Class Of Discrete-time Nonlinear Systems Research Articles

General regression neural network-based data-driven model-free predictive functional control for a class of discrete-time nonlinear systems

General regression neural network-based data-driven model-free predictive functional control for a class of discrete-time nonlinear systems

Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

Adaptive-critic-based hybrid intelligent optimal tracking for a class of nonlinear discrete-time systems

In this paper, a hybrid intelligent tracking control approach is developed to address optimal tracking problems for a class of nonlinear discrete-time systems. The generalized value iteration algorithm is utilized to attain the admissible tracking control with off-line training, while the on-line near-optimal control method is established to enhance the control performance. It is emphasized that the value iteration performance is improved by introducing the acceleration factor. By collecting the input–output data of the unknown system plant, the model neural network is constructed to provide the partial derivative of the system state with respect to the control law as the approximate control matrix. A novel computational strategy is introduced to obtain the steady control of the reference trajectory. The critic and action neural networks are utilized to approximate the cost function and the tracking control, respectively. Considering approximation errors of neural networks, the stability analysis of the specific systems is provided via the Lyapunov approach. Finally, two numerical examples with industrial application backgrounds are involved for verifying the effectiveness of the proposed approach.

Adaptive control of a class of discrete-time nonlinear systems yielding linear-like behavior

In adaptive control it is typically proven that an asymptotic form of stability holds, and that at best a bounded-noise bounded-state property is proven. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear time-invariant (LTI) discrete-time plant so that the closed-loop system enjoys linear-like behavior: exponential stability, a bounded noise gain, and a convolution bound on the exogenous signals; the key idea is to carry out parameter estimation by using the original projection algorithm together with restricting the parameter estimates to a convex set. In this paper, we extend this approach to a class of nonlinear plants and show how to carry out adaptive control so that we obtain the same desirable linear-like closed-loop properties. First, we consider plants with a known sign of the control gain; second, we consider the case when that sign is unknown, where two parameter estimators and a simple switching mechanism are used.

Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Discrete-time super-twisting controller using neural networks

This paper presents a neural super-twisting controller for a class of discrete-time nonlinear systems. A general plot of the control problem consists in considering a discrete-time nonlinear system with a block controllable structure, and assuming that the equations of the nonlinear system have virtual controls, a discrete-time super-twisting algorithm is applied such that each equation follows a desired trajectory until the real control is achieved. On the other hand, taking into account the capacity of neural networks to learn the behaviour of complex systems, it is proposed a neural network with a block controllable structure for identifying and controlling a discrete-time nonlinear system. Neural network weights are trained with the cubature Kalman filter algorithm. To show the effectiveness of the proposed neural super-twisting controller, a numerical simulation is performed on a Quanser 2-DOF helicopter.

Robust Stability and Stabilization Conditions for Nonlinear Networked Control Systems With Network-Induced Delay via T–S Fuzzy Model

Robust stability and stabilization problems for a class of discrete-time nonlinear systems are studied in this article. The control signal is transmitted to the nonlinear systems through a lossy communication channel in which time-varying network-induced delay occurs. A Takagi–Sugeno (T–S) fuzzy model is used to represent the nonlinear systems. Using membership function boundary information, a novel membership-function-dependent (MFD) analysis approach is presented. Unlike most previous results, the proposed MFD analysis approach does not need to increase the number of slack variables to reduce conservatism. Combining auxiliary matrices and this approach, we propose some new fuzzy Lyapunov–Krasovskii functionals (FLKFs) that do not require the restrictions of positive definiteness imposed on Lyapunov matrices. Using the FLKF and MFD analysis approach, a sufficient condition in the form of linear matrix inequalities (LMIs) is developed to guarantee the stability of T–S fuzzy time-varying delay systems. Based on the results for stability, less conservative stabilization conditions are also derived. Finally, numerical examples show that less conservative results can be obtained by the proposed approach. The inverted pendulum system with state delay or network-induced delay is also studied to verify the effectiveness of the suggested approach.

