Learning the Dynamics of Embedded Clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks.In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations—generally in line with Siegelmann's theoretical work—which supply insights into how embedded structures of languages can be handled in analog hardware.     

Stability of fully asynchronous discrete-time discrete-state dynamic networks

We consider networks of a large number of neurons (or units, processors, ...), whose dynamics are fully asynchronous with overlapping updating. We suppose that the neurons take a finite number of states (discrete states), and that the updating scheme is discrete in time. We make no hypotheses on the activation function of the neurons; the networks may have multiple cycles and basins. We derive conditions on the initialization of the networks, which ensures convergence to fixed points only. Application to a fully asynchronous Hopfield neural network allows us to validate our study.     

Algebraic method of simplifying Boolean networks using semi‐tensor product of Matrices

The huge state space of large Boolean networks makes analysis and synthesis difficult. This paper, using a new matrix analysis tool called semi‐tensor product of matrices, to explain a simplification method of Boolean networks in a mathematical manner. The idea consists of two steps. First, remove the nodes whose logical dynamics are independent of themselves directly; second, use the logical functions (LFs) of the removed nodes to substitute for their corresponding variables in the LFs of other nodes; such nodes evolve directly with both themselves and the removed nodes. We discover that the simplified and original Boolean networks share some important topological structures such as attractor cycles, steady states and paths. An algebraic algorithm is provided to find all of the cycles and steady states of simplified Boolean networks. Finally we apply the results to the metastatic melanoma network to check the effect of the simplification method.     

具有未建模动态系统的自适应动态面输出反馈控制

针对一类具有未建模动态和动态扰动且状态不可量测的非线性系统,利用神经网络逼近未知函数设计K-滤波器重构系统状态,提出一种自适应输出反馈控制策略。通过对未建模动态的新刻画,避免动态信号的引入。采用动态面设计方法,取消理论分析中产生的未知连续函数的估计,降低设计的复杂性。利用Lyapunov方法证明了闭环系统的所有信号是半全局一致终结有界的,并通过仿真结果验证了所提出方案的有效性。     

Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.     

数据驱动的多智能体网络鲁棒包容控制

针对输入受限的受扰多智能体网络, 提出具有领航层、估计层、控制层和跟随者层的新型鲁棒包容控制方 案. 首先, 设计有限时间估值器获得跟随者的期望状态, 然后基于包容误差引入非均方折扣代价函数, 从而将鲁棒包 容控制问题转换成受限最优控制问题. 并应用Laypunov拓展原理证明得到的最优控制策略使得网络实现一致最终 有界稳定. 在系统动态完全未知的情况下, 采用提出的积分增强学习算法和执行器–评价器结构, 在线得到近似最 优控制策略. 仿真结果验证了理论方案的有效性和可行性.     

Mapping the forms of meaning in small worlds

Prox is a stochastic method to map the local and global structures of real‐world complex networks, which are called small worlds. Prox transforms a graph into a Markov chain; the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph's edges. It is the dynamics of the particles' trajectories that map the structural properties of the graphs that are studied. Concrete examples are presented in a graph of synonyms to illustrate this approach. © 2008 Wiley Periodicals, Inc.     

Applications of neural network prediction of conformational states for small peptides from spectra and of fold classes.

Electronic structures of small peptides were calculated 'ab initio' with the help of Density Functional Theory (DFT) and molecular dynamics that rendered a set of conformational states of the peptides. For the structures of these states it was possible to derive atomic polar tensors that allowed us to construct vibrational spectra for each of the conformational states with low energy. From the spectra, neural networks could be trained to distinguish between the various states and thus be able to generate a larger set of relevant structures and their relation to secondary structures of the peptides. The calculations were done both with solvent atoms (up to ten water molecules) and without, and hence the neural networks could be used to monitor the influence of the solvent on hydrogen bond formation. The calculations at this stage only involved very short peptide fragments of a few alanine amino acids but already at this stage they could be compared with reasonable agreements to experiments. The neural networks are shown to be good in distinguishing the different conformers of the small alanine peptides, especially when in the gas phase. Also the task of predicting protein fold-classes, defined from line-geometry, seems promising.     

Fuzzy self-adaptive radial basis function neural network-based control of a seven-link redundant industrial manipulator

This paper proposes a method for the identification of dynamics and control of a multi-link industrial robot manipulator using Runge-Kutta-Gill neural networks (RKGNNs). RKGNNs are used to identify an ordinary differential equation of the dynamics of the robot manipulator. A structured function neural network (NN) with sub-networks to represent the components of the dynamics is used in the RKGNNs. The sub-networks consist of shape adaptive radial basis function (RBF) NNs. An evolutionary algorithm is used to optimize the shape parameters and the weights of the RBFNNs. Due to the fact that the RKGNNs can accurately grasp the changing rates of the states, this method can effectively be used for long-term prediction of the states of the robot manipulator dynamics. Unlike in conventional methods, the proposed method can even be used without input torque information because a torque network is part of the functional network. This method can be proposed as an effective option for the dynamics identification of manipulators with high degrees-offreedom, as opposed to the derivation of dynamic equations and making additional hardware changes as in the case of statistical parameter identification such as linear least-squares method. Experiments were carried out using a seven-link industrial manipulator. The manipulator was controlled for a given trajectory, using adaptive fuzzy selection of nonlinear dynamic models identified previously. Promising experimental results are obtained to prove the ability of the proposed method in capturing nonlinear dynamics of a multi-link manipulator in an effective manner.     

