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In this paper, adaptive neural tracking control problem is considered for non-strict-feedback high-order nonlinear systems with quantized input signal. Compared with the logarithmic quantizer, the quantizer introduced in this paper can avoid chattering problem. The dynamic surface control (DSC) technique is introduced to solve the problem of ‘explosion of complexity’, which is appeared in the classic adaptive backstepping control of high-order nonlinear systems. The structural properties of radial basis function neural networks (RBF NNs) are used to simplify the design difficulty from the functions of whole state variables. According to the classic adaptive backstepping technique and neural network algorithm, an output tracking controller is designed, which can guarantee that all the signals of the closed-loop system are semiglobally uniformly bounded and the output of the system can track the reference signal. Finally, a numerical example is presented to verify the effectiveness of the proposed method.

Extreme-learning-machine based auto-encoder (ELM-AE) is regarded as a useful architecture with fast learning speed and general approximation ability, and stacked ELM is used to develop efficient and effective deep learning networks. However, considering features learned from conventional ELM-AEs have issues of weak nonlinear representation ability and random factors in feature projection, this paper proposes an improved ELM-AE architecture which utilize low-rank matrix factorization to learn optimal low-dimensional features. Two superiorities can be obtained compared to conventional ELM-AEs. One is the dimensionality of the hidden layer in ELM-AE could be set arbitrarily, e.g. a higher-dimension hidden layer could lower the random effect in feature learning and enhance features representation ability. The other is enhancing features nonlinear ability, since features are learned directly from the nonlinear outputs of hidden layer. Finally, comparison experiments on numerical and image datasets are implemented in this paper to verify the superior performance of the proposed ELM-AE in this paper.

From the perspective of large-scale system, a directed complex dynamic network (DCDN) may be considered as a coupling system of the node subsystem (NS) and the link subsystem (LS). In this paper, by using the outgoing link vector and incoming link vector for DCDN, the dynamics of LS is described by employing the vector differential equation instead of the matrix differential equation. Since the outgoing and incoming link vectors have the stronger geometric intuition, the results in this paper show that this kind model of links can not only reflect the direction of links but also find the dynamic tracking goal of links more easily when the state synchronization of NS emerges. Furthermore, by employing the simple mathematical conditions, the nonlinear controller of NS and the coupling term of LS are proposed to ensure achieving the asymptotical state synchronization for DCDN. Finally, the numerical simulations are given to demonstrate the validity of the results in this paper.

This paper tackles the event-triggering filtering problem for a class of nonlinear networked control systems subject to the prescribed disturbance attenuation level. To alleviate the data transmission burden of communication channels, an event-triggering mechanism is adopted, where the data can be transmitted only if certain condition is fulfilled. The T-S fuzzy model approach is utilized to approximate the nonlinear dynamics. It is the purpose of this paper to design a filter for the addressed nonlinear system ensuring that the filtering error system is asymptotically stable whereas the prespecified H ∞ criterion is guaranteed. By using Lyapunov approach in combination with matrix analysis method, the sufficient conditions are established for the existence of desired filtering parameters in terms of the solvability of certain linear matrix inequalities. Finally, a numerical simulation example is put forward to demonstrate the validity and effectiveness of the developed theoretical results.

This paper presents a novel nonlinear adaptive sensor fusion method for integrated navigation systems with varying noise parameters. The innovation is utilizing deep neural networks to mine the noise-related patterns of specific sensors and combining it with conventional nonlinear filters. This hybrid approach improves the feasibility and robustness of adaptive filtering by achieving an effective estimation of the originally weakly observable noise parameters. The specific sensors are defined as α -type sensors whose errors are entirely generated by themselves. The mathematical model for analyzing α -type sensors output sequence and the deep neural network for mining the patterns of interest are established. All adaptive filtering systems using α -type sensors can benefit from this paper. Specifically, it is applied to inertial and satellite integrated navigation system. The numerical experiments indicate that the proposed filter achieves promising accuracy and robustness improvement as compared to conventional nonlinear filters. And the comparisons between different nonlinear approximation algorithms indicate that the first-order approximation is accurate enough for our application.

This paper solves the fault-tolerant control (FTC) problem of uncertain nonlinear systems in nonstrict-feedback form. The controlled plants considered in this paper are more complicated than existing ones, which is composed of the unknown nonlinearities, unmeasured states, and sensor faults and unknown dead zone input nonlinearity. Fuzzy logic systems and a fault-estimation-based state observer are used for identifying the unknown nonlinearities and obtaining the unmeasured states, respectively. By designing the sensor faults compensation and the dead zone inverse compensation methods, an observer-based fault-tolerant compensation control scheme is developed under backstepping recursive design frame. And it is testified that the closed-loop signals are bounded, and the tracking performance is satisfied even when the controlled systems are not free of sensor faults and unknown dead zone input nonlinearity. An electromechanical system is used to test the effectiveness of the developed control strategy.

The problem of distributed fixed-time leader-following consensus tracking control for nonholonomic chained-form dynamic systems with nonlinear disturbances is considered in this paper. Compared with the existing works, this paper considers a class of more general nonholonomic multi-agent systems where both the leader and the followers have nonlinear uncertainties. For undirected graphs, a distributed observer for each follower is investigated such that both the leader state and input can be estimated by the followers in a fixed time. Based on the distributed observers, a consensus tracking controller is proposed to ensure that the tracking errors convergence to zero within a fixed time. Lyapunov analysis proves the stability of the closed-loop system. A simulation example of wheeled mobile robots is given to demonstrate the effectiveness of the proposed controllers.

