RHONN identifier-control scheme for nonlinear discrete-time systems with unknown time-delays

This work presents a neural identifier-control scheme for uncertain nonlinear discrete-time systems with unknown time-delays. This scheme is based on a neural identifier to get a model of the system and a discrete-time block control technique based on sliding modes to generate the control law. The neural identifier is based on a Recurrent High Order Neural Network (RHONN) trained with an Extended Kalman Filter (EKF) based algorithm. Applicability is shown using real-time test results for linear induction motors. Also, a Lyapunov analysis is added in order to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed neural identifier-control scheme.     

Discrete-time recurrent high order neural networks for nonlinear identification

This paper focuses on the problem of discrete-time nonlinear system identification via recurrent high order neural networks. It includes the respective stability analysis on the basis of the Lyapunov approach for the NN training algorithm. Applicability of the proposed scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.     

Adaptive-critic-based model reference control for unknown nonlinear systems with input constraints

In this paper, the optimal model reference adaptive control (MRAC) problem is studied for the unknown discrete-time nonlinear systems with input constraint under the premise of considering robustness to uncertainty. Through an input constraint auxiliary system, a new adaptive-critic-based MRAC algorithm is proposed to transform the above problem into the optimal regulation problem of the auxiliary error system with lumped uncertainty. In order to realize the chattering-free sliding model control for the auxiliary error system, an action-critic variable is introduced into the adaptive identification learning. In this case, the closed-loop control system is robust to the disturbance and the neural network approximation error. The uniformly ultimate bounded property is proved by the Lyapunov method, and the effectiveness of the algorithm is verified by a simulation example.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

Real-time output trajectory tracking neural sliding mode controller for induction motors

This paper deals with real-time discrete adaptive output trajectory tracking for induction motors in the presence of bounded disturbances. A recurrent high order neural network structure is used to design a nonlinear observer and based on this model, a discrete-time control law is derived, which combines discrete-time block control and sliding modes techniques. Applicability of the scheme is illustrated via experimental results in real-time for a three phase induction motor.     

Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.     

Event-Triggered formation control for time-delayed discrete-Time multi-Agent system applied to multi-UAV formation flying

This paper studies the formation control for a time-delayed discrete-time multi-agent system (MAS). An event-triggered controller is proposed to reduce the communication load of the system. Based on the designed event-triggered condition and properties of Schur stable matrix, the stability of formation for discrete-time MAS is proved. Utilizing the virtual simulation platform integrated Robot Operating System (ROS) and Gazebo, a virtual scene with unmanned aerial vehicles (UAVs) models is built and the verification for the theoretical algorithm is completed. Finally, an experimental platform with four practical UAVs is constructed and the result shows that the expected formation is achieved and controller proposed can solve the formation control problem for time-delayed discrete-time MASs. Besides, the effectiveness of the event-triggered mechanism on reducing communication frequency is comfirmed in practical scenarios.     

Decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems

This paper presents a novel approach to address the decentralized fault tolerant model predictive control of discrete-time interconnected nonlinear systems. The overall system is composed of a number of discrete-time interconnected nonlinear subsystems at the presence of multiple faults occurring at unknown time-instants. In order to deal with the unknown interconnection effects and changes in model dynamics due to multiple faults, both passive and active fault tolerant control design are considered. In the Active fault tolerant case an online approximation algorithm is applied to estimate the unknown interconnection effects and changes in model dynamics due to multiple faults. Besides, the decentralized control strategy is implemented for each subsystem with the model predictive control algorithm subject to some constraints. It is showed that the proposed method guarantees input-to-state stability characterization for both local subsystems and the global system under some predetermined assumptions. The simulation results are exploited to illustrate the applicability of the proposed method.     

Adaptive neural network control for a class of discrete-time nonlinear interconnected systems with unknown dead-zone

In this paper, the problem of adaptive neural network control design is addressed for a kind of discrete-time nonlinear interconnected systems with unknown dead-zone. The control purpose of this paper is to design an adaptive neural network controller to ensure the systems stability and achieve the desired control performance. The neural networks are utilized to approximate the unknown functions. On the basis of utility functions, the critic signals are considered in the designed control signals. In order to offset the impact of unknown asymmetric dead-zone in the controlled system, the adaptive assistant signal is constructed. Based on the gradient descent rule, the weight tuning laws are obtained. The difference Lyapunov function theory is adopted to prove the studied system stability. The viability of the devised control strategy is further testified via some simulation results.     

Existence and global exponential stability of a periodic solution for a discrete-time interval general BAM neural networks

In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23]. An example is provided to show the correctness of our analysis.     

An algorithmic approach for system decomposition and balanced realized model reduction

This paper deals with the development of an algorithm for unstable continuous/discrete-time system decomposition into completely stable and completely unstable subsystems using real Schur transformation technique. The application of the proposed algorithm is investigated for unstable LTI plant or controller reduction and the available balanced realized model reduction theories applicable for stable systems are extended for unstable, continuous/discrete-time systems. The algorithm and its applications are illustrated with MATLAB-based computer-simulated results for continuous and discrete-time systems.     

Aperiodically intermittent control for synchronization of discrete-time delayed neural networks

This paper is concerned with the aperiodically intermittent control (AIC) for the synchronization of discrete-time neural networks with time delay. The synchronization is analyzed by the piecewise Lyapunov function approach and the piecewise Lyapunov–Krasovskii functional approach, respectively. The average activation time ratio of AIC is estimated, which is more general and less conservative than the minimum activation time ratio. Finally, a numerical example is exploited and detailed comparisons are presented to demonstrate the effectiveness and less conservativeness of the obtained results.     

