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.James, Matthew R.Subject: search.filters.subject.Systems Integration

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Now showing 1 - 4 of 4
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    Partially Observed Differential Games, Infinite Dimensional HJI Equations, and Nonlinear HControl
    (1994) James, Matthew R.; Baras, John S.; ISR
    This paper presents new results for partially observed nonlinear differential games, which are applied to the nonlinear output feedback Hrobust control problem. Using the concept of information state, we solve these problems in terms of an infinite dimensional partial differential equation, viz., the Hamilton-Jacobi-Isaacs equation for partial observed differential games. We give definitions of smooth and viscosity solutions, and prove that the value function is a viscosity solution of the HJI equation. We prove a verification theorem, which implies that the optimal controls are separated in that they depend on the observations through the information state. This constitutes a separation principle for partially observed differential games. We also present some new results concerning the certainty equivalence principle.
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    Robust Output Feedback Control for Discrete - Time Nonlinear Systems
    (1993) James, Matthew R.; Baras, John S.; ISR
    In this paper we present a new approach to the solution of the output feedback robust control problem. We employ the recently developed concept of information state for output feedback dynamic games, and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state. The resulting controller is an information state feedback controller, and is intrinsically infinite dimensional. Stability results are obtained using the theory of dissipative systems, and indeed, our results are expressed in terms of dissipation inequalities.
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    Output Feedback Risk - Sensitive Control and Differential Games for Continuous - Time Nonlinear Systems
    (1993) James, Matthew R.; Baras, John S.; Elliott, Robert J.; ISR
    In this paper we carry out a formal analysis of an output feedback risk-sensitive stochastic control problem. Using large deviation limits, this problem is related to a deterministic output feedback differential game. Both problems are solved using appropriate information states. The use of an information state for the game problem is new, and is the principal contribution of our work. Our results have implications for the nonlinear robust stabilization problem.
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    Asymptotic Nonlinear Filtering and Large Deviations with Application to Observer Design
    (1988) James, Matthew R.; Baras, J.; ISR
    An important problem in control theory is the design of observers for nonlinear control systems. By observer we mean a deterministic dynamical system which uses observed information to compute an estimate of the state of the control system in such as way that the error decays to zero. Baras and Krishnaprasad have proposed that an observer design might result from a study of an asymptotic nonlinear filtering problem obtained by adding small noise terms to the equations defining the control system. The purpose of this thesis is to study this asymptotic filtering problem and to develop observer designs based on their idea. Asymptotic nonlinear filtering problems have been studied by several authors, and are closely related to large deviations (Wentzell-Freidlin theory). We prove using vanishing viscosity and control theoretic methods a logarithmic limit result for solutions of the Zakai equation. This limit is characterized by a Hamilton-Jacobi equation which, as noted by Hijab, arises in Mortensen's deterministic minimum energy estimation. We make a careful study of this equation in the light of the relatively recent theory of viscosity solutions due to Crandall and Lions. We study the weak limit of the conditional measures and filter. Inspired by Hijab's large deviation result for pathwise conditional measures, we obtain a large deviation principle "in probability" for the conditional measures, and also a large deviation principle for the distributions of these measures. This asymptotic analysis suggests that the limiting filter is a candidate observer. We present an exact infinite dimensional observer for uncontrolled observable systems. In the case of uncontrolled nonlinear dynamics and linear observations, Bensoussan obtained a finite dimensional observer which is an approximation to the limiting filter. A detectability condition was used to prove exponential decay of the error, provided the initial condition lies in a bounded region. We extend his approach to the general case of controlled nonlinear dynamics and nonlinear observation. In particular, we obtain an observer for a class of fully nonlinear systems with no constraints on the initial conditions. The Benes case is considered.