This paper investigates the problem of neural network (NN) prescribed performance tracking control for a class of switched stochastic nonlinear pure-feedback systems which contain unknown nonlinear functions, unmeasured state variables, and unknown hysteresis input. It provides an adaptive NN controller which is not restricted to a particular type of hysteresis input. A general mathematical model is introduced to describe two kinds of hysteresis nonlinearities and to utilize in the control design producer. Other focus of this paper is on the performance constraint problem to avoid performance degradation and system damage in practical control systems. Prescribed performance control (PPC) and backstepping technique are thus synthesized to develop an adaptive NN output feedback tracking control scheme under deterministic switching signal. Regarding this concern, to cope with the cause of non-differentiable difficulties and complex deductions in traditional PPC, a new asymmetry error transformation is employed. Moreover, radial basis function NNs (RBFNNs) are applied to approximate the unknown nonlinear functions and to construct a NN nonlinear observer to estimate the immeasurable state variables. Based on Lyapunov stability theory, it is demonstrated that the proposed controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a small neighborhood of the origin with the prescribed performance bounds. Finally, two simulation examples are provided to confirm the advantages of the presented control design approach.

For time series prediction, hybrid systems that combine linear and nonlinear models can provide more accurate performance than a single model. However, the irregularity of the error series and the unknown nature of combinations of different forecasters may strongly impact the performance of hybrid systems. Therefore, in this paper, we propose a novel method for time series prediction, in which error decomposition and a nonlinear combination of forecasters are introduced. The proposed method performs the following: (i) linear modeling to obtain the error series, (ii) error decomposition by using variational mode decomposition (VMD), (iii) nonlinear modeling and a phase fix procedure for the error subseries, and (iv) a combination of forecasters through an appropriate combination function generated by a nonlinear model. By using the proposed method, this paper constructs two hybrid systems, in which the autoregressive integrated moving average (ARIMA) is used for linear modeling, and two artificial intelligence (AI) models, namely, the multilayer perceptron (MLP) and support vector regression (SVR), are used for nonlinear modeling and combination, respectively. Finally, four time series data sets, six evaluation metrics, two single models and thirteen hybrid systems are used to assess the effectiveness of the proposed method. The empirical results show that hybrid systems based on error decomposition and a nonlinear combination of forecasters can achieve better performance than some existing systems and models.

This paper studies the problem of adaptive output-feedback formation tracking control for networked uncertain nonholonomic mobile robots (NMRs) with different limited communication distances, while achieving connectivity preservation and collision avoidance. In robot control, equipping all the speed sensors not only increases the cost of the system but also risks losing accuracy and reliability. In this paper, it is assumed that the velocities of the nonholonomic mobile robots in this paper are unknown, they are estimated according to the output of the systems by an adaptive observer via a neural network. The designed dynamic surface based on nonlinear transformation errors can achieve the above three control objectives at the same time, avoiding the situation of using multiple potential functions to solve such problems, which will lead to conflicts in the selection of the design parameters. Compared with the existing references about formation tracking to maintain connectivity and avoid collisions, the main contribution of this paper is to design an observer of robot speed estimation and use only a neural network to estimate the unknown nonlinear term of the system itself. The unknown nonlinearity produced in the process of controller design does not need an additional neural network. Furthermore, the effectiveness of the proposed strategy is verified by simulation examples.

This paper addresses global Mittag-Leffler lag quasi-synchronization (GMLQS) of fractional-order memristor-based neural networks (FMNNs). Firstly, for a general class of fractional-order nonlinear systems with interval uncertainties, a kind of linear feedback pinning controller, which works by feeding back partial state errors to the partial controlled variables, is designed to achieve global Mittag-Leffler ultimate boundedness (GMUB). Correspondingly, a GMUB criterion in the form of linear matrix inequality (LMI) is derived with the aid of a Lyapunov function and a newly established fractional-order differential inequality. Then, the linear feedback pinning controller is employed for GMUB of the synchronization error system, which is equivalent to GMLQS of FMNNs. Since there exists the propagation delay between drive-response FMNNs and the synchronization error system can not be obtained straightforwardly, an identical equation about Caputo’s fractional derivatives is established to overcome this difficulty. Moreover, the detailed pinning control scheme design procedures for a prescribed GMLQS performance are presented, where the performance involves both ultimate error bound and transient behavior. In the control scheme, an auxiliary LMI and an optimization objective function are introduced, which can significantly reduce control cost. Finally, a numerical example is presented to show the feasibility of the control scheme. The results obtained in this paper have improved the existing criterion on quasi-synchronization of FMNNs, and will also provide a novel insight into pinning control of fractional-order nonlinear systems.

This paper is mainly concerned with fixed-time synchronization control for a class of Cohen–Grossberg neural networks (CGNNs) with nonlinear coupling and time-varying delay based on synchronization dynamics. First, by using a derived sufficient condition of fixed-time synchronization (FTS) for nonlinear coupled CGNNs (NCCGNNs) with time-varying delay, a novel fixed-time synchronization controller with time-varying delay is designed. Second, by combining the synchronization dynamic viewpoint and the obtained fixed-time synchronization control rule, several useful fixed-time synchronization controllers (FTSCs) are derived. Third, comparisons with known conclusions are provided to show the innovation and feasibility of the proposed fixed-time synchronization control methods. Finally, two examples are given to verify the effectiveness of the theoretical results. Compared with related works, the advantages of this paper are as follows: (1) The designed novel FTSCs can scientifically and efficiently process the time-varying delay of the addressed coupled CGNNs; (2) The derived settling time of the FTS built on FTSCs can reflect the effect of the proposed system’s parameters on the synchronization convergence time.

