Model Reduction for Control System Design

Obinata, Goro; Anderson, Brian D. O.

doi:10.1007/978-1-4471-0283-0

Cited by 303 publications

(87 citation statements)

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“…Proof. Note that the commutative property G(z)K(z)H −1 (z) = H −1 (z)G(z)K(z) holds, as a consequence the property H −1 (z)H c (z) = H c (z)H −1 (z) also holds true [28]. Now we haveW (z):…”

Section: Relationship Between Closed Loop Configurationsmentioning

confidence: 93%

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Ahmad

Houlis

Sreeram

et al. 2017

Asian Journal of Control

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In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

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Section: Relationship Between Closed Loop Configurationsmentioning

confidence: 93%

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Ahmad

Houlis

Sreeram

et al. 2017

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Commonly, model-reduction is referring to reducing dimension of state-space while retaining certain system properties. [42][43][44][45][46] Recently, new methods have been proposed using polynomial-chaos 47,48 model reduction of stochastic systems. However, here, we use model reduction to mean reduction of the infinite-dimensional function space, associated with the state-trajectories x(t, ), using polynomial chaos.…”

Section: Synthesis With Reduced-order Modelmentioning

confidence: 99%

Robust LQR design for systems with probabilistic uncertainty

Bhattacharya

2019

Intl J Robust & Nonlinear

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Summary In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller.

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“…It should be noted that once we have those results in [3], the lower bounds and the optimal reducedorder models in the discrete-time setting follow immediately by applying a bilinear transformation between the imaginary axis and the unit circle [19]. It is nonetheless interesting to develop LMI techniques for purely discrete-time systems and, in particular, it should be significant to find specific LMI conditions for the optimal H ∞ model reduction in the aforementioned cases.…”

Section: Introductionmentioning

confidence: 96%

On ℋ︁_∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

Ebihara

Hirai

Hagiwara

2008

Asian Journal of Control

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In this paper, we address the H ∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel singular values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel singular value, we show that the H ∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.

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Model Reduction for Control System Design

Cited by 303 publications

References 0 publications

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Robust LQR design for systems with probabilistic uncertainty

On ℋ︁_∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

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Model Reduction for Control System Design

Cited by 303 publications

References 0 publications

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Robust LQR design for systems with probabilistic uncertainty

On ℋ︁∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities

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On ℋ︁_∞ model reduction for discrete‐time linear time‐invariant systems using linear matrix inequalities