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Inputtostate stability of networked control systems
 Automatica
, 2004
"... Abstract — A new class of uniformly globally asymptotically stable (UGAS) protocols in networked control systems (NCS) is considered. It shown that if the controller is designed without taking into account the network so that it yields inputtostate stability (ISS) with respect to external disturban ..."
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Cited by 15 (0 self)
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Abstract — A new class of uniformly globally asymptotically stable (UGAS) protocols in networked control systems (NCS) is considered. It shown that if the controller is designed without taking into account the network so that it yields inputtostate stability (ISS) with respect to external disturbances (not necessarily with respect to the error that will come from the network implementation), then the same controller will achieve semiglobal practical ISS for the NCS when implemented via the network with a UGAS protocol. The adjustable parameter with respect to which semiglobal practical ISS is achieved is the socalled maximal allowable transfer interval (MATI) between transmission times. I.
Optimal control of spatially distributed systems
 IEEE Tran. on Automatic Control, September 2006, accepted. [Online]. Available: http://www.grasp.upenn.edu/ ∼ motee/ TACMoteeJ06SD.pdf
"... Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over ar ..."
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Cited by 11 (4 self)
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Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over arbitrary graphs. The key idea of the paper is the introduction of a special class of operators called spatially decaying (SD) operators. We study the structural properties of infinitehorizon linear quadratic optimal controllers for such systems by analyzing the spatial structure of the solution to the corresponding operator Lyapunov and Riccati equations. We prove that the kernel of the optimal feedback of each subsystem decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the system. I.
An LMI solution to the robust synthesis problem for multirate sampleddata systems
, 1909
"... In this paper we present new techniques for the solution of the multirate sampleddata H1 synthesis problem. This makes use of the mathematical tools developed in [4] and [5]. Necessary and sufficient conditions are given for the existence of a controller acheiving the desired performance, and all ..."
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Cited by 5 (0 self)
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In this paper we present new techniques for the solution of the multirate sampleddata H1 synthesis problem. This makes use of the mathematical tools developed in [4] and [5]. Necessary and sufficient conditions are given for the existence of a controller acheiving the desired performance, and all such controllers are parametrized. The problem is shown to be equivalent to a finite dimensional convex optimisation problem expressed in the form of linear matrix inequalities, for which standard numerical software is available. 1 Introduction In this paper we construct a solution for the multirate sampleddata H1 synthesis problem, illustrated in Figure 1. Given a continuoustime system with multiple input and output channels, we would like to control it using a digital controller via multiple sample and hold devices, each of which may be running at a different rate. The control objective is to minimize the induced norm from the input w to the output z. In this paper we give necessary a...
Disturbance rejection and robustness for LTV Systems
 Proceedings of the 2006 American Control Conference
"... Abstract — In this paper, we consider the optimal disturbance rejection problem for (possibly infinite dimensional) linear timevarying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. In particular, after reducing the problem to a shortest distance ..."
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Cited by 4 (4 self)
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Abstract — In this paper, we consider the optimal disturbance rejection problem for (possibly infinite dimensional) linear timevarying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. In particular, after reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, which satisfy a “timevarying ” allpass or flatness condition. With the use of the theory of Mideals of operators, it is shown that the computation of timevarying (TV) controllers reduces to a search over compact TV Youla parameters. This involves the norm of a TV compact Hankel operator and its maximal vectors. Moreover, an operator identity to compute the optimal TV Youla parameter is also derived. The results are generalized to the mixed sensitivity problem for TV systems as well, where it is shown that the optimum is equal to the operator induced of a TV mixed HankelToeplitz operator generalizing analogous results known to hold in the LTI case. Finally, a numerical algorithm to compute optimal TV controllers is proposed. DEFINITIONS AND NOTATION B(E, F) denotes the space of bounded linear operators from a Banach space E to a Banach space F, endowed with the operator norm. ℓ2 denotes the usual Hilbert space of square summable sequences with the standard norm Pk the usual truncation operator for some integer k, which sets all outputs after time k to zero. An operator A ∈ B(E, F) is said to be causal if it satisfies the operator equation PkAPk = PkA, ∀k positive integers The subscript “c” denotes the restriction of a subspace of operators to its intersection with causal (see [7] for the definition) operators. “⊗ ” denotes for the tensor product. “ ⋆ ” stands for the adjoint of an operator or the dual space of a Banach space depending on the context [5], [6]. I.