In this paper, the H∞ filtering problem is addressed for a class of nonlinear stochastic discrete-time systems subject to Round-Robin protocol, measurement outliers, randomly occurring parameter uncertainties and randomly occurring nonlinearities. First of all, the considered system is influenced by the parameter uncertainties, nonlinear dynamics and external disturbances. Next, mutually independent Bernoulli-distributed white sequences are employed to describe the phenomena of randomly occurring parameter uncertainties and nonlinearities, respectively. Besides, the Round-Robin protocol is introduced to prevent the occurrence of data collisions during the signal transmission. Moreover, a filter with adaptive saturation is constructed to weaken the impact of the measurement outliers. Through constructing a suitable Lyapunov function, sufficient conditions are established to ensure that the error system dynamics is exponentially mean-square stable and satisfies the H∞ performance. Subsequently, the filter gains are designed by solving a set of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the filtering scheme proposed in this paper.

An adaptive dynamic programming (ADP) based event-triggered control method is established in this paper to solve the optimal control problem of unknown continuous-time nonlinear systems with input constraints. First, the unknown system is identified using two neural networks (NNs). Second, the threshold for event-triggering condition is designed, which guarantees the system stability. Then, a critic NN is employed to approximate the value function and the closed-loop system is proved to be uniformly ultimately bounded. Finally, the simulation results demonstrate the feasibility of the developed ADP method. The main contributions of this paper are that the developed ADP-based event-triggered control method avoids the Zeno phenomenon effectively and updates the weights of three NNs simultaneously in the process of implementation. Meanwhile, an improved critic NN weight updating criterion is adopted, which does not require an initial admissible control.

The problem of event-triggered guaranteed cost consensus for nonlinear multi-agent systems with time delay and uncertain parameters is solved in this paper. First, a distributed event-triggered strategy is presented, by which control protocol is updated only at the triggering time instants, leading to significant saving of communication resources. Second, based on the Lyapunov method and the proposed event-triggered strategy, some criteria are obtained to ensure that guaranteed cost consensus can be achieved. Moreover, it is proved that the Zeno behavior is excluded under the proposed event-triggered scheme. Third, an algorithm is given to design suitable control gains in terms of linear matrix inequalities. Finally, the validity of the proposed results in this paper is verified via numerical simulation.

Matrix completion is extensively studied due to its wide applications in science and technology. In this paper, we concentrate our study on the matrix completion problem for image analysis tasks due to their immense importance and pervasive use in many fields. A rich collection of models has been proposed to capture both linear and nonlinear relationships latent in a matrix. Even though nonlinear models possess more powerful matrix completion capabilities than their linear counterparts, these models generally carry higher model complexity and tuning difficulties. To take advantage of the superior discriminative power offered by nonlinear models while curbing its deployment overheads, this paper proposes a novel nonlinear matrix completion model utilizing a deep learning-based approach. In contrast to existing nonlinear models, the new model carefully explores and exploits spatial locality among adjacent matrix elements exhibited in patches of various sizes and locations in a target matrix. Building upon this idea, a new patch-based nonlinear matrix completion algorithm is designed. The algorithm leverages a convolutional neural network to learn the predictive relationship between a matrix element and its surrounding elements through an end-to-end trainable fashion, leading to a capable and easy-to-deploy nonlinear matrix completion solution. To identify an optimal patch size suited for tackling a given matrix completion task without exhaustively enumerating all candidate patch sizes, the new algorithm is coupled with a fast stochastic search procedure, yielding a good trade-off between computational efficiency and accuracy. Extensive experiments are conducted to validate the effectiveness and advantages of the proposed algorithm for nonlinear matrix completion problem in comparison with a series of state-of-the-art algorithms. Experimental results consistently demonstrate the superiority of the new algorithm in completing images with a variety of random and textual noises.

This paper investigates the leader-following bipartite consensus problem for second-order multi-agent systems with nonlinear dynamics, node-delay and signed digraph topology. By using pinning control strategies, an event-triggered controller is designed to achieve bipartite consensus in multi-agent systems, where a novel event-triggered function is proposed. Two cases are discussed in this paper according to whether the node-delay is differentiable or not. When the node-delay is differentiable, an LMI (Linear Matrix Inequality) condition is derived for reaching bipartite consensus in multi-agent systems by using M-matrix theory. When the node-delay is non-differentiable, some bipartite consensus conditions are developed based on Jensen inequality and the reciprocally convex approach. Moreover, it is shown that Zeno-behavior can be avoided for the designed event-triggered controller. Finally, some numerical examples are provided to illustrate the effectiveness and correctness of the theoretical analysis.

