In cyber-physical systems (CPSs) that interact between physical and information components, there are many sensors that are connected through a communication network. In such cases, the reduction of communication costs is important. Event-triggered control that the control input is updated only when the measured value is widely changed is well known as one of the control methods of CPSs. In this paper, we propose a design method of output feedback controllers with decentralized event-triggering mechanisms, where the notion of uniformly ultimate boundedness is utilized as a control specification. Using this notion, we can guarantee that the state stays within a certain set containing the origin after a certain time, which depends on the initial state. As a result, the number of times that the event occurs can be decreased. First, the design problem is formulated. Next, this problem is reduced to a BMI (bilinear matrix inequality) optimization problem, which can be solved by solving multiple LMI (linear matrix inequality) optimization problems. Finally, the effectiveness of the proposed method is presented by a numerical example.

Information-theoretic lower bounds of the Bayes risk have been investigated for a problem of parameter estimation in a Bayesian setting. Previous studies have proven the lower bound of the Bayes risk in a different manner and characterized the lower bound via different quantities such as mutual information, Sibson's α-mutual information, f-divergence, and Csiszár's f-informativity. In this paper, we introduce an inequality called a “meta-bound for lower bounds of the Bayes risk” and show that the previous results can be derived from this inequality.

In this paper, event-triggered control over a sensor network is studied as one of the control methods of cyber-physical systems. Event-triggered control is a method that communications occur only when the measured value is widely changed. In the proposed method, by solving an LMI (Linear Matrix Inequality) feasibility problem, an event-triggered output feedback controller such that the closed-loop system is asymptotically stable is derived. First, the problem formulation is given. Next, the control problem is reduced to an LMI feasibility problem. Finally, the proposed method is demonstrated by a numerical example.

An important problem in mathematics and data science, given two or more metric spaces, is obtaining a metric of the product space by aggregating the source metrics using a multivariate function. In 1981, Borsík and Doboš solved the problem, and much progress has subsequently been made in generalizations of the problem. The triangle inequality is a key property for a bivariate function to be a metric. In the metric aggregation, requesting the triangle inequality of the resulting metric imposes the subadditivity on the aggregating function. However, in some applications, such as the image matching, a relaxed notion of the triangle inequality is useful and this relaxation may enlarge the scope of the aggregators to include some natural superadditive functions such as the harmonic mean. This paper examines the aggregation of two semimetrics (i.e. metrics with a relaxed triangle inequality) by the harmonic mean is studied and shows that such aggregation weakly preserves the relaxed triangle inequalities. As an application, the paper presents an alternative simple proof of the relaxed triangle inequality satisfied by the robust Jaccard-Tanimoto set dissimilarity, which was originally shown by Gragera and Suppakitpaisarn in 2016.

Event-triggered control is a method that the control input is updated only when a certain triggering condition is satisfied. In networked control systems, quantization errors via A/D conversion should be considered. In this paper, a new method for quantized event-triggered control with switching triggering conditions is proposed. For a discrete-time linear system, we consider the problem of finding a state-feedback controller such that the closed-loop system is uniformly ultimately bounded in a certain ellipsoid. This problem is reduced to an LMI (Linear Matrix Inequality) optimization problem. The volume of the ellipsoid may be adjusted. The effectiveness of the proposed method is presented by a numerical example.

In this paper, we proposed a method for radar modulation identification based on the measurement of inequality in the frequency domain. Gini's coefficient was used to exploit the inequality in the powers of spectral components. The maximum likelihood classifier was used to classify the detected radar signal into four types of modulations: unmodulated signal (UM), linear frequency modulation (LFM), non-linear frequency modulation (NLFM), and frequency shift keying (FSK). The simulation results demonstrated that the proposed method achieves an overall identification accuracy of 98.61% at a signal-to-noise ratio (SNR) of -6dB without a priori information such as carrier frequency, pulse arrival times or pulse width.