Event-triggered design for discrete-time nonlinear systems with control constraints

In order to solve the constrained-input problem and reduce the computing resources, a novel event-triggered optimal control method is proposed for a class of discrete-time nonlinear systems. In the proposed method, the event-triggered control policy is applied to the globalized dual heuristic dynamic programming (GDHP) algorithm. Compared with the traditional adaptive dynamic programming (ADP) control, the event-triggered GDHP control can reduce the computation while ensuring the system performance. In this paper, a non-quadratic function is given to code the control constraints and the trigger condition with the stability analysis is provided. Neural networks (NN) are constructed in the GDHP structure, where the model network is designed to identify the unknown nonlinear system, the critic network is used to learn the cost function and its partial derivative, and the action network is designed to obtain the approximate optimal control law. Three simulation examples are presented to demonstrate the performance of the proposed event-triggered design for constrained discrete-time nonlinear systems.

An Improved Partial-Form MFAC Design for Discrete-Time Nonlinear Systems With Neural Networks

This article investigates the partial-form model-free adaptive control (MFAC) issue for a class of discrete-time nonlinear systems. An improved partial-form MFAC design named IPFMFAC-NN is proposed, where neural networks are introduced to enhance the control performance. With the excellent approximation ability of radial basis function (RBF) neural networks, the pseudo gradient (PG) values of control method can be directly approximated online using the measured input and output data of the controlled system. Besides, long short-term memory (LSTM) neural networks are used to tune the essential parameters of the control method online with system error set and gradient information set. Finally, the effectiveness and applicability are verified by SISO discrete nonlinear system simulation and three-tank system simulation, and experimental results demonstrate that the proposed method achieves the best control performance in all five indices. Especially compared with the partial-form MFAC, the proposed method reduces the RMSE index by 43.83% and 6.39%, respectively in two simulations, making it a promising control method for discrete-time nonlinear systems.

Robust Neural Tracking Controller Design for a Class of Discrete-Time Nonlinear Systems Under Arbitrary Switching

In this article, the problem of robust tracking control is investigated for a class of discrete-time switched nonlinear uncertain system in strict-feedback form, and a novel robust neural tracking control scheme through backstepping technique is proposed for the first time. In order to handle the problem of causality contradiction, the original discrete-time nonlinear switched system is transformed into a special maximum n-step ahead predictor which suits the application of backstepping technique. The radial basis function(RBF) neural networks are adopted to approximate the unknown lumped function at the last step of backstepping procedure, not necessary to approximate all the virtual control laws at each intermediate step. Thus, the process of controller design is significantly simplified in contrast with the existing results. The stability analysis proves the proposed approach guarantees the semi-globally uniformly ultimately bounded(SGUUB) of the closed-loop system, and the tracking error asymptotically converges to an arbitrarily small neighborhood of origin by appropriately designing control parameters. Finally, simulation results are provided to demonstrate the correctness and effectiveness of the proposed scheme.

TS Fuzzy Observer-Based Controller Design for a Class of Discrete-Time Nonlinear Systems

This article presents an observer-based control design approach for a class of nonlinear discrete-time systems. The model nonlinearities are handled in two ways: 1) A Takagi–Sugeno fuzzy representation is used for nonlinearities that depend on measured states, and 2) nonlinearities that depend on unmeasured states are kept in their original form and handled using a slope-bound condition. The observer-based controller design conditions are given as linear matrix inequalities. The approach we propose significantly improves results in the literature by providing less restrictive design conditions. These improvements are illustrated in a detailed analytical and numerical comparison on a synthetic example; while a pendulum-on-a-cart example shows that the approach works both in simulation and in real-time experiments.

Recursive Elimination Method in Moving Horizon Estimation for a Class of Nonlinear Systems and Non-Gaussian Noise

This paper proposes a recursive elimination method for optimal filtering problems of a class of discrete-time nonlinear systems with non-Gaussian noise. By this method, most of the computations to ...

Discrete-time homogeneity: Robustness and approximation

In this paper we study robustness properties of discrete-time homogeneous systems. We also analyse stability and robustness properties of a more general class of nonlinear discrete-time systems that can be approximated by homogeneous ones. We apply the results to the investigation of stability properties of discretized continuous-time systems.

New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay

In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.

