Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.     

Leader-following consensus of nonlinear discrete-time multi-agent systems with limited communication channel capacity

This paper considers the problem of the leader-following consensus of generally nonlinear discrete-time multi-agent systems with limited communication channel capacity over directed fixed communication networks. The leader agent and all follower agents are with multi-dimensional nonlinear dynamics. We propose a novel kind of consensus algorithm for each follower agent based on dynamic encoding and decoding algorithms and conduct a rigorous analysis for consensus convergence. It is proved that under the consensus algorithm designed, the leader-following consensus is achievable and the quantizers equipped for the multi-agent systems can never be saturated. Furthermore, we give the explicit forms of the data transmission rate for the connected communication channel. By properly designing the system parameters according to restriction conditions, we can ensure the consensus and communication efficiency with merely one bit information exchanging between each pair of adjacent agents per step. Finally, simulation example is presented to verify the validity of results obtained.     

Observer-based finite-time H∞ control for uncertain discrete-time nonhomogeneous Markov jump systems

The problem of observer-based finite-time H_∞ control for discrete-time Markov jump systems with time-varying transition probabilities and uncertainties is studied in this paper, in which time-varying transition probabilities are modelled as convex polyhedron, and the parameter uncertainty satisfies norm-bounded. First of all, a Luenberger observer is designed to measure the system state. Then, observer-based controller is constructed to ensure the stochastic finite-time boundedness of the resulting closed-loop system with an H_∞ performance. Furthermore, sufficient conditions are derived in light of linear matrix inequalities. In the end, the flexibility and applicability of the developed methods are demonstrated by two illustrative examples.     

Auxiliary model based recursive generalized least squares identification algorithm for multivariate output-error autoregressive systems using the decomposition technique

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.     

Passivity analysis of coupled neural networks with reaction–diffusion terms and mixed delays

In this paper, we intend to discuss the passivity of coupled neural networks (NNs) with reaction–diffusion terms and mixed delays. By constructing appropriate Lyapunov functional, and with the help of liner matrix inequalities, some inequality techniques, several sufficient conditions are derived to guarantee the output strictly passive, input strictly passive, passive of the proposed neural network model. Then, a stability criterion is presented according to the obtained passivity results. Moreover, the proposed neural network model herein is more general than some recent studies, which can improve and enrich the previous research results. Finally, a numerical example is presented to show the effectiveness of the theoretical criteria.     

Adaptive robust control for planar n-link underactuated manipulator based on radial basis function neural network and online iterative correction method

This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Global consensus tracking of discrete-time saturated networked systems via nonlinear feedback laws

This paper revisits the coordinated tracking of networked systems in the presence of input saturation. For discrete-time networked systems with high-order integrator typed dynamics and input saturation, nonlinear feedback laws are constructed and then sufficient conditions are established to guarantee the global consensus tracking of the systems. Finally, numerical simulations are given to support the theoretical results.     

Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays

We study the consensus control of discrete-time second-order multi-agents systems with time delays and multiplicative noises, where the consensus protocol is designed by both the local relative position measurements and each agent’s absolute velocity. Due to the existence of time delays and multiplicative noises, the classical methods for deterministic models with time delays cannot work. In this paper, we apply stochastic stability theorem of discrete-time stochastic delay equations to find some explicit sufficient conditions for both mean square and almost sure consensus. It is proven that for any given noise intensities and time delays, the second-order multi-agent consensus can be achieved by choosing appropriate control gains in the relative position measurement and absolute velocity, respectively. Numerical simulation is given to demonstrate the effectiveness of the proposed protocols as well as the theoretical results.     

Adaptive synchronization of multi-agent systems via variable impulsive control

This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.     

Optimal control and pattern formation for a haptotaxis model of solid tumor invasion

This paper deal with an optimal control problem for a haptotaxis model of solid tumor invasion by considering the multiple treatments of cancer (a combination of radiotherapy and chemotherapy). Firstly, we obtain the existence and uniqueness of weak solution for the controlled system with spatial dimensions $N=1,2,3$ by applying the Leray–Schauder fixed point theorem and developing adapted a priori estimates. Subsequently, the existence of optimal pair are proved by means of the technique of minimizing sequence. Furthermore, we verify the Lipschitz continuity of control-to-state mapping based on some a priori estimates, hence derive the first-order necessary optimality condition and establish the optimality systems. Finally, the ringlike diffusion and aggregation patterns and the dynamics of tumor invasion as well as the optimal control strategies are presented numerically, which demonstrate that the optimal treatment strategies are capable of breaking the pattern formation, and preventing the tumor invading and metastasizing, even eliminating the tumor possibly. The results of this work improved and extended previous results partially.     