Event-triggered control is a control method that the measured signal is sent to the controller only when a certain triggering condition on the measured signal is satisfied. In this paper, we propose a linear quadratic regulator (LQR) with decentralized triggering conditions. First, a suboptimal solution to the design problem of LQRs with decentralized triggering conditions is derived. A state-feedback gain can be obtained by solving a convex optimization problem with LMI (linear matrix inequality) constraints. Next, the relation between centralized and decentralized triggering conditions is discussed. It is shown that control performance of an LQR with decentralized event-triggering is better than that with centralized event-triggering. Finally, a numerical example is illustrated.

State-of-the-art background subtraction and foreground detection methods still face a variety of challenges, including illumination changes, camouflage, dynamic backgrounds, shadows, intermittent object motion. Detection of foreground elements via the robust principal component analysis (RPCA) method and its extensions based on low-rank and sparse structures have been conducted to achieve good performance in many scenes of the datasets, such as Changedetection.net (CDnet); however, the conventional RPCA method does not handle shadows well. To address this issue, we propose an approach that considers observed video data as the sum of three parts, namely a row-rank background, sparse moving objects and moving shadows. Next, we cast inequality constraints on the basic RPCA model and use an alternating direction method of multipliers framework combined with Rockafeller multipliers to derive a closed-form solution of the shadow matrix sub-problem. Our experiments have demonstrated that our method works effectively on challenging datasets that contain shadows.

This paper is concerned with exploring an extended approach for the stability analysis and synthesis for Markovian jump nonlinear systems (MJNLSs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the MJNLSs with incomplete transition description. In this paper, not all the elements of the rate transition matrices (RTMs), or probability transition matrices (PTMs) are assumed to be known. By fully considering the properties of the RTMs and PTMs, sufficient criteria of stability and stabilization is obtained in both continuous and discrete-time. Stabilization conditions with a mode-dependent fuzzy controller are derived for Markovian jump fuzzy systems in terms of linear matrix inequalities (LMIs), which can be readily solved by using existing LMI optimization techniques. Finally, illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

In this letter, we consider the global exponential stabilization problem by output feedback for a class of nonlinear systems. Along with a newly proposed matrix inequality condition, the proposed control method has improved flexibility in dealing with nonlinearity, over the existing methods. Analysis and examples are given to illustrate the improved features of our control method.

This study proposes an improvement to the Triangular Inequality Elimination (TIE) algorithm for vector quantization (VQ). The proposed approach uses recursive and intersection (RI) rules to compensate and enhance the TIE algorithm. The recursive rule changes reference codewords dynamically and produces the smallest candidate group. The intersection rule removes redundant codewords from these candidate groups. The RI-TIE approach avoids over-reliance on the continuity of the input signal. This study tests the contribution of the RI rules using the VQ-based, G.729 standard LSP encoder and some classic images. Results show that the RI rules perform excellently in the TIE algorithm.

We develop a distance function for finite Chu spaces based on their behavior. Typical examples are given to show the coincidence between the distance function and intuition. We show by example that the triangle inequality should not be satisfied when it comes to comparing two processes.

In this letter, delay-dependent stability criterion for linear time-delay systems with multiple time varying delays is proposed by employing the Lyapunov-Krasovskii functional approach and integral inequality. By the N-segmentation of delay length, we obtain less conservative results on the delay bounds which guarantee the asymptotic stability of the linear time-delay systems with multiple time varying delays. Simulation results show that the proposed stability criteria are less conservative than several other existing criteria.

This paper proposes a robust adaptive fuzzy PID control scheme augmented with a supervisory controller for unknown systems. In this scheme, a generalized fuzzy model is used to describe a class of unknown systems. The control strategy allows each part of the control law, i.e., a supervisory controller, a compensator, and an adaptive fuzzy PID controller, to be designed incrementally according to different guidelines. The supervisory controller in the outer loop aims at enhancing system robustness in the face of extra disturbances, variation in system parameters, and parameter drift in the adaptation law. Furthermore, an H∞ control design method using the fuzzy Lyapunov function is presented for the design of the initial control gains that guarantees transient performance at the start of closed-loop control, which is generally overlooked in many adaptive control systems. This design of the initial control gains is a compound search strategy called conditional linear matrix inequality (CLMI) approach with IROA (Improved random optimal algorithm), it leads to less complex designs than a standard LMI method by fuzzy Lyapunov function. Numerical studies of the tracking control of an uncertain inverted pendulum system demonstrate the effectiveness of the control strategy. From results of this simulation, the generalized fuzzy model reduces the rule number of T-S fuzzy model indeed.

