LQ-optimal control of infinite-dimensional systems by spectral factorization

Callier, Frank M.; Winkin, Joseph J.

doi:10.1016/0005-1098(92)90035-e

Cited by 63 publications

(43 citation statements)

References 16 publications

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“…[11,13]) for the linearized model given by (2.5)-(2.9). More precisely the aim is to find a control law which minimizes the following cost criterion:…”

Section: Lq-optimal Control Designmentioning

confidence: 99%

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

2008

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Abstract. The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential equation in the space variable. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed. Mathematics Subject Classification.

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“…[11,13]) for the linearized model given by (2.5)-(2.9). More precisely the aim is to find a control law which minimizes the following cost criterion:…”

Section: Lq-optimal Control Designmentioning

confidence: 99%

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

2008

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“…See [39,Section 2] for the appropriate definition. In the case of the stable classical system (1) and its anti-stable adjoint (6), in the time-invariant setting the states of Ψ and Ψ * are given by (12) and the outputs are given by (5) and (10). In the initial value setting with initial time zero the states and outputs of the same systems are given by…”

Section: Well-posed Linear Systems and Time-invariant Operatorsmentioning

confidence: 99%

“…The recent literature includes (but is certainly not restricted to) [1], [2], [4], [5], [6], [7], [9], [12] [13], [14], [20], [21], [23], [24], [25], [26], [27], [28], [30], [31], [42], [48], [49], [51], and the other papers in our list of references.…”

Section: Introductionmentioning

confidence: 99%

Quadratic optimal control of stable well-posed linear systems

Staffans

1997

Trans. Amer. Math. Soc.

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Abstract. We consider the infinite horizon quadratic cost minimization problem for a stable time-invariant well-posed linear system in the sense of Salamon and Weiss, and show that it can be reduced to a spectral factorization problem in the control space. More precisely, we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution. If both the system and the spectral factor are regular, then the feedback operator can be expressed in terms of the Riccati operator, and the Riccati operator is a positive self-adjoint solution of an algebraic Riccati equation. This Riccati equation is similar to the usual algebraic Riccati equation, but one of its coefficients varies depending on the subspace in which the equation is posed. Similar results are true for unstable systems, as we have proved elsewhere.

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“…For non-Fourier heat conduction, we consider them inadequate to track the robust performance specified both in space and in time. The second and third entries concern infinite dimensionality, wherein Grabowski, Desoer, Callier, Winkin [20][21][22][23], and others have adequately developed spectral factorization, algebra of transfer functions and semigroup theories applicable to control purposes. In practice, an infinite-dimensional transfer function from pointed input to pointed output can further be identified in the frequency domain with fraction order [24][25][26][27][28], serving for 1D-H∞/µ feedback loopshaping.…”

Section: Introductionmentioning

confidence: 99%

Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism

Chou

Hong

Chiang

et al. 2014

Entropy

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Abstract:In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal μ / ∞ H control is developed by expansion of the conventional 1D-μ / ∞ H control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fractionorders, into DSP-engine embedded microcontrollers. OPEN ACCESSEntropy 2014, 16 4938

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LQ-optimal control of infinite-dimensional systems by spectral factorization

Cited by 63 publications

References 16 publications

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Quadratic optimal control of stable well-posed linear systems

Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism

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