problem falls within the category of online optimization methods. We introduce the notion of geodesic dithers which is a perturbation of the optimizing trajectory in the tangent bundle of the ambient state manifolds and obtain the extremum seeking closed loop as a perturbation of the averaged gradient system. The main results are obtained by applying closeness of solutions and averaging theory on Riemannian manifolds. The main results are further extended for optimization on Lie groups. Numerical examples on Riemannian manifolds (Lie groups) SOp3q and SEp3q are also presented at the end of the paper.
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ItemTime scale modeling for consensus in sparse directed networks with time-varying topologies( 2016-08-30)The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to densely and intensively connected clusters into aggregate variables. It will be shown that under suitable conditions, the states of the agents in each cluster converge fast toward a local agreement. Local agreements correspond to aggregate variables which slowly converge to consensus. Existing results concerning the time-scale separation in large networks focus on fixed and undirected graphs. The aim of this work is to extend these results to the more general case of time-varying directed topologies. It is noteworthy that in the fixed and undirected graph case the average of the states in each cluster is time-invariant when neglecting the interactions between clusters. Therefore, they are good candidates for the aggregate variables. This is no longer possible here. Instead, we find suitable time-varying weights to compute the aggregate variables as time-invariant weighted averages of the states in each cluster. This allows to deal with the more challenging time-varying directed graph case. We end up with a singularly perturbed system which is analyzed by using the tools of two time-scales averaging which seem appropriate to this system.
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ItemOn Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs( 2017-05-12)The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary condition is proposed to attain the following objective for the perturbed graph: the real parts of the non-zero eigenvalues of its Laplacian matrix are positive. A sufficient condition is also presented that ensures the aforementioned objective for unperturbed graph. It is then highlighted the case where the condition becomes necessary and sufficient. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.
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ItemSupervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm( 2017-09-05)A supervisory observer is a multiple-model architecture, which estimates the parameters and the states of nonlinear systems. It consists of a bank of state observers, where each observer is designed for some nominal parameter values sampled in a known parameter set. A selection criterion is used to select a single observer at each time instant, which provides its state estimate and parameter value. The sampling of the parameter set plays a crucial role in this approach. Existing works require a sufficiently large number of parameter samples, but no explicit lower bound on this number is provided. The aim of this work is to overcome this limitation by sampling the parameter set automatically using an iterative global optimisation method, called DIviding RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np parameter samples where np is the dimension of the parameter set. Then, the algorithm iteratively adds samples to improve its estimation accuracy. Convergence guarantees are provided under the same assumptions as in previous works, which include a persistency of excitation condition. The efficacy of the supervisory observer with the DIRECT sampling policy is illustrated on a model of neural populations.
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ItemA Robust Circle-criterion Observer-based Estimator for Discrete-time Nonlinear Systems in the Presence of Sensor Attacks and Measurement Noise( 2018-05-11)We address the problem of robust state estimation and attack isolation for a class of discrete-time nonlinear systems with positive-slope nonlinearities under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of circle-criterion observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose a estimator that provides robust estimates of the system state in spite of sensor attacks and measurement noise; and an algorithm for detecting and isolating sensor attacks. Our results make use of the ISS property of the observers to check whether the trajectories of observers are consistent with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the results.