Passivity Criteria Research Articles

Passivity and synchronization of coupled reaction–diffusion neural networks with multiple coupling and uncertain inner coupling matrices

In this paper, a coupled reaction–diffusion neural networks (CRDNNs) model with multiple time-delays and uncertain inner coupling matrices is presented, and then some sufficient conditions are derived to make sure such network is passive. Subsequently, the uncertain CRDNNs with multiple time-delays and state couplings are considered, and the passivity criteria are given by exploiting some inequality techniques and Lyapunov functional. Similarly, the synchronization for such two networks are also investigated. Eventually, we provided two numerical examples to verify the validity of these acquired results.

Passivity Analysis for Memristor-Based Inertial Neural Networks With Discrete and Distributed Delays

The existing results of passivity for neural networks mainly concentrated on first-order derivative of the states, whereas it is also significant to study the passivity with high-order derivative. In this paper, a class of memristor-based inertial neural networks (MINNs) with external inputs and outputs are concerned. First, by choosing appropriate variable transformation, the original networks are rewritten as first-order differential equations. Then a criterion of passivity for the MINNs is presented by nonsmooth analysis and linear matrix inequality (LMI) techniques, which could also result in NP-hard problem since it needs at least exponential-time to solve the passivity condition. Meanwhile, based on the obtained passivity criterion, asymptotic stability criterion is accordingly derived for MINNs. In order to avoid the NP-hard problem, we employ matrix-analysis-techniques with the property that the difference-matrix between the given matrix and the proposed matrix is seminegative definite. Then the time complexity for solving the proposed passivity criterion is reduced to constant-time with respect to the number of LMIs. Robust passivity for MINNs is also studied for bounded uncertain parameters. The MINN widens the application ranges for designing neural networks. Finally, relevant simulation examples are given to show the effectiveness of the obtained results.

Time Domain Control for Passive Variable Motion and Force Scaling in Delayed Teleoperation

Scaling of motion and forces has always been of high relevance in teleoperation setups since it allows the adaptation of workspaces of master and slave devices or to increase precision. Teleoperation setups are often affected by a delay in the communication channel. Most state of the art control approaches that guarantee stability despite delay are based on the passivity criterion which is highly restrictive to standard scaling methods. This paper proposes different time domain control concepts that regulate the motion or force scaling based on the energy flow in delayed teleoperation systems. The approach focuses on setups with motion down-scaling and is applicable to variable motion and impedance scaling. The scaling control is integrated in a state of the art time delay control concept and its performance is analyzed in experiments.

Passivity and Passification of Fuzzy Memristive Inertial Neural Networks on Time Scales

A class of Takagi–Sugeno (T–S) fuzzy memristor-based inertial neural networks (FMINNs) is studied on time scales. The second-order derivative of the state variable in the network denotes the inertial term. At first, one timescale-type FMINNs is formulated on the basis of T–S fuzzy rules. By a variable transformation, the original network is transformed into first-order differential equations. Then, passivity criteria for the FMINNs are presented based on the characteristic function approach, linear matrix inequality techniques, and the calculus of time scales. Furthermore, two classes of control protocols, i.e., memristor- and fuzzy-related control protocols are designed to solve the passification problem for the considered FMINNs. The optimization problem of the passivity performance is also involved. Finally, simulation examples are given to show the effectiveness and validity of the obtained results, and an application is also given in pseudorandom number generation.

Passivity Analysis of Delayed Neural Networks Based on Lyapunov-Krasovskii Functionals With Delay-Dependent Matrices.

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

Analysis and pinning control for passivity of coupled different dimensional neural networks

Abstract In this paper, we discuss the passivity of coupled different dimensional neural networks. On the one hand, several passivity criteria for the coupled neural networks with different dimensional nodes are proposed by making using of some inequality techniques and Lyapunov functional method. Furthermore, we study the pinning passivity of coupled different dimensional neural networks with fixed and adaptive coupling strength, and obtain some sufficient conditions to ensure the pinning passivity of the considered network by designing proper pinning controllers. On the other hand, the passivity analysis and pinning control problem for coupled different dimensional delayed neural networks are studied similarly. Finally, the effectiveness of the derived results are verified by two numerical examples.

