NP-hardness of the stable matrix in unit interval family problem in discrete time

Mercado, A.; Liu, K. J. Ray

doi:10.1016/s0167-6911(00)00095-5

Cited by 12 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[10], [11]). We establish a new NP-hardness result and discuss ways to walk around computational complexities using compositional analysis and over-approximations.…”

Section: A Related Workmentioning

confidence: 99%

Robust stability of multi-hop control networks

Weiss

D’Innocenzo

Alur

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

View full text Add to dashboard Cite

Abstract-We propose formal models for analyzing robustness of multi-hop control networks, where data from sensors to controllers and from controllers to actuators is sent through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors (errors with short time span), we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability (stability with probability one) in presence of transient link failures, and give efficient decision procedures. The last part of the paper deals with errors that have random time span. We show that, under some conditions, the permanent failure model can be used as a reliable abstraction.

show abstract

“…[10], [11]). We establish a new NP-hardness result and discuss ways to walk around computational complexities using compositional analysis and over-approximations.…”

Section: A Related Workmentioning

confidence: 99%

Robust stability of multi-hop control networks

Weiss

D’Innocenzo

Alur

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

View full text Add to dashboard Cite

show abstract

“…If the spectral radius ρ(BF) [17], that is, the maximum eigenvalue of BF, is inside the unit circle, the system has feasible solutions and there exists a positive power allocation vector to achieve the desired targeted SINRs. By Perron-Frobenius theorem [17,18], the optimum power vector for this problem isP = (I − BF) −1 u. Many adaptive algorithms [3,4,19] have been developed to reduce the system complexity by the following distributed iteration:…”

Section: System Model Beamforming and Power Controlmentioning

confidence: 99%

Joint Power Control and Blind Beamforming over Wireless Networks: A Cross Layer Approach

Han

Farrokhi

Liu

2004

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

Traditional joint power control and beamforming achieve the targeted signal-to-interference-noise ratio (SINR) at the receivers by assuming the knowledge of the measurements of channel parameters and SINR. Blind beamforming is an effective technique for beamforming and channel estimation without the need of training sequences, thus not consuming extra bandwidth. In this paper, we propose a novel joint power control and blind beamforming algorithm that reformulates the power control problem in such a way that it does not need any prior knowledge and additional measurements in the physical layer. In contrast to the traditional schemes that optimize SINR and, as a result, minimize bit error rate (BER), our proposed algorithm achieves the desired BER by adjusting a quantity available from blind beamforming. By sending this quantity to the transmitter through a feedback channel, the transmit power is iteratively updated in a distributed manner in the wireless networks with cochannel interferences (CCIS). Our proposed algorithm is more robust to estimation errors. We have shown in both analysis and simulation that our algorithm converges to the desired solution. In addition, a Cramer-Rao lower bound (CRB) is derived to compare with the performance of our proposed joint power control and blind beamforming system.

show abstract

“…It has been shown that the existence of the derivative of the spectral radius ρ(D k F k ) by the following theorem [7]. Theorem 1: let λ be a simple eigenvalue of DF, with right and left eigenvectors x and y, respectively.…”

Section: Capacity Refinement Algorithmmentioning

confidence: 99%

Capacity optimization using subspace method over multicell OFDMA networks

Han

Farrokhi

Liu

2004

2004 IEEE Wireless Communications and Networking Conference (IEEE Cat. No.04TH8733)

View full text Add to dashboard Cite

Abstract-Capacity optimization in a multi-cell OFDMA system where each cell has multiple users is investigated in this work. The objective is to find an assignment of users to the sets of subcarrier, their transmission rates for the subcarrier, and power allocation such that the total system capacity is increased, while users meet a minimum total rate requirement and a power constraint. Since the optimal solution involves an exhaustive search or complex nonlinear integer programming, we develop sub-optimal low complexity algorithms. We propose a two-step scheme: First an initial channel and data rate allocations are determined by two initialization algorithms. Then we refine the assigned rates by an iterative algorithm. From simulation results, the proposed algorithms can efficiently allocate resources to increase the overall system capacity and reduce the allocation outages.

show abstract

NP-hardness of the stable matrix in unit interval family problem in discrete time

Cited by 12 publications

References 6 publications

Robust stability of multi-hop control networks

Robust stability of multi-hop control networks

Joint Power Control and Blind Beamforming over Wireless Networks: A Cross Layer Approach

Capacity optimization using subspace method over multicell OFDMA networks

Contact Info

Product

Resources

About