In this paper, we investigate the general decay synchronization (GDS) of memristor-based BAM neural networks (MBAMNNs) with mixed time delays as well as discontinuous activations. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides via functional differential inclusions. Then, by constructing suitable Lyapunov-krasovskii functionals and employing some useful inequality techniques, several novel conditions ensuring the GDS of considered BAM neural networks are obtained through designing two different types of nonlinear controllers. The results we proposed in this paper are general since GDS have generalized the traditional asymptotical synchronization, exponential synchronization, polynomial synchronization and contained them as its special cases. Finally, two examples and their numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

This paper is concerned about barrier Lyapunov function(BLF)-based adaptive dynamic surface control(DSC) for a class of stochastic nonlinear systems of full state constraints with hysteresis input and time delay. All states of the system are guaranteed to be constrained in bounded compact set. The pure feedback nonlinear system is transformed into a strictly feedback nonlinear system with nonaffine nonlinear terms by using the mean value theorem. By using backstepping design of BLF combine with DSC technique, the explosion of complexity is avoided. Based on the neural network with the finite covering lemma, the time-delay functions are solved. Simultaneously, the backlash-like hysteresis input control in this paper is considered. The two cases of symmetric and asymmetric BLFs are discussed separately. An adaptive controller is designed to ensure that the output tracking error converges on a small region of the origin. Finally, the control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of two simulation cases are presented to prove the effectivity of the theoretical analysis.

This paper investigates the adaptive neural fault-tolerant control problem for a class of strict-feedback nonlinear systems with simultaneous actuator and sensor faults. The faults considered in this paper are bias (lock-in-place), drift, loss of accuracy, and loss of effectiveness faults. Only one parameter law is updated at each step to reduce the computational burden. By utilizing the adaptive neural network backstepping control strategy, the closed-loop nonlinear system is guaranteed to be semi-globally uniform ultimate bounded, and all the signals are bounded. Finally, a simulation example is given to show the effectiveness of the proposed control strategy.

Interval type-2 fuzzy neural network (IT2FNN) has attracted considerable interest for modeling nonlinear dynamic systems in recent years. However, this promising technique is confronting the problem that constructing a suitable IT2FNN is a potential challenge ignored by most researchers. To solve this problem, a self-constructing interval type-2 fuzzy neural network (SC-IT2FNN), based on the cooperative strategies, is proposed in this paper. The main contributions of this paper are: First, a comprehensive evaluation algorithm (CEA), cooperating with the parameter optimization, is developed to design the structure of SC-IT2FNN to enhance its generalization performance. Second, a hierarchical optimization mechanism, cooperating with the nonlinear and linear parameters of SC-IT2FNN, is proposed to accelerate its learning speed. Third, the convergence of SC-IT2FNN is theoretically analyzed in detail to ensure its successful applications. Finally, several benchmark nonlinear systems and a real application are utilized to evaluate the effectiveness of SC-IT2FNN. The results demonstrate that our proposed SC-IT2FNN significantly improve the modeling performance in terms of high accuracy and compact structure.

This paper investigates the relay tracking problem for networked nonlinear multi-agent systems with communication delays. By setting up monitoring agents in a certain area, the object of this paper is to track the targets which cross over the monitoring area through the relay cooperative tracking strategy. Based on an improved data-driven control method, a data-driven relay tracking control strategy is proposed. It is shown that under the presented relay tracking strategy, all pursued agents asymptotically achieve tracking the target agents. Moreover, with the introduced delay compensation mechanism in the control strategy, the communication delays are compensated actively. Finally, some simulations are provided to illustrate the performance of the proposed strategies.

In this paper, we have made an effort to investigate the general decay projective synchronization (GDPS) problem of a type of delayed memristor-based BAM neural networks. First, we introduced a type of novel nonlinear controller. Then, we derived some sufficient conditions ensuring the GDPS of considered networks by employing differential inclusion theory and using well-known Lyapunov functional method. Lastly, an example is given to show the correctness of obtained results. To the authors’ knowledge, the results derived in this paper are the only available ones on the projective synchronization of BAM neural networks, combining the three main factors, i.e., memristor, general decay and time-varying delays.

This paper proposes finite-horizon optimal tracking control approach based on data for completely unknown discrete-time nonlinear affine systems. First, the identifier is designed by input and output data, which is used to identify system function and system model. And based on tracking error, the system function is transformed to the augmentation system with finite-time optimal performance. In finite time, by minimizing the performance index function, the iterative approximate dynamic programming (ADP) is utilized to solve Hamilton–Jacobi–Bellman (HJB) equation. The idea is carried by the policy iterative (PI) based on the model neural network, which makes the iterative control of the augmentation system available at the each step. At the same time, the action neural network is utilized to acquire the approximate optimal tracking control law and the critic neural network is used for approximating the optimal performance index function for the augmentation system. Afterwards, the paper show the analysis process that the convergence and stability for the iterative ADP algorithm and the weight estimation errors based on the PI, respectively. The end of the paper, a simulation example is applied to show the theoretical results and proposed approach.

This paper investigates the problem of adaptive neural tracking control for a class of uncertain switched nonlinear systems in nonstrict-feedback structure. It should be pointed out that both the issues of unknown backlash-like hysteresis and output dead-zone are involved in the considered systems. A Nussbaum-type gain function is presented in this paper to overcome the difficulty existing in tracking the output dead-zone with unknown control direction, and the variable separation technique is applied to decompose the unknown functions containing all state variables into the sum of smooth functions with each error dynamic. Then by combining the backstepping approach and the approximation capability of radial basis function neural networks, an adaptive neural tracking control strategy is constructed, which guarantees that all the signals of the closed-loop systems are controlled to be semi-globally uniformly ultimately bound and the tracking error converges to a small region around the origin. Finally, the effectiveness of the proposed control strategy is verified by two simulation examples.