Novel results on passivity and exponential passivity for multiple discrete delayed neutral-type neural networks with leakage and distributed time-delays

This paper investigates the problem of passivity and exponential passivity for neutral-type neural networks (NNNs) with leakage, multiple discrete delay and distributed time-delay, via some novel sufficient conditions. Based on an appropriate Lyapunov-Krasovskii functional (LKF), free weighting matrix approach and some inequality techniques, enhanced passivity criteria for the concerned neural networks is established in the form of Linear matrix inequalities (LMIs). The feasibility of the attained passivity and exponential passivity criterions easily verified by the aid of LMI control toolbox in MATLAB software. Furthermore, we have compared our method with previous one in the existing literature, which depicts its less conservativeness. To substantiate the superiority and effectiveness of our analytical design, two examples with their numerical simulations are provided.

Exponential passivity conditions on neutral stochastic neural networks with leakage delay and partially unknown transition probabilities in Markovian jump

This paper studies the problem of exponential passivity for neutral stochastic neural networks (NSNN) with leakage delay and Markovian jump. The Markovian jump has partially unknown transition probabilities (PUTPs). By utilizing the Itô differential rule, choosing a suitable Lyapunov–Krasovskii functional and combining with the inequality technique, the sufficient delay-dependent exponential passivity criteria are obtained. These sufficient conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by LMI toolbox in Matlab. Finally, two simulated numerical examples are discussed in detail to illustrate the effectiveness of the established results.

FINITE-TIME PASSIVITY OF DISCRETE-TIME T-S FUZZY NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper focuses on the problem of finite-time boundedness and finite-time passivity of discrete-time T-S fuzzy neural networks with time-varying delays. A suitable Lyapunov--Krasovskii functional(LKF) is established to derive sufficient condition for finite-time passivity of discrete-time T-S fuzzy neural networks. The dynamical system is transformed into a T-S fuzzy model with uncertain parameters. Furthermore, the obtained passivity criteria is established in terms of Linear matrix inequality (LMI), which can be easily checked by using the efficient MATLAB LMI toolbox. Finally, some numerical cases are given to illustrate the effectiveness of the proposed approach.

Generalized passivity of coupled neural networks with directed and undirected topologies

Abstract The generalized passivity is discussed for coupled neural networks (CNNs) with directed and undirected topologies, respectively. Firstly, some generalized passivity definitions are proposed for general systems, in which output and input vectors may have different dimensions. By exploiting concepts of passivity and matrix theory, several criteria are established to guarantee the generalized passivity of CNNs with directed and undirected topologies. However, in many circumstances, CNNs with known coupling weights is not passive. Therefore, some control schemes for updating the coupling weights are also presented. By using these adaptive control schemes, several criteria for ensuring network passivity are derived. In addition, two simulation examples are presented to show the correctness of proposed passivity criteria.

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities.

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays

Abstract The problem for passivity of a class of recurrent neural networks (RNNs) with impulse and multi-proportional delays is investigated in this paper. Several delay-dependent and delay-independent passivity criteria for the given system are obtained by establishing appropriate Lyapunov–krasovskill functionals and applying matrix inequality approach. The passivity criteria here are presented in the form of linear matrix inequalities (LMIs), which can be easily verified by Matlab Toolbox. Simultaneously, the criteria obtained here include the passivity results of RNNs without impulse or without delays as special cases and can also be extended to other RNNs with more complicated impulsive noise. Finally, two numerical examples with some simulations shows that the proposed results are effective.

Multivariate theory‐based passivity criteria for linear fractional networks

SummaryIn traditional linear network theory, the positive‐real (PR) criteria are widely used to judge the passivity of elements and networks in the light of the fact that there exists an equivalent relationship between the passivity and the PR property of their immittance functions (matrices). However, the equivalence will no longer hold when the fractional elements are introduced into the network, and the PR criteria are not suitable in complex frequency domain anymore. On the other hand, the rapid development of fractional‐order circuits and systems and the corresponding study in fractional circuit analysis and designs put forward an urgent requirement for the passivity criterion, which can tackle linear fractional networks. Hence, in this paper, we propose new passivity criteria for linear fractional networks by aid of generalized Tellegen's theorem and multivariable PR theory. By using the proposed criteria, the passivity of linear fractional networks can be judged, and the steps of the proposed criterion are illustrated by examples.

Auxiliary function-based integral inequality approach to robust passivity analysis of neural networks with interval time-varying delay

Abstract In this paper, we study the problem of passivity for uncertain neural networks with interval time-varying delay. Firstly, a suitable augmented Lyapunov–Krasovskii functional (LKF) containing two triple integral terms is constructed and an auxiliary function-based integral inequality (AFBI) is used to manipulate the augmented single integral terms in the derivative of LKF. Secondly, a special form of the AFBI is applied to deal with the delay-product-type term, which was used to be ignored in the time derivative of a triple integral term. As a result, less conservative delay-dependent passivity criteria are derived for normal delayed neural networks (DNNs) in the form of linear matrix inequalities (LMIs). In addition, with the same LKF, delay-dependent passivity criteria are obtained for normal DNNs without the delay-product-type term. Subsequently, these criteria are extended to DNNs with parameter uncertainties. Finally, four numerical examples and simulations are provided to illustrate the effectiveness of the proposed criteria.