Propagation of nonclassical correlations through one-dimensional quantum networks

We investigate transfer of nonclassical correlations through one-dimensional quantum networks for several schemes by employing concurrence and local quantum uncertainty as the measures and the extended Werner-like states as the initial resources. The exact dynamics of quantum correlations are derived, and the differences of dynamics between concurrence and local quantum uncertainty are analyzed. Besides, the influences of node number and initial parameters on the generation of quantum correlations between the two end nodes are discussed. Moreover, we explore the effects of duplex encodings and double channels on distribution of quantum correlations.     

Explicit synchronisation of heterogeneous dynamics networks via three-layer communication framework

This paper addresses the explicit synchronisation of heterogeneous dynamics networks via three-layer communication framework. The main contribution is to propose an explicit synchronisation algorithm, in which the synchronisation errors of all the agents are decoupled. By constructing a three-layer node model, the proposed algorithm removes the assumptions that the topology is fixed and the synchronisation process is coupled. By introducing appropriate assumptions, the algorithm leads to a class of explicit synchronisation protocols based on the states of agents in different layers. It is proved in the sense of Lyapunov that, if the dwell time is larger than a threshold, the explicit synchronisation can be achieved for closed-loop heterogeneous dynamics networks under switching topologies. The results are further extended to the cases in which the switching topologies are only frequently but not always connected. Simulation results are presented with four single-link manipulators to verify the theoretical analysis.     

Matrix expression and vaccination control for epidemic dynamics over dynamic networks

This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks (SISED-DN) is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.     

Anomaly detection in complex system based on epsilon machine

Epsilon machine is a computational mechanics theory and its most effective reconstruction algorithm is causal state splitting reconstruction (CSSR). As CSSR can only be applied to symbol series, symbolising real series to symbol series is necessary in practice. Epsilon machine discovers the hidden pattern of a system. In reconstructed results, the hidden pattern is expressed as the set of causal states. Based on the variation of causal states, a novel anomaly detection algorithm, structure vector model, is presented. The vector is composed of the causal states, and the anomaly measure is defined with the distance of different vectors. An example of the crankshaft fatigue demonstrates the effectiveness of the model. The mechanism of the model is discussed in detail from three aspects, computational mechanics, symbolic dynamics and complex networks. The new idea defining anomaly measure based on the variation of hidden patterns can be interpreted reasonably with the hierarchical structure of complex networks. The jump in anomaly curves is a nature candidate for the threshold, which confirms the positive meaning of the model. Finally, the parameter choice and time complexity are briefly analysed.     

Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback

This paper focuses on adaptive control of nonaffine nonlinear systems with zero dynamics using multilayer neural networks. Through neural network approximation, state feedback control is firstly investigated for nonaffine single-input-single-output (SISO) systems. By using a high gain observer to reconstruct the system states, an extension is made to output feedback neural-network control of nonaffine systems, whose states and time derivatives of the output are unavailable. It is shown that output tracking errors converge to adjustable neighborhoods of the origin for both state feedback and output feedback control.     

Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning

This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of uncertain nonlinear system using reinforcement learning. A new design approach of wavelet based adaptive reduced order observer is proposed. The proposed wavelet adaptive reduced order observer performs the task of identification of unknown system dynamics in addition to the reconstruction of states of the system. Reinforcement learning is used via two wavelet neural networks (WNN), critic WNN and action WNN, which are combined to form an adaptive WNN controller. The “strategic” utility function is approximated by the critic WNN and is minimized by the action WNN. Owing to their superior learning capabilities, wavelet networks are employed in this work for the purpose of identification of unknown system dynamics. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. A numerical example is provided to verify the effectiveness of theoretical development.     

Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

Expressive power of first-order recurrent neural networks determined by their attractor dynamics

We provide a characterization of the expressive powers of several models of deterministic and nondeterministic first-order recurrent neural networks according to their attractor dynamics. The expressive power of neural nets is expressed as the topological complexity of their underlying neural ω-languages, and refers to the ability of the networks to perform more or less complicated classification tasks via the manifestation of specific attractor dynamics. In this context, we prove that most neural models under consideration are strictly more powerful than Muller Turing machines. These results provide new insights into the computational capabilities of recurrent neural networks.     

State estimation for two‐dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays

This paper is concerned with the state estimation problem for two‐dimensional (2D) complex networks with randomly occurring nonlinearities and randomly varying sensor delays. To describe the fact that measurement delays may occur in a probabilistic way, the randomly varying sensor delays are introduced in the delayed sensor measurements. The randomly occurring nonlinearity, on the other hand, is included to account for the phenomenon of nonlinear disturbances appearing in a random fashion that is governed by a Bernoulli distributed white sequence with known conditional probability. The stochastic Brownian motions are also considered, which enter into not only the coupling terms of the complex networks but also the measurements of the output systems. Through available actual network measurements, a state estimator is designed to estimate the true states of the considered 2D complex networks. By utilizing an energy‐like function, the Kronecker product and some stochastic analysis techniques, several sufficient criteria are established in terms of matrix inequalities under which the 2D estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the explicit expression of the estimator gains is also characterized. Finally, a numerical example is provided to demonstrate the effectiveness of the design method proposed in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability analysis and controller design for consensus in discrete-time networks with heterogeneous agent dynamics

In this paper, we study the heterogeneous consensus problem in directed networks consisting of first- and second-order agents that can only receive the position states of their neighbors. Necessary and sufficient conditions on the controller parameters are obtained in order to achieve consensus in the network. The mathematical expressions of the consensus equilibria are given for two different scenarios. Furthermore, we propose a systematic method for choosing controller parameters to ensure stability in a network of agents with heterogeneous dynamics. Several numerical examples are also provided to illustrate the theoretical results.