An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.     

A tunable multivariable nonlinear robust observer for biological systems

This paper presents a robust nonlinear asymptotic observer with adjustable convergence rate with a great potential of applicability for biological systems in which the main state variables are difficult and expensive to measure or such measurements do not exist. This observer scheme is based on the classical asymptotic observer, which is modified to allow the tuning of the convergence rate. It is shown that the proposed observer provides fast and satisfactory estimates when facing load disturbances, system failures and parameter uncertainty while maintaining the excellent robustness and stability properties of the classical asymptotic observer. The implementation of the tunable observer is carried out by numerical simulations of a mathematical model of an anaerobic digestion process used for wastewater treatment. The key results are examined and further developed.     

Adaptive fuzzy control with output feedback for H infinity tracking of SISO nonlinear systems

Observer-based adaptive fuzzy H(infinity) control is proposed to achieve H(infinity) tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The key ideas in the design of the proposed controller are (i) to transform the nonlinear control problem into a regulation problem through suitable output feedback, (ii) to design a state observer for the estimation of the non-measurable elements of the system's state vector, (iii) to design neuro-fuzzy approximators that receive as inputs the parameters of the reconstructed state vector and give as output an estimation of the system's unknown dynamics, (iv) to use an H(infinity) control term for the compensation of external disturbances and modelling errors, (v) to use Lyapunov stability analysis in order to find the learning law for the neuro-fuzzy approximators, and a supervisory control term for disturbance and modelling error rejection. The control scheme is tested in the cart-pole balancing problem and in a DC-motor model.     

Full-state tracking control of a mobile robot using neural networks

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.     

Monitoring in a predator–prey systems via a class of high order observer design

The goal of this work is the monitoring of the corresponding species in a class of predator–prey systems, this issue is important from the ecology point of view to analyze the population dynamics. The above is done via a nonlinear observer design which contains on its structure a high order polynomial form of the estimation error. A theoretical frame is provided in order to show the convergence characteristics of the proposed observer, where it can be concluded that the performance of the observer is improved as the order of the polynomial is high. The proposed methodology is applied to a class of Lotka–Volterra systems with two and three species. Finally, numerical simulations present the performance of the proposed observer.     

Network Evolution Induced by Asynchronous Stimuli through Spike-Timing-Dependent Plasticity

In sensory neural system, external asynchronous stimuli play an important role in perceptual learning, associative memory and map development. However, the organization of structure and dynamics of neural networks induced by external asynchronous stimuli are not well understood. Spike-timing-dependent plasticity (STDP) is a typical synaptic plasticity that has been extensively found in the sensory systems and that has received much theoretical attention. This synaptic plasticity is highly sensitive to correlations between pre- and postsynaptic firings. Thus, STDP is expected to play an important role in response to external asynchronous stimuli, which can induce segregative pre- and postsynaptic firings. In this paper, we study the impact of external asynchronous stimuli on the organization of structure and dynamics of neural networks through STDP. We construct a two-dimensional spatial neural network model with local connectivity and sparseness, and use external currents to stimulate alternately on different spatial layers. The adopted external currents imposed alternately on spatial layers can be here regarded as external asynchronous stimuli. Through extensive numerical simulations, we focus on the effects of stimulus number and inter-stimulus timing on synaptic connecting weights and the property of propagation dynamics in the resulting network structure. Interestingly, the resulting feedforward structure induced by stimulus-dependent asynchronous firings and its propagation dynamics reflect both the underlying property of STDP. The results imply a possible important role of STDP in generating feedforward structure and collective propagation activity required for experience-dependent map plasticity in developing in vivo sensory pathways and cortices. The relevance of the results to cue-triggered recall of learned temporal sequences, an important cognitive function, is briefly discussed as well. Furthermore, this finding suggests a potential application for examining STDP by measuring neural population activity in a cultured neural network.     