Global behavior of a two-stage contact process on complex networks

Masuda and Konno [14] first formulated a two-stage contact process on complex networks with heterogeneous degree distribution, and they derived a critical birth or infection rate β_c, above which there exists a unique positive equilibrium. The global behavior of this model is not well understood, and the authors have not given a rigorous mathematical analysis of their model. In this paper, we investigate the global behavior in detail and show that the global behavior is completely determined by a threshold R₀. In particular, by comparison arguments, we establish the global asymptotic stability of the trivial equilibrium E₀ for R₀?<?1; by constructing a bounded function, we show that the system is uniformly persistent for R₀?>?1. Furthermore, by means of a monotone iterative approach, we obtain a sufficient condition for the global asymptotic stability of the positive equilibrium E*.     

Fault-tolerant control for commercial aircraft with actuator faults and constraints

In this paper, a constrained control scheme based on model reference adaptive control is investigated for the longitudinal motion of a commercial aircraft with actuator faults and saturation nonlinearities. Actuator faults and constraints are both important factors adversely affecting the stability and performance of flight control systems. An adaptive adjustment law based on Lyapunov function is utilized to adjust the fault-tolerant control law. Both additive and multiplicative faults are considered in the designed controller to deal with the three types of actuator faults: locked in place, loss of effectiveness, and bias. Moreover, different techniques are implemented in the basic and fault-tolerant controller to anti-windup. Proofs for the stability of the two modified controllers which improve the performance of control system operating in the presence of actuator faults and saturations are proposed. Finally, a numerical example of the anti-windup fault-tolerant controller for a commercial aircraft is demonstrated. The stability and performance improvements can be accrued with the presented fault-tolerant control scheme.     

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.     

Gradient-based iterative identification method for multivariate equation-error autoregressive moving average systems using the decomposition technique

This paper studies the parameter estimation problems of multivariate equation-error autoregressive moving average systems. Firstly, a gradient-based iterative algorithm is presented as a comparison. In order to improve the computational efficiency and the parameter estimation accuracy, a decomposition-based gradient iterative algorithm is presented by using the decomposition technique. The key is to transform an original system into two subsystems and to estimate the parameters of each subsystem, respectively. Compared with the gradient-based iterative algorithm, the decomposition-based algorithm requires less computational efforts, and the simulation results indicate that this algorithm is effective.     

Filtering based parameter estimation for observer canonical state space systems with colored noise

This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.     

Finite-time stabilization of memristor-based inertial neural networks with discontinuous activations and distributed delays

In this paper, the finite-time stabilization problem for memristor-based inertial neural networks (MINNs) with discontinuous activations (DAs) and distributed delays is investigated. To deal with the discontinuous property of the MINNs, the nonsmooth analysis theory is invoked. Furthermore, to simplify the MINNs with second-order state derivative, an order-reduced method is adopted. Then the second-order MINNs is transformed into a simpler first-order differential system. Moreover, the verifiable algebraic criteria are derived for the finite-time stabilization of MINNs with DAs and distributed delays under the designed control approach. Finally, the effectiveness of the obtained results are illustrated via numerical simulations.     

Stability analysis of systems with two additive time-varying delay components via an improved delay interconnection Lyapunov–Krasovskii functional

This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.     

Soft sensor modeling with a selective updating strategy for Gaussian process regression based on probabilistic principle component analysis

Considering the deviation of the working condition and the high updating frequency of the traditional moving window methods, this paper proposes a selective strategy of moving window for the Gaussian process regression in the latent probabilistic component space. First, the probabilistic principle component analysis (PPCA) is employed to deal with the multi-dimensional issue and extract essential information of the process data. Because the latent probabilistic components are more sensitive to the deviation of the working condition in the industrial process than the original data, the regression performance is improved under the PPCA framework. Under the proposed strategy, the soft sensor is able to detect the change of the working condition, and the updating is activated only when the predicted error exceeds the preset threshold, otherwise the model is kept unchanged. Furthermore, the promotion of both predicted accuracy and efficiency can be obtained by regulating the threshold. To test the effectiveness of the proposed method, a wastewater case study is provided, and the result shows that the proposed strategy works better under the probabilistic than other conventional methods.     

Combined state and parameter estimation for a bilinear state space system with moving average noise

This paper considers the identification problem of bilinear systems with measurement noise in the form of the moving average model. In particular, we present an interactive estimation algorithm for unmeasurable states and parameters based on the hierarchical identification principle. For unknown states, we formulate a novel bilinear state observer from input-output measurements using the Kalman filter. Then a bilinear state observer based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm is proposed to estimate the unknown system parameters. A linear filter is utilized to improve the parameter estimation accuracy and a filtering based BSO-MI-ESG algorithm is presented using the data filtering technique. In the numerical example, we illustrate the effectiveness of the proposed identification methods.