This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations. Index Terms-Fuzzy systems, parameterized linear matrix inequality (PLMI).

Abstract-This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

No abstract

No abstract

The infinite Projected Entangled Pair States (iPEPS) algorithm [J. Jordan et al, PRL 101, 250602 (2008)] has become a useful tool in the calculation of ground state properties of 2d quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly-entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings, and (ii) improved overall stability. Besides, we extend the application of the local gauge fixing, successfully implemented for finite-size PEPS [M. Lubasch, J. Ignacio Cirac, M.-C. Bañuls, PRB 90, 064425 (2014)], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method, but also accelerates the convergence of the alternating least squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.

No abstract

This paper considers joint optimization of cooperative beamforming and relay assignment for multi-user multirelay wireless networks to maximize the minimum of the received signal-to-interference-plus-noise ratios (SINR). Separated continuous optimization of beamforming and binary optimization of relay assignment already pose very challenging programs. Certainly, their joint optimization, which involves nonconvex objectives and coupled constraints in continuous and binary variables, is among the most challenging optimization problems. Even the conventional relaxation of binary constraints by continuous box constraints is still computationally intractable because the relaxed program is still highly nonconvex. However, it is shown in this paper that the joint programs fit well in the d.c (difference of two convex functions/sets) optimization framework. Efficient optimization algorithms are then developed for both cases of orthogonal and nonorthogonal transmission by multiple users. Simulation results show that the jointly optimized beamforming and relay assignment not only save transmission bandwidth but can also maintain well the network SINRs. Index Terms-Cooperativebeamforming, power allocation, relay selection, relay assignment, wireless relay networks, d.c. programming. 1536-1276 (c) , IEEE Transactions on Wireless Communications 2 straints. Although these d.c. programs are still very hard, they motivate exploring hidden convex structures of the problem at hand in order to obtain the constructive solutions [36], [37]. It has been recognized for a long time [36] that the d.c. structure of binary constraints has yet to be explored as the binary constraints seem to be more suitable in a d.m. (difference of two monotonic functions/sets) setting [38], [39]. Moreover, different from a binary quadratic problem [40], which has been successfully solved by d.c. optimization, the constructive d.c.representations of the mixed-binary programs considered in the present paper are not available. Through elegant variable changes and effective approximations, our contribution is to reformulate these problems as tractable d.c. programs, which become solvable by d.c. iterations of polynomial complexity and also re-optimization processes. Simulation results show that the proposed computational procedures are capable of locating approximation solutions that are very close to the global optimal solutions. This is evidenced by the fact that the approximation solutions achieve SINR performances that are very close to their upper bounds.The paper is structured as follows. Section II provides a fundamental background on a class of mixed binary optimization and d.c. programming for finding its solution. Its application to the joint program of beamforming and relay assignment for the case of orthogonal transmission of the users is presented in Section III. Section IV is devoted to the problem of jointly optimized beamforming and relay assignment in nonorthogonal transmission of the users. Simulations are presented in Section V. Section VI ...

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths and switching dynamics. We then derive a closed form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.