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

ABSTRACTFinite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov–Krasovskii's functional and utilisation of Jensen’s inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Analysis and pinning control for passivity of multi-weighted complex dynamical networks with fixed and switching topologies

Abstract In this paper, we respectively discuss passivity and pinning passivity of multi-weighted complex dynamical networks. By employing Lyapunov functional approach, several passivity criteria for the complex dynamical network with fixed topology and multi-weights are established. In addition, under the designed pinning adaptive state feedback controller, some sufficient conditions are obtained to ensure the passivity of the multi-weighted complex dynamical network with fixed topology. Furthermore, similar methods are used to derive several criteria for passivity and pinning passivity of complex dynamical networks with switching topology and multi-weights. Finally, two numerical examples with simulation results are given to show the correctness of the obtained passivity criteria.

Dissipativity and passivity analysis for memristor-based neural networks with leakage and two additive time-varying delays

Abstract In this paper, the problems of dissipativity and passivity analysis for memristor-based neural networks (MNNs) with both time-varying leakage delay and two additive time-varying delays are studied. By introducing an improved Lyapunov–Krasovskii functional (LKF) with triple integral terms, and combining the reciprocally convex combination technique, Wirtinger-based integral inequality with free-weighting matrices technique, some less conservative delay-dependent dissipativity and passivity criteria are obtained. The proposed criteria that depend on the upper bounds of the leakage and additive time-varying delays are given in terms of linear matrix inequalities (LMI), which can be solved by MATLAB LMI Control Toolbox. Meanwhile, the criteria for the system with a single time-varying delay are also provided. Finally, some examples are given to illustrate the effectiveness and superiority of the obtained results.

Passivity-based synchronization of stochastic switched complex dynamical networks with additive time-varying delays via impulsive control

The issue of passivity-based synchronization for switched complex dynamical networks with additive time-varying delays, stochastic and reaction–diffusion effects is investigated. In this paper, stochastic, passivity theory and impulsive control are taken to investigate this problem. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Ito differential rule and matrix analysis techniques, we established a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the switched complex dynamical networks is robustly passive in the sense of expectation. By constructing a suitable Lyapunov–Krasovskii functional using Jensen’s inequality, integral inequality technique and the passivity criterion of addressed complex dynamical networks is obtained. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares. Illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results.

Passivity Analysis of Coupled Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions

Two coupled reaction-diffusion neural networks (CRDNNs) with different dimensions of input and output are considered in this paper. The only difference between them is whether time-varying delay is incorporated in the mathematical model of network. We respectively analyze dissipativity and passivity of these CRDNNs. First, for the systems with different dimensions of input and output vectors, two new passivity definitions are proposed. Then, by exploiting some inequality techniques, several dissipativity and passivity criteria for these CRDNNs are established. Furthermore, we analyze stability of passive CRDNNs. Finally, two examples with simulation results are presented to verify the effectiveness of the proposed criteria.

The Input-to-State Stable (ISS) Approach for Stabilizing Haptic Interaction With Virtual Environments

Passivity has been a major criterion for designing a stable haptic interface due to its numerous advantages. However, passivity-based controllers have suffered from the design conservatism of the passivity criterion, particularly when users want to increase the maximum apparent impedance. Based on the input-to-state stable (ISS) criterion and an analogy between haptic interfaces and systems with hysteresis, this paper proposes a control framework that is less conservative than passivity-based controllers. The proposed ISS approach allows a non-predetermined finite amount of output energy to be extracted from the system. Therefore, the proposed method can increase the maximum apparent impedance compared with passivity-based approaches. The focus of this paper is on how the proposed approach is designed to satisfy the input-to-state stability criterion in real time without prior knowledge of the system. This paper also extends the primary single-port ISS approach to a two-port ISS approach for multiple-degree-of-freedom generalization. The experimental and numerical results demonstrate that the proposed ISS approach is able to stabilize a higher impedance range than the time-domain passivity approach. The experimental results also confirm that the proposed approach provides higher actual apparent impedance to the operator compared with the energy-bounding and force-bounding approaches.