A neural network controller for the path tracking control of a hopping robot involving time delays

In this paper a hopping robot motion with offset mass is discussed. A mathematical model has been considered and an efficient single layered neural network has been developed to suit to the dynamics of the hopping robot, which ensures guaranteed tracking performance leading to the stability of the otherwise unstable system. The neural network takes advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot parameters. Time delays in the control mechanism play a vital role in the motion of hopping robots. The present work also enables us to estimate the maximum time delay admissible with out losing the guaranteed tracking performance. Further this neural network does not require offline training procedures. The salient features are highlighted by appropriate simulations.     

Compensation type algorithms for neural nets: stability and convergence

Plasticity of synaptic connections plays an important role in the temporal development of neural networks which are the basis of memory and behavior. The conditions for successful functional performance of these nerve nets have to be either guaranteed genetically or developed during ontogenesis. In the latter case, a general law of this development may be the successive compensation of disturbances. A compensation type algorithm is analyzed here that changes the connectivity of a given network such that deviations from each neuron's equilibrium state are reduced. The existence of compensated networks is proven, the convergence and stability of simulations are investigated, and implications for cognitive systems are discussed.     

Neural pattern dynamics in an oscillator model of the thalamo-reticular system.

One of development issues for information processing with synchronous oscillations in the brain is how new information is coded and how a comparison with already existing information is performed. In the present work we study a simple neural network model of the thalamo-reticular system based on the Wilson-Cowan model of neuronal oscillatory behavior. Our results show that both cortical control over the thalamus and external sensory input are essential in coordinating and generating spatio-temporal patterns of synchronous activity. A main finding of the numerical simulations is that the network connectivity and the intrinsic oscillatory properties of the neurons result in distinct collective behaviors within the network. By varying the connectivity schemes comparable with lesionated or damaged brain regions our results are in good agreement with in vivo experimental results. Suppressing the sensory input results in temporal oscillatory activity in the beta and gamma range and a strong spatial dependence of the network activity.     

Motif-based protein sequence classification using neural networks.

We present a system for multi-class protein classification based on neural networks. The basic issue concerning the construction of neural network systems for protein classification is the sequence encoding scheme that must be used in order to feed the neural network. To deal with this problem we propose a method that maps a protein sequence into a numerical feature space using the matching scores of the sequence to groups of conserved patterns (called motifs) into protein families. We consider two alternative ways for identifying the motifs to be used for feature generation and provide a comparative evaluation of the two schemes. We also evaluate the impact of the incorporation of background features (2-grams) on the performance of the neural system. Experimental results on real datasets indicate that the proposed method is highly efficient and is superior to other well-known methods for protein classification.     

Incorporating ecological connectivity into ecological functional zoning: A case study in the middle reaches of Yangtze River urban agglomeration

Ecological functional zoning is critical for multiobjective sustainable management of social-ecological systems. However, the framework of ecological functional zoning needs to be further improved. In terms of the index system, the existing “element-structure–function” index system mainly considers the structural characteristics that have a negative impact on ecological processes, e.g., disturbances, while ignoring positive impacts, e.g., connectivity, which may weaken the role of key nodes in the ecosystem and is not conducive to regional ecological protection. In terms of research methodology, the widely used self-organizing feature mapping neural network (SOFM) produces a number of clusters that easily exceed expectations, thus increasing management difficulties. Therefore, there is an urgent need to explore new combining methods. Here, an improved index system combining ecological connectivity and ecological functions and a traditional index system including only ecological functions were constructed, and a zoning method combining a self-organizing feature mapping neural network and fuzzy mean clustering (SOFM-FCM) was used for functional zoning of the middle reaches of the Yangtze River urban agglomeration. The advantages of functional zoning incorporating ecological connectivity were verified by comparing the results of both zoning procedures before and after improvement. The results indicate that the study area could be divided into ecological conservation areas, biodiversity conservation areas, urban development areas, and grain production areas. The zoning schemes before and after the improved framework were reliable compared with the national planning scheme, but there was 20.6% inconsistency in the results after the improved framework. This was mainly manifested by the shift from biodiversity conservation areas to ecological conservation areas and from urban development areas to food production areas. This shift was more conducive to improving spatial continuity and landscape multifunctionality, thus maximizing ecological conservation, pushing back smart urban growth, and achieving food security. This study expands the research perspective concerned with ecological functional zoning, and these results can provide an important reference for regional ecological protection and related research.     

