Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems
TL;DR: This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays by designing a Luenberger-type observer, and develops a convex optimization algorithm for the filter design.
Abstract: This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays. Our aim is to estimate the states by designing a Luenberger-type observer, such that the filter error dynamics are mean-square exponentially stable with an expected decay rate and an attenuation level. Sufficient conditions for the existence of passive filters are obtained, and a convex optimization algorithm for the filter design is given. In addition, a cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem, which can be readily solved by the existing optimization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed techniques.
Citations
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TL;DR: A novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note.
Abstract: In this technical note, the sliding-mode control (SMC) problem is investigated for T–S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system.
299 citations
Cites background from "Neural Network-Based Passive Filter..."
...As is shown in [27] and [28], the probability distributions in semi-MJSs are more relaxed than ones in traditional MJSs....
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TL;DR: Some novel sufficient conditions are obtained to guarantee that the closed-loop system reaches a specified cost value under the designed jumping state feedback control law in terms of linear matrix inequalities.
Abstract: This paper is concerned with the guaranteed cost control problem for a class of Markov jump discrete-time neural networks (NNs) with event-triggered mechanism, asynchronous jumping, and fading channels. The Markov jump NNs are introduced to be close to reality, where the modes of the NNs and guaranteed cost controller are determined by two mutually independent Markov chains. The asynchronous phenomenon is considered, which increases the difficulty of designing required mode-dependent controller. The event-triggered mechanism is designed by comparing the relative measurement error with the last triggered state at the process of data transmission, which is used to eliminate dispensable transmission and reduce the networked energy consumption. In addition, the signal fading is considered for the effect of signal reflection and shadow in wireless networks, which is modeled by the novel Rice fading models. Some novel sufficient conditions are obtained to guarantee that the closed-loop system reaches a specified cost value under the designed jumping state feedback control law in terms of linear matrix inequalities. Finally, some simulation results are provided to illustrate the effectiveness of the proposed method.
199 citations
Cites background from "Neural Network-Based Passive Filter..."
...IN RECENT years, many researchers have shown much effort on neural networks (NNs) which has gained several theoretical and technological achievements due to their revealed potential of extensive applications including neurons therapy, associative memory, the robotic manipulator, automatic control, signal processing, and so on [1]–[15]....
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TL;DR: This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks by using a mode-dependent piecewise Lyapunov-Krasovskii functional and some solvability conditions are established in light of a linear matrix inequality framework.
Abstract: This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.
191 citations
Cites background or methods from "Neural Network-Based Passive Filter..."
...Considering the phase-type S-MSSs, the positive L1 filter has been proposed by using the critical properties of the supplementary variable and the plant transformation technique [34]....
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...Recent years have witnessed many applications of S-MSSs (see, e.g., [25]–[35])....
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...See https://www.ieee.org/publications/rights/index.html for more information. effectively attenuates the influence of quantization error on the nonlinear S-MSSs [30]....
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...Therefore, a key problem to be solved in finite-time event-triggered control for S-MSSs is naturally given whether there exists a novel event-triggered feedback controller to realize stochastic finite-time stability in the presence of FDI attacks....
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...(ii) Compared with S-MSSs under the ideal network transmission [25]–[35], by the use of Wirtinger’s integral inequality (WII) and free-matrix-based integral inequality (FMBII), a feedback controller is designed to resist the FDI attacks for a given finite-time level....
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TL;DR: This paper deals with the quantized control problem for nonlinear semi-Markov jump systems subject to singular perturbation under a network-based framework and devise a fuzzy controller, which not only assures the mean-square errors of the corresponding system but also allows a higher upper bound of the singularly perturbed parameter.
Abstract: This paper deals with the quantized control problem for nonlinear semi-Markov jump systems subject to singular perturbation under a network-based framework. The nonlinearity of the system is well solved by applying Takagi–Sugeno (T-S) fuzzy theory. The semi-Markov jump process with the memory matrix of transition probability is introduced, for which the obtained results are more reasonable and less limiting. In addition, the packet dropouts governed by a Bernoulli variable and the signal quantization associated with a logarithmic quantizer are deeply studied. The major goal is to devise a fuzzy controller, which not only assures the mean-square $\bar { \sigma }$ -error stability of the corresponding system but also allows a higher upper bound of the singularly perturbed parameter. Sufficient conditions are developed to make sure that the applicable controller could be found. The further examination to demonstrate the feasibility of the presented method is given by designing a controller of a series DC motor model.
