The Experts below are selected from a list of 108 Experts worldwide ranked by ideXlab platform
T E Duncan - One of the best experts on this subject based on the ideXlab platform.
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Adaptive Boundary and Point Control of Linear Stochastic Distributed Parameter Systems
Siam Journal on Control and Optimization, 1994Co-Authors: T E Duncan, B. Maslowski, B. Pasik-duncanAbstract:An adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and solved in this paper. The distributed parameter system is modeled by an evolution equation with an infinitesimal generator for an analytic semigroup. Since there is boundary or point control, the linear transformation for the control in the state equation is also an unbounded Operator. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. Strong consistency is verified for a family of least squares estimates of the unknown parameters. An Ito formula is established for smooth functions of the solution of this linear stochastic distributed parameter system with boundary or point control. The certainty equivalence adaptive control is shown to be self-tuning by using the continuity of the solution of a stationary Riccati equation as a function of parameters in a Uniform Operator Topology. For a quadratic cost functional of the state and the control, the certainty equivalence control is shown to be self-optimizing; that is, the family of average costs converges to the optimal ergodic cost. Some examples of stochastic parabolic problems with boundary control and a structurally damped plate with random loading and point control are described that satisfy the assumptions for the adaptive control problem solved in this paper.
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Boundary and Point Control of Parameter S ys terns
1992Co-Authors: T E Duncan, B. Pasik-duncan, B. MaslowskiAbstract:An adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and its solution is given in this paper. The distributed parameter system is an evolution equation with an infinitesimal generator for an analytic semigroup. Since there is boundary or point control, the linear transformation for the control in the state equation is also an unbounded Operator. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. Strong consistency is verified for a family of least squares estimates of the unknown parameters. An It6 formula can be verified for smooth functions of the solution of this linear stochastic distributed parameter system with boundary control. equivalence adaptive control is shown to be self-tuning by noting the continuity of the solution of a stationary Riccati equation as a function of parameters in a Uniform Operator Topology. For a quadratic cost functional of the state and the control the certainty equivalence control is shown to be self-optimizing, that is, the family of average costs converges to the optimal ergodic cost. parabolic problems with boundary control can be given that satisfy the conditions of the adaptive control problem considered here as well as a structurally damped plate with random loading and point control. The certainty
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Uniform Operator continuity of the stationary riccati equation in hilbert space
Applied Mathematics and Optimization, 1992Co-Authors: A Chojnowskamichalik, T E Duncan, B PasikduncanAbstract:In this paper the continuity in the Uniform Operator Topology of the solution of the stationary Riccati equation in Hilbert space as a function of parameters is verified. The assumptions for this verification are the Uniform Operator continuity of the uncontrolled semigroup with respect to parameters, the Uniform finiteness of the infimum of the quadratic cost functionals over the admissible controls, and Uniform detectability. Some families of semigroups are described that satisfy the condition of continuity in the Uniform Operator Topology with respect to parameters. The Uniform Operator continuity of the solution of the stationary Riccati equation with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.
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Adaptive control of linear stochastic evolution systems
Stochastics and Stochastics Reports, 1991Co-Authors: T E Duncan, B. Pasik-duncan, B. GoldysAbstract:An adaptive control problem for some linear stochastic evolution systems in Hilbert spaces is formulated and solved in this paper. The solution includes showing the strong consistency of a family of least squares estimates of the unknown parameters and the convergence of the average quadratic costs with a control based on these estimates to the optimal average cost. The unknown parameters in the model appear affinely in the infinitesimal generator of the C 0 semigroup that defines the evolution system. A recursive equation is given for a family of least squares estimates and the bounded linear Operator solution of the stationary Riccati equation is shown to be a continuous function of the unknown parameters in the Uniform Operator Topology
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Some aspects of the continuity of the stationary Riccati equation in Hilbert space
29th IEEE Conference on Decision and Control, 1990Co-Authors: T E Duncan, B. Pasik-duncan, A. Chojnowska-michalikAbstract:In adaptive control and other problems in control it is important to know that the solution of the stationary Riccati equation for a linear regulator control problem is a continuous function of parameters. Although this result is well known for finite-dimensional linear regulator control problems, it has not been previously verified for infinite-dimensional linear regulator problems in the form that is required for adaptive control. Specifically, it is shown in this study that the symmetric, nonnegative solution of the stationary Riccati equation in Hilbert space is a continuous function of parameters in the Uniform Operator Topology.
