Browsing by Author "Michalska, H"

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    A geometric approach to feedback stabilization of nonlinear systems with drift
    (2003) Michalska, H; Torres Torriti, Miguel Attilio
    The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov type function, but requires the solution of a nonlinear programming satisficing problem stated in terms of the logarithmic coordinates of flows. As opposed to other approaches, point-to-point steering is not required to achieve asymptotic stability. Instead, the flow of the controlled system is required to intersect periodically a certain reachable set in the space of the logarithmic coordinates.
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    A software package for Lie algebraic computations
    (SIAM PUBLICATIONS, 2005) Torres Torriti, M; Michalska, H
    The paper presents a computer algebra package that facilitates Lie algebraic symbolic computations required in the solution of a variety of problems, such as the solution of right-invariant differential equations evolving on Lie groups. Lie theory is a powerful tool, helpful in the analysis and design of modern nonlinear control laws, nonlinear filters, and the study of particle dynamics. The practical application of Lie theory often results in highly complex symbolic expressions that are difficult to handle efficiently without the aid of a computer software tool. The aim of the package is to facilitate and encourage further research relying on Lie algebraic computations.
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    Feedback stabilization of strongly non-linear systems using the CBH formula
    (2004) Michalska, H; Torres Torriti, Miguel Attilio
    This paper presents an approach to the construction of stabilizing feedback for strongly non-linear systems. The class of systems of interest includes systems with drift which are a. ne in the controls and which cannot be stabilized by continuous state feedback. The approach is independent of the selection of a Lyapunov function, but requires the on-line solution of a non-linear programming satisficing problem stated in terms of expressions resulting from the composition of flows via the Campbell - Baker - Hausdorff formula.