Global optimization for the Biaffine Matrix Inequality problem

Abstract-Cognitive radio networks require fast and reliable spectrum sensing to achieve high network utilization by secondary users. Optimization approaches to spectrum sensing todate have largely focused on maximizing throughput for secondary users while considering only a single parameter variable pertinent to sensing -notably the threshold or duration, but not both. In this work, we investigate the impact of true joint minimization under two performance criteria: a) minimization of the average time to detection of a spectrum hole and b) joint maximization of the aggregate opportunistic throughput. We show that the resulting non-convex problem is actually biconvex under practical conditions for which effective algorithms can be developed that yields reliable numerical procedures to solve the resulting optimization problem. The results show that the proposed approach can considerably improve system performance (in terms of the mean time to detect a spectrum hole and also the aggregate opportunistic throughput of both primary and secondary users), relative to the scenarios with only a single sensing variable or a sub-optimal ad-hoc optimization approach used for two variable case.

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“…Floudas [16] and Goh [17] provide two such algorithms to solve for the global minimum of biconvex problems.…”

Section: Discussionmentioning

confidence: 99%

Efficient Spectrum Sensing for Cognitive Radio Networks via Joint Optimization of Sensing Threshold and Duration

Luo

Roy

2012

IEEE Trans. Commun.

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“…Thus, it is now possible to use bilinear matrix inequality solution methods (Fukuda and Kojima, 2001;Goh et al, 1995;Balakrishnan and Boyd, 1992) to solve the matrix inequalities of (17)- (18) and (22) to minimize the L 2 -gain γ.…”

Section: An Override Control Strategy Using a Non-smooth Lyapunov Funmentioning

confidence: 99%

A robust override scheme enforcing strict output constraints for a class of strictly proper systems

2008

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This paper presents an override controller which ensures that constrained output variables retain certain prescribed strict bounds. The class of nominal closed loop systems considered for the constrained output regulation problem is strictly proper and minimum phase, assuming for each output measurement constraint one available actuator and the first Markov parameter to be full rank. This necessitates the open-loop plant to have the same input-toconstrained-output characteristics. The advantage of the considered class of nominal systems is that an output constraint translates directly into a state constraint for which it is possible to use a particular non-smooth Lyapunov function. The non-smooth Lyapunov function is defined by the level of the output constraint creating an invariant set for which the strict output constraints are satisfied. The override strategy is designed to retain a minimal effect on the nominal control loop in case no output constraint is violated.

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“…However, in such algorithms decent directions are essentially constrained to be aligned with a strict subset of the overall co-ordinates at each step. Correspondingly, convergence to a locally optimal solution cannot be guaranteed [15]. In particular, the algorithm can converge to a saddle point when one exists.…”

Section: Algorithmmentioning

confidence: 99%

“…Although various branch and bound type algorithms have been proposed for solving these problems (e.g. [15]), they are known to be useful only when there is a small number of variables which need to be fixed to yield affine constraints [16]. In the context of the problem considered here, the number of such variables corresponds to the number of frequency response samples, which could be large.…”

Section: A Co-ordinate Decent Approachmentioning

confidence: 99%

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

Date

Cantoni

2005

Systems & Control Letters

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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 →

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Global optimization for the Biaffine Matrix Inequality problem

Cited by 95 publications

References 30 publications

Efficient Spectrum Sensing for Cognitive Radio Networks via Joint Optimization of Sensing Threshold and Duration

Efficient Spectrum Sensing for Cognitive Radio Networks via Joint Optimization of Sensing Threshold and Duration

A robust override scheme enforcing strict output constraints for a class of strictly proper systems

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

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