Institute for Systems Research

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Author: search.filters.author.Dayawansa, Wijesuriya P.Subject: search.filters.subject.geometric control

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    Optimal Control of a Rigid Body with Two Oscillators
    (1993) Yang, R.; Krishnaprasad, Perinkulam S.; Dayawansa, Wijesuriya P.; ISR
    This paper is concerned with the exploration of reduction and explicit solvability of optimal control problems on principal bundles with connections from a Hamiltonian point of view. The particular mechanical system we consider is a rigid body with two driven oscillators, for which the bundle structure is (SO (3) x 者, 者, SO (3)). The optimal control problem is posed by considering a special nonholonomic variational problem, in which the nonholonomic distribution is defined via a connection. The necessary conditions for the optimal control problem are determined intrinsically by a Hamiltonian formulation. The necessary conditions admit the structure group of the principal bundle as a symmetry group of the system. Thus the problem is amendable to Poisson reduction. Under suitable hypotheses and approximations, we find that the reduced system possesses additional symmetry which is isomorphic to S1. Applying Poisson reduction again, we obtain a further reduced system and corresponding first integral. These reductions imply explicit solvability for suitable values of parameters.
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    Stabilization of Globally Noninteractive Nonlinear Systems via Dynamic State-Feedback
    (1991) Battilotti, S.; Dayawansa, Wijesuriya P.; ISR
    We consider the problem of semiglobal asymptotic stabilization and noninteracting control via dynamic state-feedback for a class of nonlinear control systems. It is assumed that the plant has been already rendered noninteractive. A sufficient condition for the stabilization of the overall system, without destroying the noninteraction property, is given in terms of stabilizability of certain subsystems.
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    Noninteracting Control with Stability for a Class of Nonlinear Systems
    (1991) Battilotti, S.; Dayawansa, Wijesuriya P.; ISR
    In this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved (without stability) by means of invertible static state-feedback. The use of both static state-feedback and dynamic state-feedback is investigated. We prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability. We use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem.
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    Mechanical Systems with Partial Damping: Two Examples
    (1991) Wang, L.S.; Krishnaprasad, Perinkulam S.; Dayawansa, Wijesuriya P.; ISR
    We discuss the problem of constructing steady state motions of mechanical systems with partial damping. A planar three bar linkage with viscous damping at one of the joints is considered as an example. We show that for a generic set of system parameters all steady state motions are confined to relative equilibria. We also consider the example of two rigid bodies with one-board rotors coupled via a ball-in-socket joint with viscous friction and show that in the steady state, the system is at a relative equilibrium.