182 citations
Additional excerpts
...In S-MJSs, the ST could obey other types of probability distribution [9]....
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TL;DR: Two kinds of classical control schemes are utilized to address the proposed synthesis problem of the containment control with respect to continuous-time semi- Markovian multiagent systems with semi-Markovian switching topologies.
Abstract: This article is concerned with the problem of the containment control with respect to continuous-time semi-Markovian multiagent systems with semi-Markovian switching topologies. Two kinds of classical control schemes, which are dynamic containment control and static containment control schemes, are utilized to address the proposed synthesis problem. Based on the linear matrix inequality (LMI) method, the dynamic containment controller and static containment controller are designed to plunge into the studied semi-Markovian multiagent systems, respectively. Moreover, the random switching topologies with the semi-Markovian process, the partly unknown transition rates, and the generally uncertain transition rates are taken into account, which can be applicable to more practical situations. Finally, the simulation results are provided to illustrate the effectiveness of the proposed theoretical results.
163 citations
Cites methods from "Neural Network-Based Passive Filter..."
...By employing the Luenberger-type observer, the exponential passive filtering was studied for the S-MJSs with the mixed time delays in [42]....
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References
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02 Sep 2004
TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.
Abstract: The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems
7,676 citations
TL;DR: This work used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli, which periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells.
Abstract: Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks
4,488 citations
"Neural Network-Based Passive Filter..." refers methods in this paper
...Example 3: To illustrate the applications of the results developed in this paper, we employ a synthetic oscillatory network of transcriptional regulators in Escherichia coli, which has been used to model repressilators, and experimentally investigated in [4] and [17]....
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TL;DR: Results provide direct evidence that transcriptional delays can drive oscillatory gene activity and highlight the importance of considering delays when analyzing genetic regulatory networks, particularly in processes such as developmental pattern formation, where short half-lives and feedback inhibition are common.
694 citations
"Neural Network-Based Passive Filter..." refers background or methods in this paper
...B̄ = (bi j ) ∈ Rn×n is the delayed connection weight matrix of the genetic network, which is defined as in [17]....
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...Example 3: To illustrate the applications of the results developed in this paper, we employ a synthetic oscillatory network of transcriptional regulators in Escherichia coli, which has been used to model repressilators, and experimentally investigated in [4] and [17]....
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TL;DR: Two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems.
Abstract: In this paper, the problem of sampled-data synchronization for Markovian jump neural networks with time-varying delay and variable samplings is considered. In the framework of the input delay approach and the linear matrix inequality technique, two delay-dependent criteria are derived to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems. The desired mode-independent controller is designed, which depends upon the maximum sampling interval. The effectiveness and potential of the obtained results is verified by two simulation examples.
567 citations
"Neural Network-Based Passive Filter..." refers methods in this paper
...In the framework of the input delay approach and the LMI technique, two delay-dependent criteria are derived in [26] to ensure the stochastic stability of the error systems, and thus, the master systems stochastically synchronize with the slave systems....
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TL;DR: Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals.
Abstract: In this paper, the existence and uniqueness of the equilibrium point and its global asymptotic stability are discussed for a general class of recurrent neural networks with time-varying delays and Lipschitz continuous activation functions. The neural network model considered includes the delayed Hopfield neural networks, bidirectional associative memory networks, and delayed cellular neural networks as its special cases. Several new sufficient conditions for ascertaining the existence, uniqueness, and global asymptotic stability of the equilibrium point of such recurrent neural networks are obtained by using the theory of topological degree and properties of nonsingular M-matrix, and constructing suitable Lyapunov functionals. The new criteria do not require the activation functions to be differentiable, bounded or monotone nondecreasing and the connection weight matrices to be symmetric. Some stability results from previous works are extended and improved. Two illustrative examples are given to demonstrate the effectiveness of the obtained results.
526 citations
"Neural Network-Based Passive Filter..." refers background in this paper
...INTRODUCTION NEURAL networks (NNs) have been successfully applied to various areas, such as economic load dispatch, signal processing, pattern recognition, automatic control, and combinatorial optimization (see [2], [3], [7], [14], [16], [19], [21], [28], [33]–[35], and the references therein)....
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