B. Pasik-duncan - One of the best experts on this subject based on the ideXlab platform.
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Adaptive Boundary and Point Control of Linear Stochastic Distributed Parameter Systems
Siam Journal on Control and Optimization, 1994Co-Authors: T E Duncan, B. Maslowski, B. Pasik-duncanAbstract:An adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and solved in this paper. The distributed parameter system is modeled by an evolution equation with an infinitesimal generator for an analytic semigroup. Since there is boundary or point control, the linear transformation for the control in the state equation is also an unbounded Operator. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. Strong consistency is verified for a family of least squares estimates of the unknown parameters. An Ito formula is established for smooth functions of the solution of this linear stochastic distributed parameter system with boundary or point control. The certainty equivalence adaptive control is shown to be self-tuning by using the continuity of the solution of a stationary Riccati equation as a function of parameters in a Uniform Operator Topology. For a quadratic cost functional of the state and the control, the certainty equivalence control is shown to be self-optimizing; that is, the family of average costs converges to the optimal ergodic cost. Some examples of stochastic parabolic problems with boundary control and a structurally damped plate with random loading and point control are described that satisfy the assumptions for the adaptive control problem solved in this paper.
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Boundary and Point Control of Parameter S ys terns
1992Co-Authors: T E Duncan, B. Pasik-duncan, B. MaslowskiAbstract:An adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and its solution is given in this paper. The distributed parameter system is an evolution equation with an infinitesimal generator for an analytic semigroup. Since there is boundary or point control, the linear transformation for the control in the state equation is also an unbounded Operator. The unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control. Strong consistency is verified for a family of least squares estimates of the unknown parameters. An It6 formula can be verified for smooth functions of the solution of this linear stochastic distributed parameter system with boundary control. equivalence adaptive control is shown to be self-tuning by noting the continuity of the solution of a stationary Riccati equation as a function of parameters in a Uniform Operator Topology. For a quadratic cost functional of the state and the control the certainty equivalence control is shown to be self-optimizing, that is, the family of average costs converges to the optimal ergodic cost. parabolic problems with boundary control can be given that satisfy the conditions of the adaptive control problem considered here as well as a structurally damped plate with random loading and point control. The certainty
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Some aspects of the adaptive boundary and point control of linear distributed parameter systems
[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992Co-Authors: T.e. Duncan, B. Pasik-duncan, B. MaslowskiAbstract:An adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system (DPS) is formulated and its solution is given. The unknown linear stochastic DPS is described by an evolution equation, in which the unknown parameters appear in the infinitesimal generator of an analytic semigroup and in the unbounded linear transformation for the boundary control. An Ito formula can be verified for smooth functions of the solution of the linear stochastic DPS boundary control considered here. The certainty equivalence adaptive control is shown to be self-tuning by noting the continuity of the solution of a stationary Riccati equation as a function of parameters in a Uniform Operator Topology. For a quadratic cost functional of the state and the control, the certainty equivalence control is shown to be self-optimizing, i.e., the family of average costs converges to the optimal ergodic cost.
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Adaptive control of linear stochastic evolution systems
Stochastics and Stochastics Reports, 1991Co-Authors: T E Duncan, B. Pasik-duncan, B. GoldysAbstract:An adaptive control problem for some linear stochastic evolution systems in Hilbert spaces is formulated and solved in this paper. The solution includes showing the strong consistency of a family of least squares estimates of the unknown parameters and the convergence of the average quadratic costs with a control based on these estimates to the optimal average cost. The unknown parameters in the model appear affinely in the infinitesimal generator of the C 0 semigroup that defines the evolution system. A recursive equation is given for a family of least squares estimates and the bounded linear Operator solution of the stationary Riccati equation is shown to be a continuous function of the unknown parameters in the Uniform Operator Topology
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Some aspects of the continuity of the stationary Riccati equation in Hilbert space
29th IEEE Conference on Decision and Control, 1990Co-Authors: T E Duncan, B. Pasik-duncan, A. Chojnowska-michalikAbstract:In adaptive control and other problems in control it is important to know that the solution of the stationary Riccati equation for a linear regulator control problem is a continuous function of parameters. Although this result is well known for finite-dimensional linear regulator control problems, it has not been previously verified for infinite-dimensional linear regulator problems in the form that is required for adaptive control. Specifically, it is shown in this study that the symmetric, nonnegative solution of the stationary Riccati equation in Hilbert space is a continuous function of parameters in the Uniform Operator Topology.