This paper investigates the consensus asymptotic convergence problem for a class of nth-order strict-feedback multiagent systems, which include the input quantization, actuator faults, unknown nonlinear functions and directed communication topology. Because the upper bounds of the time-varying stuck faults and external disturbance are commonly difficult to accurately determine, it is also assumed that these upper bounds are unknown in this paper. First, a group of first-order filters are designed to estimate the bounds of the reference signal for each agent. Second, smooth functions are introduced to compensate the effect of quantization and bounded stuck faults. Meanwhile, a new back-stepping method is used to propose an intermediate control law and an adaptive design procedure, and the final distributed control protocols are established. All closed-loop signals are uniformly bounded, and the tracking errors asymptotically converge to zero. Finally, a practical example simulation is provided to demonstrate the effectiveness of the proposed scheme.

Probabilistic models have proven their strength to model many natural phenomena as close as possible to reality, in particular, the probabilistic self organizing map (PRSOM) that belongs to the unsupervised learning models. It allows to provide an estimation of the probability density function through the likelihood maximization. This latter function depends on several parameters given by the model architecture. In this context, the aim of this paper is to deal with the architecture choice problem that consists in determining the optimal number of components needed for a better performance. In this paper, we propose a new optimization model that describes the problem above. We present the architecture of PRSOM in a mathematical system of a non linear objective function with mixed variables under linear and quadratic constraints. Due to the complexity of the resolution, we suggest the continuous Hopfield neural network (CHN) that we support by a deep stability analysis. Performance of the proposed model is demonstrated through the dataset clustering.

In this paper, the resilient state estimation problem is discussed for a class of discrete nonlinear complex networks with time-delay subject to the stochastic communication protocol (SCP). The SCP is employed to determine which node has the priority of accessing to the communication networks at each transmission instant. A switch-based approach is utilized to establish the updating rule of the measurement output under the SCP. The aim of the paper is to design a resilient state estimator for the addressed complex networks with time-delay and SCP, where sufficient conditions are given to ensure that the estimation error is exponentially ultimate bounded in the mean-square sense and the asymptotic upper bound of the estimation error is given. Moreover, the expression forms of the desired estimator gains are obtained via the solutions to a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the validity of the proposed resilient state estimation method.

In this paper, neural networks (NNs)-based adaptive dynamic surface control is investigated for a class of pure-feedback nonlinear systems with unknown time delay and input hysteresis nonlinearities. The design difficulty appeared in this paper due to time delay is handled by combining neural networks with finite covering lemma instead of using Krasovskii functionals, and the assumptions on the time-delay functions are removed based the finite covering lemma and NNs. Meanwhile, completely unknown backlash-like hysteresis control input that frequently exists in practice is also considered. By combining the adaptive backstepping recursive design technique with the universal approximation ability of neural networks, an adaptive neural control algorithm is systemically designed for the system under consideration, and the explosion of complexity exists in traditional backstepping design is avoided by using dynamic surface technique. It is shown that the designed adaptive controller can guarantee that all the signals are ultimately uniformly bounded and the desired signal can be tracked with a small domain of the origin. A numerical example and an example of a real plant for adjustable metal cutting system are provided to show the feasibility of the proposed method.

This paper investigates the consensus problem of the second-order nonlinear multi-agent systems (MAS) with unknown periodic time-varying parameters (UPTVP) and imprecise communication topology structure (ICTS). T–S fuzzy models is used to express the ICTS, and the concept of fuzzy union connected (FUC) is defined. Under the condition that the ICTS is FUC, an adaptive repetitive learning control protocol is presented such that all the followers can track the leader asymptotically. With the information of leader agent is known to a small portion of following agents, an auxiliary control term was presented for each follower agent to handle leaders dynamics. The distributed MAS consensus is analyzed based on the Lyapunov stability theory. Furthermore, the proposed protocol is further promoted to solve the formation control problem. Finally, simulation results are shown to demonstrate the validity of the proposed design methods in this paper.

The action-dependent heuristic approximate dynamic (ADHDP) for nonlinear multi-input multi-output (MIMO) system needs different forms to adapt to variable practical objects. Due to some inappropriate network structure or training algorithm, unsuccessful designs or undesirable control effect is common in reality. Thus, at first, this paper addresses the chain rule problem of the compound derivative in training the nonlinear MIMO ADHDP. Then, this paper researches and proposes four actor-critic algorithms systematically according to four typical nonlinear systems. That is, the action-network extension, the sub-network, the cascaded action-network and the combined method. To illustrate the four methods, their detailed structures, derivation procedures and training algorithms are derived. The Lyapunov stability for the nonlinear MIMO ADHDP is proved as well. Through examples of an idling engine and aircraft controlling, the simulation results show the effectiveness of these methods. Besides, the property, advantages, disadvantages and the applicability of these methods are compared and highlighted. The four methods can be used to meet the design requirement of almost all the nonlinear MIMO ADHDP control systems. For incoming scholars in search of a nonlinear MIMO ADHDP to achieve the best control effect, the four actor-critic structures and algorithms can be a reference.

This paper focuses on studying the distributed leader-following consensus problem of heterogeneous second-order time-varying nonlinear multi-agent systems (HSTN_MASs) under directed switching topology. Firstly, based on the relative position and relative velocity measurements among neighborhood agents, a class of distributed tracking protocols are proposed. Then the state transformations are provided to solve the time-varying nonlinearity and translate the leader-following problem into the stabilization control problem. By constructing the topology-dependent Lyapunov function and choosing appropriate time-varying regulation factor and coupling strength, it is shown that the exponential tracking of HSTN_MASs can be achieved. Moreover, this paper discusses the distributed leaderless consensus problem of HSTN_MASs. Finally, several simulation examples are given to illustrate the validity of theoretical results.