The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we describe how upper bounds on the maximal quantum violation of Bell inequalities can be obtained by an extension of Tsirelson's theorem, and survey very recent results on how exact bounds may be obtained by solving an infinite series of semidefinite programs.

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect parametric uncertainty. The new model formulates the interconnect parametric uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) and Linear Matrix Inequalities (LMI's), the porposed model reduces the order of the original interconnect network while preserves the stability. The LFT based new model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) generated from Lur'e equations. In case of large number of uncertain parameters, the new model may be applied successively: the uncertain parameters are partitioned into groups, and with regard to each group, LFT based model is applied in turns.

This paper proposes the sliding mode control using LMI techniques and adaptive recurrent fuzzy neural network (RFNN) for a class of uncertain nonlinear time-delay systems. First, a novel TS recurrent fuzzy neural network (TS-RFNN) is developed to provide more flexible and powerful compensation of system uncertainty. Then, the TS-RFNN based sliding model control is proposed for uncertain time-delay systems. In detail, sliding surface design is derived to cope with the non-Isidori-Bynes canonical form of dynamics, unknown delay time, and mismatched uncertainties. Based on the Lyapunov-Krasoviskii method, the asymptotic stability condition of the sliding motion is formulated into solving a Linear Matrix Inequality (LMI) problem which is independent on the time-varying delay. Furthermore, the input coupling uncertainty is also taken into our consideration. The overall controlled system achieves asymptotic stability even if considering poor modeling. The contributions include: i) asymptotic sliding surface is designed from solving a simple and legible delay-independent LMI; and ii) the TS-RFNN is more realizable (due to fewer fuzzy rules being used). Finally, simulation results demonstrate the validity of the proposed control scheme.

In this letter, we propose a new H2 smoother (H2S) with a finite impulse response (FIR) structure for discrete-time state-space signal models. This smoother is called an H2 FIR smoother (H2FS). Constraints such as linearity, quasi-deadbeat property, FIR structure, and independence of the initial state information are required in advance to design H2FS that is optimal in the sense of H2 performance criterion. It is shown that H2FS design problem can be converted into the convex programming problem written in terms of a linear matrix inequality (LMI) with a linear equality constraint. Simulation study illustrates that the proposed H2FS is more robust against uncertainties and faster in convergence than the conventional H2S.

We investigate the problem of joint transmitter and receiver power allocation with the minimax mean square error (MSE) criterion for uplink transmissions in a multi-carrier code division multiple access (MC-CDMA) system. The objective of power allocation is to minimize the maximum MSE among all users each of which has limited transmit power. This problem is a nonlinear optimization problem. Using the Lagrange multiplier method, we derive the Karush-Kuhn-Tucker (KKT) conditions which are necessary for a power allocation to be optimal. Numerical results indicate that, compared to the minimum total MSE criterion, the minimax MSE criterion yields a higher total MSE but provides a fairer treatment across the users. The advantages of the minimax MSE criterion are more evident when we consider the bit error rate (BER) estimates. Numerical results show that the minimax MSE criterion yields a lower maximum BER and a lower average BER. We also observe that, with the minimax MSE criterion, some users do not transmit at full power. For comparison, with the minimum total MSE criterion, all users transmit at full power. In addition, we investigate robust joint transmitter and receiver power allocation where the channel state information (CSI) is not perfect. The CSI error is assumed to be unknown but bounded by a deterministic value. This problem is formulated as a semidefinite programming (SDP) problem with bilinear matrix inequality (BMI) constraints. Numerical results show that, with imperfect CSI, the minimax MSE criterion also outperforms the minimum total MSE criterion in terms of the maximum and average BERs.

This letter presents new delayed perturbation bounds (DPBs) for stabilizing receding horizon H∞ control (RHHC). The linear matrix inequality (LMI) approach to determination of DPBs for the RHHC is proposed. We show through a numerical example that the RHHC can guarantee an H∞ norm bound for a larger class of systems with delayed perturbations than conventional infinite horizon H∞ control (IHHC).