A. Chojnowska-michalik - One of the best experts on this subject based on the ideXlab platform.
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Some aspects of the continuity of the stationary Riccati equation in Hilbert space
29th IEEE Conference on Decision and Control, 1990Co-Authors: T E Duncan, B. Pasik-duncan, A. Chojnowska-michalikAbstract:In adaptive control and other problems in control it is important to know that the solution of the stationary Riccati equation for a linear regulator control problem is a continuous function of parameters. Although this result is well known for finite-dimensional linear regulator control problems, it has not been previously verified for infinite-dimensional linear regulator problems in the form that is required for adaptive control. Specifically, it is shown in this study that the symmetric, nonnegative solution of the stationary Riccati equation in Hilbert space is a continuous function of parameters in the Uniform Operator Topology.
Yuri Tomilov - One of the best experts on this subject based on the ideXlab platform.
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Joint numerical ranges and compressions of powers of Operators
Journal of The London Mathematical Society-second Series, 2018Co-Authors: Vladimír Müller, Yuri TomilovAbstract:We identify subsets of the joint numerical range of an Operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of Operator orbits into certain approximation and interpolation properties for powers in the Uniform Operator Topology. This is a far-reaching generalization of one of the main results in our recent paper posted as arXiv:1607.00040. Moreover, it yields an essential (but partial) generalization of Bourin's "pinching" theorem. It also allows us to revisit several basic results on joint numerical ranges, provide them with new proofs and find a number of new results.
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On interplay between joint numerical ranges and its consequences for asymptotics of Operator iterates
2017Co-Authors: Vladimír Müller, Yuri TomilovAbstract:We identify subsets of the joint numerical range of an Operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of Operator orbits into certain approximation and interpolation properties for powers in the Uniform Operator Topology. This is a far-reaching generalization of one of the main results in our recent paper posted as arXiv:1607.00040. Moreover, it yields an essential (but partial) generalization of Bourin's "pinching" theorem. It also allows us to revisit several basic results on joint numerical ranges, provide them with new proofs and find a number of new results.
Shûichi Ohno - One of the best experts on this subject based on the ideXlab platform.
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Topological Structure of the Space of Weighted Composition Operators on H ^∞
Integral Equations and Operator Theory, 2005Co-Authors: Takuya Hosokawa, Keiji Izuchi, Shûichi OhnoAbstract:We study properties of the topological space of weighted composition Operators on the space of bounded analytic functions on the open unit disk in the Uniform Operator Topology. Moreover, we characterize the compactness of differences of two weighted composition Operators.
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Topological Structure of the Space of Weighted Composition Operators on H
Integral Equations and Operator Theory, 2005Co-Authors: Takuya Hosokawa, Keiji Izuchi, Shûichi OhnoAbstract:We study properties of the topological space of weighted composition Operators on the space of bounded analytic functions on the open unit disk in the Uniform Operator Topology. Moreover, we characterize the compactness of differences of two weighted composition Operators.
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Topological structure of the space of composition Operators onH ^∞
Integral Equations and Operator Theory, 2001Co-Authors: Barbara Maccler, Shûichi Ohno, Ruhan ZhaoAbstract:Components and isolated points of the topological space of composition Operators on H ^∞ in the Uniform Operator Topology are characterized. Compact differences of two composition Operators are also characterized. With the aid of these results, we show that a component in C(H ^ ∞ ) is not in general the set of all composition Operators that differ from the given one by a compact Operator.