This paper investigates the matrix projective synchronization (MPS) problem for time-varying disturbed complex dynamical networks (CDNs) with uncertain nonlinear structures and different dimensional nodes. In order to well describe the practical networks, the unavoidable unknown nonlinear structure and the inevitable uncertain disturbance of each node are considered into our network model, which is different from the previous works. Besides, it is worth pointing out that the outer coupling configuration matrix, which represents the coupling strength and the topological structure, is not restricted by the dissipatively coupled condition in this paper. The definition of MPS is also introduced for the networks with different dimensional nodes. Moreover, several MPS schemes are respectively put forward for our network model according to the norm bound of the uncertain nonlinear structures and disturbances being unknown or not. Finally, two proper examples associated with numerical simulations are given to verify the effectiveness of our theoretical results.

This paper presents novel iterative learning methods along with the neural network implementation for multi-player zero-sum games. Solving zero-sum games depends on the solutions of Hamilton–Jacobi-Isaacs equations, which are nonlinear partial differential equations. These solutions are generally difficult or even impossible to be obtained analytically. To overcome this difficulty, iterative adaptive dynamic programming algorithms are utilized. In the related research works, three-network architecture, i.e., critic-actor-disturbance structure, is used to approximate the value function, control policies and disturbance policies. Different from the previous works, this paper employs single-network architecture, i.e., critic-only structure, to implement the proposed algorithms, which reduces the computation burden and the complexity of design procedure. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed methods.

This paper investigates the optimal control of uncertain nonlinear systems with external disturbance via adaptive dynamic programming, where two kinds of controllers are introduced and event-driven strategy is used to update the controllers as well as the network weights. One controller is constrained-input, and another is used to offset the external disturbance. Three kinds of neural networks (identifier network, critic network and actor network) are used to approximate the uncertain dynamics, the optimal value, control inputs and external disturbance, respectively. To the best knowledge of the authors, the advantage of this paper is that almost all the existing systems about optimal control via adaptive dynamic programming can be considered as special cases of this system, where the external disturbance is considered. By designing appropriate parameters, the uncertain nonlinear system is asymptotically stable with the event-driven controller. And, under the given learning rates of neural networks, the system state and the estimation error of neural networks are proved to be uniform ultimate boundedness (UUB) via adaptive dynamic programming. Finally, numerical simulation results are presented to verify the theoretical analysis.

The tumour suppressor gene p53 plays a key role in cell response to DNA damage, and the p53Mdm2 regulation relationship is crucial for the expression of p53. In this paper, based on gene expression time-series data of human leukaemia cells after exposure to ionising radiation, with ionising radiation as input, a nonlinear continuous time-delay dynamic stochastic mathematical model of a p53Mdm2 network is established using a continuousdiscrete extended Kalman filter algorithm. The accuracy of the established model is then validated. Numerical simulation is used to simulate the dynamic regulation in p53Mdm2 networks for low, medium, and high ionising radiation doses. The results show that the proposed algorithm is convergent and that the error rate of the model is only 1.19%. In addition, the model can simulate accurately the response of the p53Mdm2 network to different doses of ionising radiation. The methods proposed in this paper can supply the foundation for research on the dynamics of the p53Mdm2 gene regulation relationship and play a guiding role in research on the p53Mdm2 response process after DNA damage under different doses of ionising radiation.

This paper proposes the design and implementation of a model-free tire slip control for a fast and highly nonlinear Anti-lock Braking System (ABS). A reinforcement Q-learning optimal control approach is inserted in a batch neural fitted scheme using two neural networks to approximate the value function and the controller, respectively. The transition samples required for learning high performance control can be collected by interacting with the process either by online exploiting the current iteration controller (or policy) under an e-greedy exploration strategy, or by using data collected under any other controller that is capable of ensuring efficient exploration of the action-state space. Both approaches are highlighted in the paper. Fortunately, the ABS process fits this type of learning-by-interaction because it does not need an initial stabilizing controller. The validation case studies conducted on a real laboratory setup reveal that high control system performance can be achieved using the proposed approaches. Insightful comments on the observed control behavior are offered along with performance comparisons with several types of model-based and model-free controllers including relay, model-based optimal PI, an original model-free neural network state-feedback VRFT controller and a model-free neural network adaptive actor-critic one. With the ability to improve control performance starting from different supervisory controllers or to learn high performance controllers from scratch, the proposed Q-learning optimal control approach proves its performance in a wide operating range and is therefore recommended to its industrial application on ABS.

The main contributions in this paper are as follows:Neural-network-based observers are established for NMASs to recover the unknown system dynamics.Based on the observed states, an online optimal consensus controller is designed for each agent using ADP method.Only critic network architecture is adopted for each agent to reduce the computation load. This paper investigates optimal coordination tracking control for nonlinear multi-agent systems (NMASs) with unknown internal states by using an adaptive dynamic programing (ADP) method. Actually, the optimal coordination control for MASs depends on the solutions to the coupled HamiltonJacobiBellman (HJB) equations which are almost impossible to be solved analytically. And whats worse is that the accurate system models are either infeasible or difficult to obtain in practical applications. To surmount these deficiencies, a neural network (NN) based observer is designed for each agent to reconstruct its internal states by utilizing the measurable inputoutput data rather than accurate system models. Based on the observed states and Bellman optimality principle, we derive optimal coordination control policies from the coupled HJB equations. In order to implement the proposed ADP method, a critic network framework is proposed for each agent to approximate its value function and help calculate the optimal coordination control policy. Then we prove the local coordination tracking errors and weight estimation errors are uniformly ultimately bounded (UUB) while the approximated control policies converge to their target values. Finally, two simulation examples are given to show the effectiveness of the proposed ADP method.

