Robust output-feedback controller design via local BMI optimization

Kanev, Stoyan; Scherer, Carsten W.; Verhaegen, Michel; Schutter, Bart De

doi:10.1016/j.automatica.2004.01.028

Cited by 173 publications

(118 citation statements)

References 55 publications

Supporting

Mentioning

114

Contrasting

Unclassified

Order By: Relevance

“…The second part deals with the control design where such methods are applied towards objective optimization. At several places in control design literature it can be read that coordinate descent methods are not guaranteed to converge (Kanev et al (2004); Iwasaki (1999); Yamada and Hara (1998)). However no explanations are given for this, although such methods can only improve or maintain the objective.…”

Section: Lmi-based Coordinate Descent Methodsmentioning

confidence: 99%

LMIs-based coordinate descent method for solving BMIs in control design

Simon

R-Ayerbe

Stoica

et al. 2011

IFAC Proceedings Volumes

View full text Add to dashboard Cite

Section: Lmi-based Coordinate Descent Methodsmentioning

confidence: 99%

LMIs-based coordinate descent method for solving BMIs in control design

Simon

R-Ayerbe

Stoica

et al. 2011

IFAC Proceedings Volumes

View full text Add to dashboard Cite

“…In particular, the algorithm can converge to a saddle point when one exists. An alternative iterative approach to linear cost optimisation problems with bi-affine constraints was recently established in [21]. The approach involves the local optimisation of suitable non-convex functions at each step and enjoys local convergence under certain conditions.…”

Section: Algorithmmentioning

confidence: 99%

On validating closed-loop behaviour from noisy frequency-response measurements

Date

Cantoni

2005

Systems & Control Letters

View full text Add to dashboard Cite

It is shown how noisy closed-loop frequency response measurements can be used to obtain pointwise in frequency bounds on the possible difference between an otherwise unknown closed-loop system and the closed-loop comprising a nominal model of the plant and a stabilising controller. To this end, the Vinnicombe's gap metric framework for robustness analysis plays a central role. Indeed, an optimisation problem and corresponding algorithm are proposed for estimating the chordal distance between the frequency responses of the nominal plant model and a plant that is consistent with the closed-loop data and a priori information, when projected onto the Riemann sphere. NotationLet C denote the field of complex numbers, C n×m the space of n × m matrices with complex entries, T := {z ∈ C : |z| = 1} the unit circle, and D ρ := {z ∈ C : |z| < ρ} the open disc of radius ρ > 0. The symbolD ρ is used to denote the closure of D ρ and for convenience, the sets D 1 andD 1 are denoted by D andD, respectively. Given ρ ≥ 1, let H ∞,ρ := {f : C →

show abstract

“…The optimisation problem (49) contains a Bilinear Matrix Inequality (BMI) (Kanev, Scherer, Verhaegen, & De Schutter, 2004;VanAntwerp & Braatz, 2000) whose size is 2(n + m + N + n 1 + n 2 ).…”

Section: Robust Fwl Controller Designmentioning

confidence: 99%

“…A large FWL tolerance means that the resulting controller can be implemented with a processor of short word length. Combining (23), (27), (29), (30), (36), (47) and (48), the above design problem can also be expressed aswhereThe optimisation problem (49) contains a Bilinear Matrix Inequality (BMI) (Kanev, Scherer, Verhaegen, & De Schutter, 2004;VanAntwerp & Braatz, 2000) whose size is 2(n + m + N + n 1 + n 2 ).In the work Yang et al (2001), an FWL H 2 controller design problem is studied which is also formulated as a BMI optimisation problem. However, as the method proposed in Yang et al (2001) examines each vertice of the FWL perturbation hypercube D β , the related optimisation problem contains at least 2 N BMIs of a size no less than 4n.…”

mentioning

confidence: 99%

Robust Finite Word Length controller design

Chen

et al. 2009

Automatica

View full text Add to dashboard Cite

Mixed µ theoryLinear matrix inequality Bilinear matrix inequality a b s t r a c t A novel Finite Word Length (FWL) controller design is proposed in the framework of a mixed µ theory.A robust FWL controller performance measure is first developed, which takes into account the standard robust control requirements as well as the FWL implementation considerations, and the corresponding controller design problem is naturally reformulated as a mixed µ problem which can be treated effectively with the results of the mixed µ theory.© 2009 Elsevier Ltd. All rights reserved. IntroductionRobust control capable of coping with uncertainty in plant dynamics has been the focal point of the control community for the past three decades. An implicit assumption in most of the existing robust design methods is that controllers are implemented exactly, i.e. there is no uncertainty occurring in realising controllers. In reality controllers are implemented with Finite Word Length (FWL) processors. In 1997, the fragility problem was raised in the work of (Keel & Bhattacharyya, 1997) which showed by examples that a controller achieving the largest robustness to plant uncertainty most likely has a vanishingly small closed-loop stability margin with respect to the controller parameters. Thus, a control system designed by maximising its robustness to plant uncertainty may be fragile, and the resulting fragile controller will need a processor with a very long bit length in implementation to minimise the FWL effects and therefore avoid degrading the designed closed-loop performance or even destabilising the designed stable closed-loop system. However, in many practical systems, such as $ The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Masayuki Fujita under the direction of Editor Ian R. Petersen. * Corresponding author. Tel.: +44 023 8059 666; fax: +44 023 8059 450.E-mail addresses: jwu@iipc.zju.edu.cn (J. Wu), ieligang@zjut.edu.cn (G. Li), sqc@ecs.soton.ac.uk (S. Chen), chuj@iipc.zju.edu.cn (J. Chu).mass-produced electronic consumer goods, fixed-point processors of short word length are preferred because of their advantages in component cost, chip area, operation simplicity and power consumption. Therefore, it is not a practical approach to simply pursue the optimal robustness to plant uncertainty without considering the FWL effects (Franklin, Powell & Workman, 1998;Gevers & Li, 1993;Istepanian & Whidborne, 2001).A suitable robust design approach is maintaining a suboptimal robustness to plant uncertainty while simultaneously making the controller tolerance to FWL implementation as large as possible. Through this design, a robust controller can be obtained which does not require a long word-length hardware for implementation. There exist two types of main FWL errors in digital controller implementation. The first one is the rounding errors that occur in arithmetic operations, and the second one is the parameter representation errors. Typically, the...

show abstract

Robust output-feedback controller design via local BMI optimization

Cited by 173 publications

References 55 publications

LMIs-based coordinate descent method for solving BMIs in control design

LMIs-based coordinate descent method for solving BMIs in control design

On validating closed-loop behaviour from noisy frequency-response measurements

Robust Finite Word Length controller design

Contact Info

Product

Resources

About