On the role of anatomy in learning by the cerebellar cortex

The properties due to the location of neurons, synapses, and possibly even synaptic channels, in neuron networks are still unknown. Our preliminary results suggest that not only the interconnections but also the relative positions of the different elements in the network are of importance in the learning process in the cerebellar cortex. We have used neural field equations to investigate the mechanisms of learning in the hierarchical neural network. The numerical resolution of these equations reveals two important properties: (i) The hierarchical structure of this network has the expected effect on learning because the flow of information at the neuronal level is controlled by the heterosynaptic effect through the synaptic density-connectivity function, i.e. the action potential field variable is controlled by the synaptic efficacy field variable at different points of the neuron. (ii) The geometry of the system involves different velocities of propagation along different fibers, i.e. different delays between cells, and thus has a stabilizing effect on the dynamics, allowing the Purkinje output to reach a given value. The field model proposed should be useful in the study of the spatial properties of hierarchical biological systems.     

Event-driven simulation of neural population synchronization facilitated by electrical coupling

Most neural communication and processing tasks are driven by spikes. This has enabled the application of the event-driven simulation schemes. However the simulation of spiking neural networks based on complex models that cannot be simplified to analytical expressions (requiring numerical calculation) is very time consuming. Here we describe briefly an event-driven simulation scheme that uses pre-calculated table-based neuron characterizations to avoid numerical calculations during a network simulation, allowing the simulation of large-scale neural systems. More concretely we explain how electrical coupling can be simulated efficiently within this computation scheme, reproducing synchronization processes observed in detailed simulations of neural populations.     

Electrocardiogram signal quality assessment using an artificially reconstructed target lead

In real applications, even the most accurate electrocardiogram (ECG) analysis algorithm, based on research databases, might breakdown completely if a quality measurement technique is not applied precisely before the analysis. The major concentration of this study is to describe and develop a reliable ECG signal quality assessment technique. The proposed algorithm includes three major stages: preprocessing, energy-concavity index (ECI) analysis and a correlation-based examination subroutine. The preprocessing step includes the removal of baseline wanders and high-frequency disturbances. The quality measurement based on ECI includes two separate stages according to the energy and concavity of the ECG signal. The correlation-based quality measurement step is mainly established by using the correlation between ECG leads estimated by applying a suitably trained neural network. The operating characteristics of the proposed ECI are sensitivity (Se) of 77.04% with a positive predictive value (PPV) of 90.53% for detecting high-energy noise. The correlation-based technique achieved the best scores (Se = 100%; PPV = 98.92%) for detecting high-energy noise and for recognising any other kind of disturbances (Se = 92.36%; PPV = 94.77%). Although ECI analysis acts effectively against high-energy disturbances, very poor performance is obtained in cases where the energy of the disturbances is not considerable. However, the correlation-based method is able to find all kinds of disturbances. For officially evaluating the proposed algorithm, an entry was sent to the Computing-in-Cardiology Challenge 2011 on 27 February 2012; a final score (accuracy) of 93.60% was achieved.     

Robust model matching design methodology for a stochastic synthetic gene network

Synthetic biology has shown its potential and promising applications in the last decade. However, many synthetic gene networks cannot work properly and maintain their desired behaviors due to intrinsic parameter variations and extrinsic disturbances. In this study, the intrinsic parameter uncertainties and external disturbances are modeled in a non-linear stochastic gene network to mimic the real environment in the host cell. Then a non-linear stochastic robust matching design methodology is introduced to withstand the intrinsic parameter fluctuations and to attenuate the extrinsic disturbances in order to achieve a desired reference matching purpose. To avoid solving the Hamilton-Jacobi inequality (HJI) in the non-linear stochastic robust matching design, global linearization technique is used to simplify the design procedure by solving a set of linear matrix inequalities (LMIs). As a result, the proposed matching design methodology of the robust synthetic gene network can be efficiently designed with the help of LMI toolbox in Matlab. Finally, two in silico design examples of the robust synthetic gene network are given to illustrate the design procedure and to confirm the robust model matching performance to achieve the desired behavior in spite of stochastic parameter fluctuations and environmental disturbances in the host cell.     