An efficient adaptive neural controller is firstly developed for a class of high order MJNSs with unmodeled dynamics and dead zone inputs.To the best of the authors knowledge, it is also the first control solution for the pure-Markovian jumping nonlinear systems. In this paper, all of the parameters and functions, no matter known or unknown, are allowed to vary with the switching modes.The computation load can be reduced because the number of the adaptive parameters is not related to the number of the switching modes or the order of the concerned system. This paper focuses on the adaptive control design for a class of high order Markovian jump nonlinear systems with unmodeled dynamics and unknown dead-zone inputs. The unknown parameter vector, the dynamic uncertainties, the unknown nonlinear functions and the actuator dead-zone nonlinearities are all allowed to be randomly varying with the Markovian modes. By introducing the bound estimation approach, the effect of randomly jumping unknown parameters and the varying dead-zone nonlinearities are tackled. Moreover, aiming at the unmodeled dynamics and completely unknown nonlinear functions which have Markovian jumping features, several two-layer neural networks (NNs) are introduced for each mode and the adaptive backstepping control law is finally established. The stochastic stability analysis for the closed-loop system are also performed. At last, a numerical example is provided to illustrate the efficiency and advantages of the proposed method.

This paper investigates the adaptive neural network optimal output feedback control design problem for nonlinear continuous-time systems with actuator saturation. The system dynamics and states of the controlled system are unknown. A neural network state observer is constructed to estimate the system states. This paper uses two neural networks, one is used to construct the neural network state observer, the other (critic neural network) is used to approximate the cost functions, which comprise an observer-critic architecture. In this architecture, the critic neural network weights are tuned based on both the current data and the previous data, thus the conditions of the persistent excitation in the previous literatures are relaxed. By utilizing adaptive dynamic programming approach, a new observer-based optimal control scheme is developed. It is proved that the proposed adaptive neural network output feedback optimal control scheme can ensure that the whole closed-loop system is stable. Moreover, the estimate errors of the critic neural network weights are asymptotically stable. A simulation example is given to validate the effectiveness of the proposed method.

In this paper, a decentralized fault tolerant control (DFTC) scheme is proposed for a class of large-scale nonlinear systems based on self-tuned local feedback gain against partial loss of actuator effectiveness (PLOAE). Consider a large-scale nonlinear system as a set of interconnected subsystems, a decentralized control method is proposed by employing two radial basis function neural networks (RBFNNs) for the fault-free system. Then, the unknown system is identified using RBFNNs. By establishing a decentralized observer, the derived self-tuned local feedback gain is placed before the proposed decentralized controller to guarantee control performance for the subsystem suffering from PLOAE fault. Finally, simulation examples are provided to demonstrate the effectiveness of the present DFTC scheme. The main contributions of this paper are: i) The unknown large-scale nonlinear system can be identified using locally measured states, so the actuator fault can be handled in its local subsystem. It implies that the performance degradation of the faulty subsystem cannot affect the fault-free subsystems. ii) The estimated effectiveness factor is placed before the proposed decentralized scheme. The fault tolerant control structure is simple since it does not need to be redesigned in the case of PLOAE.

In this paper, an adaptive prescribed performance control problem is studied for a class of switched uncertain nonlinear systems under arbitrary switching signals. Radial basis function neural networks (RBFNNs) are employed to approximate the unknown terms. By introducing the transformation errors, the original system with prescribed performance constraints are transformed into a class of new systems without constraints. Then, we design controllers to stabilize the transformed system. In this way, the original system is stabilizable and the prescribed performance is guaranteed. Update laws are designed such that the parameter estimation is fixed until its corresponding subsystem is active. Compared with the existing results, the main contributions of this paper are characterized as follows: (1) a PPC approach is proposed for a class of switched uncertain nonlinear systems in a general form and (2) RBFNNs are used to approximate the unknown terms of each subsystem. In the end, a simulation example is developed to illustrate the effectiveness of the present approach.

This paper addresses the trajectory-tracking control problem of mobile robot systems with nonholonomic constraints, in the presence of time-varying parametric uncertainties and external disturbances. This necessitates an accurate controller to meet as much control objectives, as possible. Therefore, this paper deals with an artificial intelligence control technique to design a robust controller to meet the control objectives. The design of the intelligent controller is based on the optimal control theory, the adaptive neural network system, and the robust control technique. The trajectory-tracking problem is solved using the optimal control methodology. Since the nonholonomic wheeled mobile robot is strongly nonlinear, the neural network system is applied to approximate the nonlinear function in the optimal control law. The robust controller, for his part, is then applied to adaptively estimate an unknown upper bound of the time-varying parametric uncertainties, external disturbances and approximation error of the neural network system. The stability of the closed-loop robot system is proven using the optimal control theory and Lyapunov stability analysis. The results of the simulation studies on three typical nonholonomic mobile robots are provided to demonstrate the effectiveness of the proposed controller. In addition, a comparative study with a recent robust adaptive controller shows that our proposed intelligent controller gives better results, in the sense that the output trajectory converges to the steady state faster with smaller tracking error.