Receding horizon control of spatially distributed systems over arbitrary graphs
 in Proceedings of the 45th IEEE Conference on Decision and Control
, 2006
"... Abstract — In this paper, we study the problem of receding horizon control of spatially distributed systems with arbitrary interconnection topologies. The key idea is the introduction of spatially decaying operators (SD) which serve as the main ingredient in the cost function that couples the state ..."
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Cited by 4 (1 self)
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Abstract — In this paper, we study the problem of receding horizon control of spatially distributed systems with arbitrary interconnection topologies. The key idea is the introduction of spatially decaying operators (SD) which serve as the main ingredient in the cost function that couples the state and control of individual agents with those of others. It is shown that coupling between subsystems of many wellknown spatially distributed systems such as some of the recently studied models of distributed motion coordination with nearest neighbor interactions as well as spatially invariant systems can be characterized using such operators. We prove that for spatially distributed systems with input and state constraints in which the coupling is through an SD operator in a finite horizon cost function, optimal receding horizon controllers are piecewise affine (represented as a convolution sum plus an offset). More importantly, we prove that the kernel of each convolution sum decays exponentially in the spatial domain, thereby providing evidence that even centralized solutions to the receding horizon control problems for such systems has an inherent spatial locality. Our theoretical results are verified by numerical simulations. I.
Guaranteed Error Bounds for Model Reduction of Linear TimeVarying Systems
, 1998
"... New techniques are presented for the model reduction of linear timevarying and linear periodicallyvarying systems, including the formulation and proof of guaranteed upper bounds for the error. The commonly used method of balanced truncation for linear timeinvariant systems is generalized to the t ..."
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Cited by 3 (0 self)
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New techniques are presented for the model reduction of linear timevarying and linear periodicallyvarying systems, including the formulation and proof of guaranteed upper bounds for the error. The commonly used method of balanced truncation for linear timeinvariant systems is generalized to the timevarying case with explicit error bounds that are derived based on generalizations of the `twicethesumofthe tail' formula. The development of these reduction results for timevarying systems relies on a new operator framework for analysis of linear timevarying systems, presented in [4], in combination with the model reduction methods for uncertain systems developed in [3]. 1. Introduction In this paper, new techniques are developed for the model reduction of linear timevarying (LTV) systems. Explicit bounds are derived for the error achieved when balanced truncation methods are applied to such systems. The method of balanced truncation has previously been proposed for model reduct...
Localized Optimal Control of Spatiotemporal Chaos.
, 1997
"... Abstract — A linear output feedback control scheme is developed for a coupled map lattice system. H ∞ control theory is used to make the scheme local: both the collection of information and the feedback are implemented through an array of locally coupled control sites. Robustness properties of the c ..."
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Cited by 1 (0 self)
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Abstract — A linear output feedback control scheme is developed for a coupled map lattice system. H ∞ control theory is used to make the scheme local: both the collection of information and the feedback are implemented through an array of locally coupled control sites. Robustness properties of the control scheme are discussed. I.
Fundamental Limitations in SelfSensing Magnetic Bearings when Modeled as Linear Periodic Systems
"... In “Magnetic Bearing Measurement Configurations and Associated Robustness and Performance Li ... magnetic bearings are impractical due to fundamental limitations in the achievable closedloop robustness. Due to experimental data which appeared to contradict these results, Maslen, Montie, and Iwasak ..."
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In “Magnetic Bearing Measurement Configurations and Associated Robustness and Performance Li ... magnetic bearings are impractical due to fundamental limitations in the achievable closedloop robustness. Due to experimental data which appeared to contradict these results, Maslen, Montie, and Iwasaki showed that significantly better robustness is achievable in “Robustness limitations in selfsensing magnetic bearings” if the magnetic bearing is modeled as a linear periodic (LP) system rather than the linear time invariant (LTI) system used by Thibeault and Smith. The present paper explores why modeling the selfsensing magnetic bearing as a LP system improves the achievable robustness. This is accomplished by utilizing lifting to analyze the LP model as a MIMO discrete LTI system.