Uniform step-by-step observer for aerobic bioreactor based on super-twisting algorithm

This paper describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of aerobic bioreactor system. The observer was developed using a hierarchical structure based on a modified super-twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A nonsmooth analysis was proposed to prove the fixed-time convergence of the observer states to the bioreactor variables. The observer was tested to solve the state estimation problem of an aerobic bioreactor described by the time evolution of biomass, substrate and dissolved oxygen. This last variable was used as the output information because it is feasible to measure it online by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first-order sliding mode structure. A set of numerical simulations was developed to demonstrate how the proposed observer served to estimate real information obtained from a real aerobic process with substrate inhibition.     

Adaptive control for mimo uncertain nonlinear systems using recurrent wavelet neural network

Recurrent wavelet neural network (RWNN) has the advantages such as fast learning property, good generalization capability and information storing ability. With these advantages, this paper proposes an RWNN-based adaptive control (RBAC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The RBAC system is composed of a neural controller and a bounding compensator. The neural controller uses an RWNN to online mimic an ideal controller, and the bounding compensator can provide smooth and chattering-free stability compensation. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. Finally, the proposed RBAC system is applied to the MIMO uncertain nonlinear systems such as a mass-spring-damper mechanical system and a two-link robotic manipulator system. Simulation results verify that the proposed RBAC system can achieve favorable tracking performance with desired robustness without any chattering phenomenon in the control effort.     

Generalised local bond order parameter analysis: application to colloidal particles with dendritic polymer brushes

This study examines the self-assembly of colloidal particles with spherical dendritic brushes. The effective interaction between these particles was studied in Monte Carlo simulations of the Kremer–Grest model. Results confirmed the transferability of the effective potential at different temperatures. Using the potential of mean force obtained from Monte Carlo simulations, the structural formation of the system was studied in a three-dimensional system. The system is a crystalline state in the intermediate density range and exhibits re-entrant melting at much higher densities. Based on generalised local bond order analysis, a refined numerical method is proposed for analysing the structural formation of colloidal particles in three-dimensional systems. The numerical technique accurately reproduced the formation of the colloidal system.     

Complex Generalized Synchronization and Parameter Identification of Nonidentical Nonlinear Complex Systems

In this paper, generalized synchronization (GS) is extended from real space to complex space, resulting in a new synchronization scheme, complex generalized synchronization (CGS). Based on Lyapunov stability theory, an adaptive controller and parameter update laws are designed to realize CGS and parameter identification of two nonidentical chaotic (hyperchaotic) complex systems with respect to a given complex map vector. This scheme is applied to synchronize a memristor-based hyperchaotic complex Lü system and a memristor-based chaotic complex Lorenz system, a chaotic complex Chen system and a memristor-based chaotic complex Lorenz system, as well as a memristor-based hyperchaotic complex Lü system and a chaotic complex Lü system with fully unknown parameters. The corresponding numerical simulations illustrate the feasibility and effectiveness of the proposed scheme.     

Identification and estimation algorithm for stochastic neural system. II

The algorithm for identifying the stochastic neural system and estimating the system process which reflects the dynamics of the neural network are presented in this papar. The analogous algorithm has been proposed in our preceding paper (Nakao et al., 1984), which was based on the randomly missed observations of a system process only. Since the previous algorithm mentioned above was subject to an unfavorable effect of consecutively missed observations, to reduce such an effect the algorithm proposed here is designed additionally to observe an intensity process in a neural spike train as the information for the estimation.The algorithm is constructed with the extended Kalman filters because it is naturally expected that a nonlinear and time variant structure is necessary for the filters to realize the observation of an intensity process by means of mapping from a system process to an intensity process. The performance of the algorithm is examined by applying it to some artificial neural systems and also to cat's visual nervous systems. The results in these applications are thought to prove the effectiveness of the algorithm proposed here and its superiority to the algorithm proposed previously.