This paper studies an adaptive fuzzy control method combined with reduced-order observer technology for the position tracking control of chaotic permanent magnet synchronous motor (PMSM) drive system. Fuzzy logic systems (FLSs) are introduced to solve the problem of nonlinear and unknown functions appeared in the PMSM drive system, reduced-order observer is used to calculate its angle speed. Meanwhile, adaptive backstepping mechanism is applied for the design procedure of controllers. The control technique developed in this paper can ensure that the tracking error falls into a small neighborhood of origin. Compared with the existing results, the proposed algorithm can solve the explosion of complexity issue and it does not require measuring the speed signal of motors and the number of adaptive parameters has been reduced to only one. Simulation results show that the chaos of PMSM can be successfully suppressed by the proposed method and the system can track the reference signals very well.

This paper studies a robust fault tolerant control of a class of nonlinear switched systems with strong structural uncertainties and actuator faults. This paper presents a new robust fault tolerant state feedback method, by using the average dwell time technique to stabilize the switched nonlinear systems exponentially under an arbitrary switching law. Comparing with the existing results, the method of this paper has three features: (1) this method is applicable to the switched nonlinear systems with strong structural uncertainties and faulty actuators and also the nominal case of the considered systems, there is no need to change any structures and/or parameters of the controller. (2) The switching law is arbitrary provided that the average switching is slow enough in the average sense. (3) This method treats all actuators in the same way, no need to separate faulty actuators from the healthy ones. The simulation result verifies the effectiveness of this method.

In this paper, cluster synchronization problem is investigated for a kind of complex dynamical networks with Lurie-type non-linear dynamics. With the aid of a local update law, a pinning adaptive control strategy is proposed to solve the cluster synchronization problem of the networks. Some simple criteria for cluster synchronization are presented for the networks with external disturbances and time delays. Firstly, sufficient conditions are established to realize cluster synchronization of the networks without disturbances and delays. Then, the cluster synchronization problem of the networks with external disturbances is considered. Finally, the cluster synchronization in the networks with time-varying delays is further studied. Numerical examples are given to verify and illustrate the theoretical results. HighlightsThe cluster synchronization in networks with disturbances and delays is studied.An adaptive control strategy is presented for the networks with Lurie-type dynamics.The results in this paper do not require the global information of the networks.

In this paper, an adaptive predictive control algorithm is employed to controlling a class of continuous stirred tank reactor (CSTR) system. The main contribute of this paper is that the CSTR system are in discrete-time form and non-symmetric dead-zone inputs are considered here. The design parameters of control algorithm for the CSTR systems are not so much than before, such that the calculated amount of the control algorithm is less than before. By considering the Radial basis function neural networks (RBFNN), the unknown functions are approximated, the mean value theorem is utilized in the algorithm design process. Based on the Lyapunov analysis method, and choosing the design parameters appropriately, all the signals in the closed-loop system are proved to be semi-global uniformly ultimately bounded (SGUUB) and the tracking error is converged to a small compact set. A simulation example for CSTR systems is studied to demonstrate the effectiveness of the proposed approach.

In the paper, data-driven finite-horizon robust formation-containment control scheme is developed based on integral reinforcement learning and zero-sum game for perturbed multi-agent networks with completely unknown nonlinear dynamics. At first, distributed finite-time sliding mode estimators are designed to obtain the desired states of leaders and followers, respectively. Then finite-horizon robust leader formation control and follower containment control are achieved based on proposed model-free integral reinforcement learning algorithms implemented by critic-actor-disturbance structure, in the framework of multi-player zero-sum game where the non-quadratic performance index for each agent considers the influence of saturated inputs and disturbances of local neighbors thoroughly. Furthermore, it is proved that the whole network has bounded L 2 gain robust stability and Nash equilibrium of zero-sum game exists. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

This paper designs a novel online event-based near-optimal control scheme for multi-player nonzero-sum (NZS) games with partially unknown system dynamics. With the introduction of event-triggered mechanism (ETM), the repetitive computing burdens and communication loads of the signals are largely alleviated. Under the event-triggered mechanism, the framework of identifier-critic is structured to solve the coupled Hamilton–Jacobi equations (CHJEs) for NZS games. A feedforward neural network (FNN) is employed to construct an identifier to learn the unknown dynamics of the nonlinear system. The critic network for each player utilizes a modified tuning law, which is composed of three terms, to seek for the approximated optimal control schemes. Besides the conventional term derived from the gradient descent method, the second term derived from the experience replay (ER) technique utilizes the historical state data to update the critic network weight vector so as to remove the persistence of excitation (PE) condition. In addition, a novel term is added to stabilize the closed-loop systems. Owing to the stabilizing term, there is no need for the initial stabilizing control. In theory, the uniform ultimate boundedness (UUB) properties of the system states and the critic network weight errors are proved by utilizing Lyapunov theorem. Furthermore, the minimal intersample time is proved to be lower bounded with a positive constant which means that the Zeno behavior is excluded during the learning phases. Finally, we show the validity of the designed algorithm via simulating two examples.

Nonlinear and nonconvex optimization problem (NNOP) is a challenging problem in control theory and applications. In this paper, a novel mixture varying-gain dynamic learning network (MVG-DLN) is proposed to solve NNOP with inequality constraints. To do so, first, this NNOP is transformed into some equations through Karush–Kuhn–Tucker (KKT) conditions and projection theorem, and the neuro-dynamics function can be obtained. Second, the time varying convergence parameter is utilized to obtain a faster convergence speed. Third, an integral term is used to strengthen the robustness. Theoretical analysis proves that the proposed MVG-DLN has global convergence and good robustness. Three numerical simulation comparisons between FT-FP-CDNN and MVG-DLN substantiate the faster convergence performance and greater robustness of the MVG-DLN in solving the nonlinear and nonconvex optimization problems.