Electrical and Electronic Engineering - Research Publications
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ItemAveraging for nonlinear systems on Riemannian manifolds(IEEE, 2013)This paper provides a derivation of the averaging methods for nonlinear time-varying dynamical systems defined on Riemannian manifolds. We extend the results on ℝ n to Riemannian manifolds by employing the language of differential geometry.
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ItemExtremum seeking control for nonlinear systems on compact Riemannian manifolds(IEEE Press, 2014)This paper formulates the extremum seeking control problem for nonlinear dynamical systems which evolve on Riemannian manifolds and presents stability results for a class of numerical algorithms defined in this context. The results are obtained based upon an extension of extremum seeking algorithms in Euclidean spaces and a generalization of Lyapunov stability theory for dynamical systems defined on Rimannian manifolds. We employ local properties of Lyapunov functions to extend the singular perturbation analysis on Riemannian manifolds. Consequently, the results of the singular perturbation on manifolds are used to obtain the convergence of extremum seeking algorithms for dynamical systems on Riemannian manifolds.
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ItemCoordination of blind agents on Lie groups(IEEE, 2015)This paper presents an algorithm for the synchronization of blind agents evolving on a connected Lie group. We employ the method of extremum seeking control for nonlinear dynamical systems defined on connected Riemannian manifolds to achieve the synchronization among the agents. This approach is independent of the underlying graph of the system and each agent updates its position on the connected Lie group by only receiving the synchronization cost function.
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ItemCloseness of solutions and averaging for nonlinear systems on Riemannian manifolds(IEEE, 2013)An averaging result for periodic dynamical systems evolving on Euclidean spaces is extended to those evolving on (differentiable) Riemannian manifolds. Using standard tools from differential geometry, a perturbation result for time-varying dynamical systems is developed that measures closeness of trajectories via a suitable metric on a finite time horizon. This perturbation result is then extended to bound excursions in the trajectories of periodic dynamical systems from those of their respective averages, on an infinite time horizon, yielding the specified averaging result. Some simple examples further illustrating this result are also presented.
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ItemOn cascaded raman amplifier control(IEEE, 2006-01-01)Extremum Seeking Control is applied to the control of cascaded Raman amplifiers for long-haul wavelength division multiplexed optical communications systems. Simulation demonstrates the effectiveness of this control strategy.
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ItemAn application of extremum seeking in cascaded optical amplifier control(IEEE, 2006)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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ItemMeasurement feedback controller design to achieve input to state stability(IEEE, 2004-01-01)An approach for design of measurement feedback controllers achieving input-to-state (ISS) stability properties is presented. A synthesis procedure based on dynamic programming is given. We make use of recently developed results on controller synthesis to achieve uniform l∞ bound [6]. Our results make an important connection between the ISS literature and nonlinear H∞ design methods.
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ItemOn practical input to state stabilization for nonlinear discrete-time systems: A dynamic programming approach(IEEE, 2003-04-13)A novel technique for synthesizing dynamic state feedback controllers that achieve practical input to state stability (PISS) property for nonlinear discrete-time systems is presented. The PISS controller design for the original system is solved via an auxiliary l∞-bounded (LIB) robustness synthesis problem for an auxiliary system. A complete solution for the LIB synthesis problem has been presented recently in the literature. The obtained static state feedback LIB controller for the auxiliary system can be interpreted as a dynamic state feedback PISS controller for the original system. The obtained solution is in terms of a dynamic programming equation (or inequality).
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ItemAnalysis of input to state stability for discrete time nonlinear systems via dynamic programming(IEEE, 2003-01-01)This paper presents novel analysis results for input-to-state stability (ISS) that utilise dynamic programming techniques to characterise minimal ISS gains and transient bounds. These characterisations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimisation problems in nonlinear dissipative systems theory (including L2-gain analysis and nonlinear H∞ theory).
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ItemA hybrid model of networked control systems implemented on WirelessHART networks under source routing configuration(IEEE, 2016-01-01)A Network control system (NCS) is a control system in which communication between subsystems takes place over a digital network. Numerous results exist in the literature on modelling, analysis and design of NCSs in the presence of specific communication constraints such as packet dropouts, delays, data rates, quantization, etc. However, when analysing NCSs implemented on real physical networks, the existing results are based on restrictive assumptions. We consider NCSs over WirelessHART, the first international standard for industrial process control. With the goal of closing the gap between theory and practice, we propose for the first time a hybrid control-oriented model of WirelessHART NCSs under source routing configuration. Moreover, asymptotic and exponential stability results are presented under reasonable conditions.