Mechanical Engineering - Research Publications
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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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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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ItemA note on robustness of linear spatially distributed parameter systems and their numerical approximations(IEEE, 2007-01-01)In this paper, we investigate a relationship between robust stability properties of linear spatially distributed parameter systems (LSDPS) with disturbances and robust stability properties of their numerical approximations. Since it is hard to analytically find solutions of a partial differential equation, numerical methods, such as finite-difference methods, are always used to approximately find the solutions. Moreover, it is crucial that the numerical method reproduces (approximately) the behavior of the actual system model. For instance, if the actual system is stable in some sense, then the numerical method should possess (approximately) the same stability property and vice versa. Our results show that input-to-state exponential stability (ISES) properties of the numerical approximation with respect to disturbances are equivalent to practical ISES of the LSDPS provided that: (i) the finite-difference approximation is consistent with the model; (ii) an appropriate uniform boundedness condition holds for the numerical method. Our results can be regarded as an extension of the celebrated Lax-Richtmyer theorem to systems with disturbances, as well as its application to analysis of ISES. This question is typically not considered in the numerical analysis literature and yet it is very well noticed by in control applications.
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ItemA trajectory based approach for robust stability properties of infinite-dimensional systems(International Federation of Automatic Control (IFAC), 2007-01-01)In this paper, we present a trajectory based approach to discuss the robustness of parameterized families of systems with disturbances with respect to arbitrary closed sets in a normed space. Input-to-state stability (ISS) properties are discussed. Our results are applicable to infinite-dimensional systems with disturbances.
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ItemOn automatic seeking of optimal steady-states in biochemical processes(IFAC, 2007-01-01)It is discussed how the automatic seeking of optimal steady states biochemical reactors can be achieved by using non-model based extremum-seeking control with semi-global practical stability and convergence properties. A special attention is paid to processes with multiple steady-states and multivalued cost functions.
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ItemOn global extremum seeking in the presence of local extrema(IEEE, 2006-01-01)We analyze global extremum seeking in the presence of local extrema for static nonlinear maps controlled by a scalar extremum seeking scheme that was recently proposed in [1]. Sufficient conditions are given under which it is possible to tune the controller parameters to achieve convergence to an arbitrarily small neighborhood of the global extremum in the presence of local extrema from an arbitrarily large set of initial conditions. Several examples provide insights and highlight the potential difficulties that one would face when trying to generalize our results.
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ItemOn the choice of dither in extremum seeking systems: A case study(IEEE, 2006-01-01)We discuss how the dither (excitation signal) shape affects on the performance of extremum seeking using a benchmark situation: a static scalar map; and a simple scalar extremum seeking scheme. Our comparisons are based on the performance of the system with different dithers in terms of three performance indicators: the speed of convergence, domain of attraction and accuracy (i.e. the ultimate bound on trajectories). Our analysis explicitly shows how the dither shape affects each of these performance indicators. Our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter. Computer simulations support our theoretical findings.