Impulse-based coupling synchronization of multiple discrete-time memristor-based neural networks with stochastic perturbations and mixed delays

The global synchronization problem of multiple discrete-time memristor-based neural networks (DTMNNs) with stochastic perturbations and mixed delays is studied under impulse-based coupling control, where the coupling control only occurs at discrete impulse times. The impulse-based coupling control will further reduce the communication bandwidth for multiple DTMNNs to achieve coupling synchronization. We construct an array of multiple DTMNNs with stochastic perturbations and mixed delays and propose a novel impulse-based coupling control scheme. By utilizing Lyapunov–Krasovskii functional technique, schur complement technique and linear matrix inequality (LMI) method, some sufficient synchronization conditions depending on stochastic perturbations and mixed delays are established. At the end of this paper, a numerical example is given and the effectiveness of the impulse-based coupling control is illustrated by using MATLAB programming.     

Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning

This paper investigates a Q-learning scheme for the optimal consensus control of discrete-time multiagent systems. The Q-learning algorithm is conducted by reinforcement learning (RL) using system data instead of system dynamics information. In the multiagent systems, the agents are interacted with each other and at least one agent can communicate with the leader directly, which is described by an algebraic graph structure. The objective is to make all the agents achieve synchronization with leader and make the performance indices reach Nash equilibrium. On one hand, the solutions of the optimal consensus control for multiagent systems are acquired by solving the coupled Hamilton–Jacobi–Bellman (HJB) equation. However, it is difficult to get analytical solutions directly of the discrete-time HJB equation. On the other hand, accurate mathematical models of most systems in real world are hard to be obtained. To overcome these difficulties, Q-learning algorithm is developed using system data rather than the accurate system model. We formulate performance index and corresponding Bellman equation of each agent i. Then, the Q-function Bellman equation is acquired on the basis of Q-function. Policy iteration is adopted to calculate the optimal control iteratively, and least square (LS) method is employed to motivate the implementation process. Stability analysis of proposed Q-learning algorithm for multiagent systems by policy iteration is given. Two simulation examples are experimented to verify the effectiveness of the proposed scheme.     

Model-free algorithm for consensus of discrete-time multi-agent systems using reinforcement learning method

In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.     

Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses

This paper addresses the problem of global exponential dissipativity for a class of uncertain discrete-time BAM stochastic neural networks with time-varying delays, Markovian jumping and impulses. By constructing a proper Lyapunov–Krasovskii functional and combining with linear matrix inequality (LMI) technique, several sufficient conditions are derived for verifying the global exponential dissipativity in the mean square of such stochastic discrete-time BAM neural networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. One important feature presented in our paper is that without employing model transformation and free-weighting matrices our obtained result leads to less conservatism. Additionally, three numerical examples with simulation results are provided to show the effectiveness and usefulness of the obtained result.     

Distributed semistable LQR control for discrete-time dynamically coupled systems

A distributed linear-quadratic-regulator (LQR) semistability theory for discrete-time systems is developed for designing optimal semistable controllers for discrete-time coupled systems. Unlike the standard LQR control problem, a unique feature of the proposed optimal control problem is that the closed-loop generalized discrete-time semistable Lyapunov equation can admit multiple solutions. Necessary and sufficient conditions for the existence of solutions to the generalized discrete-time semistable Lyapunov equation are derived and an optimization-based design framework for distributed optimal controllers is presented.     

Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations

The paper is dedicated to solving the generalized periodic discrete-time coupled Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. The solvable condition and a iterative algorithm for this equation are presented. The proposed method is developed from a point of least squares method. The rationality of the method is testified by theoretical analysis, which shows that the algorithm can solve the problem within finite number of iterations. The presented approach is numerically reliable and requires less computation. A numerical example illustrates the effectiveness of the raised result.     

Global exponential stability of discrete-time higher-order Cohen–Grossberg neural networks with time-varying delays,connection weights and impulses

In this paper, an auxiliary model-based nonsingular M-matrix approach is used to establish the global exponential stability of the zero equilibrium, for a class of discrete-time high-order Cohen–Grossberg neural networks (HOCGNNs) with time-varying delays, connection weights and impulses. A new impulse-free discrete-time HOCGNN with time-varying delays and connection weights is firstly constructed, and the relationship between the solutions of original systems and new HOCGNNs is indicated by a technical lemma. From which, the global exponential stability criteria for the zero equilibrium are derived by using an inductive idea and the properties of nonsingular M-matrices. The effectiveness of the obtained stability criteria is illustrated by numerical examples. Compared with the previous results, this paper has three advantages: (i) The Lyapunov–Krasovskii functional is not required; (ii) The obtained global exponential stability criteria are applied to check whether a matrix is a nonsingular M-matrix, which can be conveniently tested; (iii) The proposed approach applies to most of discrete-time system models with impulses and delays.     

A finite iterative algorithm for the general discrete-time periodic Sylvester matrix equations

The purpose of this paper is to present an iterative algorithm for solving the general discrete-time periodic Sylvester matrix equations. It is proved by theoretical analysis that this algorithm can get the exact solutions of the periodic Sylvester matrix equations in a finite number of steps in the absence of round-off errors. Furthermore, when the discrete-time periodic Sylvester matrix equations are consistent, we can obtain its unique minimal Frobenius norm solution by choosing appropriate initial periodic matrices. Finally, we use some numerical examples to illustrate the effectiveness of the proposed algorithm.