Mechanical 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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ItemOn stability properties of nonlinear time-varying systems by semi-definite time-varying Lyapunov can(IFAC, 2008-12-01)Stability properties (uniform stability/uniform asymptotic stability) of nonlinear time-varying systems are explored using positive semi-definite time-varying Lyapunov candidates whose derivative along trajectories is either non-positive or negative semi-definite. Once these positive semi-definite time-varying Lyapunov candidates are available, conditional stability properties on some specific sets can be used to ensure stability properties ( unform stability and unform asymptotic stability) of nonlinear time-varying systems.
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ItemNew Stability Criteria for Switched Time-Varying Systems: Output-Persistently Exciting Conditions(IEEE, 2011-01-01)This paper proposes three tools to facilitate the verification of the output-persistently exciting (OPE) condition and simultaneously, provides new asymptotic stability criteria for uniformly globally stable switched systems. By introducing some related reference systems, the OPE condition of the original system can be reduced or simplified. Both the ideas of classic LaSalle invariance principle and nested Matrosov theorem are used to generate such reference systems. The effectiveness and flexibility of the proposed methods are demonstrated by two applications. From these applications, it can be seen that the flexibility of the proposed method produces a novel set of tools for checking uniform asymptotic stability of switched time-varying systems.
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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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ItemExtremum Seeking From 1922 To 2010(IEEE, 2010-01-01)Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.
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ItemDynamic Practical Stabilization of Sampled-data Linear Distributed Parameter Systems(IEEE, 2009-01-01)In this paper, dynamic practical stability properties of infinite-dimensional sampled-data systems are discussed. A family of finite-dimensional discrete-time controllers are first designed to uniformly exponentially stabilize numerical approximate models that are obtained from space and time discretization. Sufficient conditions are provided to ensure that these controllers can be used to drive trajectories of infinite-dimensional sampled-data systems to a neighborhood of the origin by properly tuning the sampling period, space and time discretization parameters and choosing an appropriate filtering process for initial conditions.
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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.