Electrical and Electronic Engineering - Research Publications
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ItemNo Preview AvailableReachability of Linear Time-Invariant Systems via Ellipsoidal Approximations(Elsevier BV, 2023-01-01)
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ItemExtremum seeking control of cascaded Raman optical amplifiers(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2008-05-01)This paper considers the control of a particular type of optical amplifier that finds application in long-haul wavelength division multiplexed optical communications systems. The objective of this consideration is to demonstrate an application of extremum seeking to the regulation of amplifier output signal power across a range of signal wavelengths, where limited control authority is available. Although such amplifiers are nonlinear and distributed parameter devices, an extremum seeking design is demonstrated to be a promising approach for achieving the stated amplifier control objectives.
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ItemAnalysis of input-to-state stability for discrete time nonlinear systems via dynamic programming(Elsevier, 2005-12-01)The input-to-state stability (ISS) property for systems with disturbances has received considerable attention over the past decade or so, with many applications and characterizations reported in the literature. The main purpose of this paper is to present analysis results for ISS that utilize dynamic programming techniques to characterize minimal ISS gains and transient bounds. These characterizations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimization problems in nonlinear dissipative systems theory (including L2-gain analysis and nonlinear H∞ theory). As such, the results presented address an obvious gap in the literature.
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ItemA unified approach to controller design for achieving ISS and related properties(Institute of Electrical and Electronics Engineers, 2005-11-01)A unified approach to the design of controllers achieving various specified input-to-state stability (ISS) like properties is presented. Both full state and measurement feedback cases are considered. Synthesis procedures based on dynamic programming are given using the recently developed results on controller synthesis to achieve uniform l/sup /spl infin// bound. Our results provide a link between the ISS literature and the nonlinear H/sup /spl infin// design literature.
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ItemA note on input-to-state stability and averaging of systems with inputs(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2001-11)Two different definitions of an average for time-varying systems with inputs and a small parameter that were recently introduction in the literature are considered: "strong" and "weak" averages. It is shown that if the strong average is input-to-state stable (ISS), then the solutions of the actual system satisfy an integral bound in a semiglobal practical sense. The integral bound that we prove can be viewed as a generalization of the notion of finite-gain L2 stability, that was recently introduced in the literature. A similar result is proved for weak averages but the class of inputs for which the integral bound holds is smaller (Lipschitz inputs) than in the case of strong averages (measurable inputs).
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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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ItemA max-plus primal space fundamental solution for a class of differential Riccati equations(SPRINGER LONDON LTD, 2017-09)
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ItemReaching Agreement in Quantum Hybrid Networks(Nature Publishing Group, 2017-07-20)We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. In this way the quantum-opeartion/classical-communication nature of hybrid quantum networks is captured, although coherent states and joint operations are not taken into consideration in order to facilitate a clear and explicit analysis. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network’s initial values.
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ItemObserver design for non-linear networked control systems with persistently exciting protocols(IEEE, 2020-07)We study the design of state observers for nonlinear networked control systems (NCSs) affected by disturbances and measurement noise, via an emulation-like approach. That is, given an observer designed with a specific stability property in the absence of communication constraints, we implement it over a network and we provide sufficient conditions on the latter to preserve the stability property of the observer. In particular, we provide a bound on the maximum allowable transmission interval (MATI) that guarantees an input-to-state stability (ISS) property for the corresponding estimation error system. The stability analysis is trajectory-based, utilises small-gain arguments, and exploits a persistently exciting (PE) property of the scheduling protocols. This property is key in our analysis and allows us to obtain significantly larger MATI bounds in comparison to the ones found in the literature. Our results hold for a general class of NCSs, however, we show that these results are also applicable to NCSs implemented over a specific physical network called WirelessHART (WH). The latter is mainly characterised by its multi-hop structure, slotted communication cycles, and the possibility to simultaneously transmit over different frequencies. We show that our results can be further improved by taking into account the intrinsic structure of the WH-NCS model. That is, we explicitly exploit the model structure in our analysis to obtain an even tighter MATI bound that guarantees the same ISS property for the estimation error system. Finally, to illustrate our results, we present analysis and numerical simulations for a class of Lipschitz non-linear systems and high-gain observers.
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ItemSynthesis of control Lyapunov functions and stabilizing feedback strategies using exit-time optimal control Part II: Numerical approach(WILEY, 2021-09)Abstract This paper continues the study (Yegorov, Dower, and Grüne et al.) and develops a curse‐of‐dimensionality‐free numerical approach to feedback stabilization, whose theoretical foundation was built in Yegorov et al. and involved the characterization of control Lyapunov functions (CLFs) via exit‐time optimal control. First, we describe an auxiliary linearization‐based technique for the construction of a local CLF and discuss how to determine its appropriate sublevel set that can serve as the terminal set in the exit‐time optimal control problem leading to a global or semi‐global CLF. Next, the curse of complexity is addressed with regard to the approximation of CLFs and associated feedback strategies in high‐dimensional regions. The goal is to enable for efficient model predictive control implementations with essentially faster (though less accurate) online policy updates than in case of solving direct or characteristics‐based nonlinear programming problems for each sample instant. We propose a computational approach that combines gradient enhanced modifications of the Kriging and inverse distance weighting frameworks for scattered grid interpolation. It in particular allows for convenient offline inclusion of new data to improve obtained approximations (machine learning can be used to select relevant new sparse grid nodes). Moreover, our method is designed so as to a priori return proper values of the CLF interpolant and its gradient on the entire terminal set of the considered exit‐time optimal control problem. Supporting numerical simulation results are also presented.