Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Author: search.filters.author.Krishnaprasad, Perinkulam S.Subject: search.filters.subject.optimal control

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    H∞ Control for Impulsive Disturbances: A State-Space Solution
    (1994) Wei, Q.F.; Dayawansa, Wijesuriya P.; Krishnaprasad, Perinkulam S.; ISR
    In this paper we formulate and study an interesting (sub) optimal H∞ control problem related to the attenuation of impulsive disturbances to a class of linear systems. Among the motivating factors is the need to study control problems related to mechanical systems subject to impulsive forces, e.g.active control of the suspension system of a vehicle, accurate pointing of guns, stabilization of an antenna on the space station subject to impact from space debris, or active damping of vibrations of flexible structures caused by impact forces [1,2]. A reasonable control objective in all these problems is to design a stabilizing controller to minimize the induced operator norm from the impulsive disturbances to the controlled outputs. We derive necessary and sufficient conditions for the existence of a (sub) optimal controller, and give a procedure to compute such a controller when one exists.
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    Optimal Control and Poisson Reduction
    (1993) Krishnaprasad, Perinkulam S.; ISR
    In this paper we make explicit a reduction of G-invariant optimal control problems on a Lie group G.
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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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    Geometric Phases, Anholonomy, and Optimal Movement
    (1991) Krishnaprasad, Perinkulam S.; Yang, R.; ISR
    In the search for useful strategies for movement of robotic systems (e.g. manipulators, platforms) in constrained environments (e.g. in space, underwater), there appear to be new principles emerging from a deeper geometric understanding of optimal movements of nonholonomically constrained systems. In our work, we have exploited some new formulas for geometric phase shifts to derive effective control strategies. The theory of connections in principal bundles provides the proper framework for questions of the type addressed in this paper. we outline the essentials of this theory. A related optimal control problem and its localizations are also considered.