Electrical and Electronic Engineering - Research Publications
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ItemNo Preview AvailableA Multi-Processor Implementation for Networked Control Systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2023)
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ItemNo Preview AvailableOn state estimation for nonlinear systems under random access wireless protocols(SPRINGER LONDON LTD, 2023-03-01)This article is dedicated to Eduardo D. Sontag on the occasion of his 70th birthday. We build upon fundamental stability concepts developed by Sontag, such as input-to-state stability and its related properties, to study a relevant application in industrial internet of things, namely estimation for wireless networked control systems. Particularly, we study emulation-based state estimation for nonlinear plants that communicate with a remote observer over a shared wireless network subject to packet losses. To reduce bandwidth usage, a stochastic communication protocol is employed to determine which node should be given access to the network. Each node has a different successful transmission probability. We describe the overall closed-loop system as a stochastic hybrid model, which allows us to capture the behaviour both between and at transmission instants, whilst covering network features such as random transmission instants, packet losses and stochastic scheduling. We then provide sufficient conditions on the transmission rate that guarantee an input-to-state stability property (in expectation) for the corresponding estimation error system. We illustrate our results in the design of circle criterion observers.
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ItemStability and Persistent Excitation in Signal Sets(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2015-05)Persistent excitation (PE) conditions have been widely used to analyze stability properties of various parameter identification algorithms and to establish uniform global asymptotic stability (UGAS) for a large class of nonlinear time-varying systems. In order to generalize such conditions to a more general setting, a new PE condition is proposed with three basic ingredients: a signal set to represent a family of time functions (e.g., trajectories); a pseudo distance measure to describe the convergence; and some binary relations (e.g., state-to-output relations). Closely related to detectability, this PE condition is a necessary condition to guarantee UGAS. Under uniform global stability and an integral inequality, it becomes a sufficient condition of UGAS. A novel concept: M-pair, which aims at simplifying the checking of the PE condition, is introduced. By using M-pair, it is possible to simplify the structure of the referred signal set (in the spirit of the classic Krasovskii-LaSalle theorem) and to extend the dimension of the reference signal set (similar to the Matrosov theorem). Thus, the framework of M-pair not only unifies these well-known results, but also generates more flexibility in checking the PE conditions. When applied to nonlinear switched systems, three new tools to verify the PE condition are obtained. Finally, an example illustrates that a nonlinear time-varying switched system with arbitrary switching can be shown to be UGAS without using a common Lyapunov function.
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ItemExtremum seeking of dynamical systems via gradient descent and stochastic approximation methods(Elsevier, 2015-06)Abstract This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data framework is the period of the synchronised sampler and hold device, which is also the waiting time during which the system dynamics settle to within a controllable neighbourhood of the steady-state input–output behaviour.
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ItemA refinement of Matrosov's theorem for differential inclusions(PERGAMON-ELSEVIER SCIENCE LTD, 2016-06)This note presents a refinement of Matrosov's theorem for a class of differential inclusions whose set-valued map is defined as a closed convex hull of finitely many vector fields. This class of systems may arise in the analysis of switched nonlinear systems when stability with arbitrary switching between the given vector fields is considered. Assuming uniform global stability of a compact set, it is shown that uniform global attractivity of the set can be verified by tailoring Matrosov functions to individual vector fields. This refinement of Matrosov's theorem is an extension of the existing Matrosov results which may be easier to apply to certain differential inclusions than existing results, as demonstrated by an example.
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ItemOptimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms(Society for Industrial and Applied Mathematics, 2018)This paper formulates the problem of extremum seeking for optimization of cost function 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 the Stiefel manifold V3;2 and the Lie group SEp3q are presented at the end of the paper.
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ItemOvercoming overshoot performance limitations of linear systems with reset control(PERGAMON-ELSEVIER SCIENCE LTD, 2019-03)It is well-known that for a class of minimum-phase relative degree one linear-time-invariant (LTI) systems, with a unit feedback control structure, overshoot necessarily happens if the plant transfer function has poles at origin or unstable poles. This work aims to overcome this overshoot performance limitation (OPL) by using a novel reset controller, which has a generalized first order reset element (GFORE) structure. By tuning parameters of this reset controller carefully, the non-overshoot performance can be ensured. Furthermore, the implementation of the proposed reset controller with a high-pass filter is provided. Parameter tuning guidelines are also provided and, finally, the proposed design is verified with a simulation example.