Event-Triggered Adaptive Critic Control Design for Discrete-Time Constrained Nonlinear Systems

In this paper, through event-triggered approach, the constrained near-optimal control problem for a class of nonlinear discrete-time systems is investigated and solved by heuristic dynamic programming (HDP) technique. The proposed method can reduce the amount of computation remarkably without deteriorating the system stability. In order to overcome the control constraints and reduce the computational burden, a nonquadratic performance index is introduced. Then, stability analysis of the event-triggered system with control constraints and an event-triggered constrained controller design algorithm are given. Three neural networks are used in the HDP scheme, which are designed to identify the unknown nonlinear system, approximate value function, and control law, respectively. In the model neural network, an effective method is developed to initialize its weights. Finally, two examples are included to demonstrate the present method.

Fuzzy $\mathcal {H}_{\infty }$ Output Feedback Control for Nonlinear NCSs With Quantization and Stochastic Communication Protocol

This article investigates the problem of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic output feedback control for a class of discrete-time nonlinear systems with quantization and stochastic communication protocol (SCP) via Takagi-Sugeno rules. A fuzzy Markov jump model is used to describe the output feedback controller with the measurement output signal quantized by the dynamic quantization strategy and the SCP scheduling behavior for the quantized signal transferring to the controller described via a Markov chain. The purpose of the addressed problem is to design a dynamic output feedback controller such that stability and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for the closed-loop system are guaranteed. For this purpose, the corresponding design conditions for the output feedback controller and the dynamic quantization parameters are presented in terms of solutions to a set of linear matrix inequalities. Finally, two simulation examples are given to prove the effectiveness of the proposed design method.

Enhanced model-free adaptive iterative learning control with load disturbance and data dropout

In this paper, an enhanced model-free adaptive iterative learning control (EMFAILC) method is proposed, which is applied for a class of nonlinear discrete-time systems with load disturbance and random data dropout. This method is a data-driven control strategy and only the I/O data are required for the controller design. Data are lost at every time instance and iteration instance independently, which allows successive data dropout both in time and iterative axes. By compensating the missing data, the proposed EMFAILC algorithm can track the desired time-varying trajectory. The convergence and effectiveness of the proposed approach are verified by both the rigorous mathematical analysis and the simulation results.

Data-driven model-free sliding mode learning control for a class of discrete-time nonlinear systems

This paper proposes a data-driven model-free sliding mode learning control (MFSMLC) for a class of discrete-time nonlinear systems. In this scheme, the control design does not depend on the mathematical model of the controlled system. The nonlinear system can be transformed into a dynamic linear data system by a novel dynamic linearization method. A recursive learning control algorithm is designed for the nonlinear system that can drive the sliding variable reach and remain on the sliding surface only by using output and input data. Moreover, the chattering is reduced because there is no non-smooth term in MFSMLC. After the strict stability analysis, the effectiveness of MFSMLC is validated by MATLAB simulations.

Delay-Dependent H∞ Control for T-S Fuzzy Systems with Local Nonlinear Models: An LMI Approach

This paper studies the stabilization design scheme with H∞ performance for a large class of nonlinear discrete-time systems. The system under study is modeled by Takagi-Sugeno (T-S) model with local nonlinearity and state delay. First, the model is changed into an equivalent fuzzy switching model. And then, according to projection theorem and piecewise Lyapunov function (PLF), two new H∞ control methods are proposed for fuzzy switched systems, which consider the time delay information of the system. Finally, the relationship among all fuzzy subsystems is considered. Because the results are only expressed by a series of linear matrix inequalities (LMIs), the controller can be directly designed by the linear matrix inequalities toolbox of MATLAB.

Extended Kalman filtering subject to random transmission delays: Dealing with packet disorders

This paper studies the extended Kalman filtering problem for a class of nonlinear discrete-time systems with random transmission delays (RTDs) and RTD-induced packet disorders. The relationship between the RTDs and the resulting packet disorders is discussed. The bounded RTDs, which take place in the sensor-to-filter channel, are modeled as independent and identically distributed random variables obeying a certain probability distribution. A novel filter structure is proposed that utilizes an integer-valued function of the mathematical expectation of the RTDs so as to compensate the RTD-induced effects. Under the proposed extended Kalman filter, an upper bound for the filtering error covariance is derived by solving two Riccati-like difference equations, and subsequently minimized (in the sense of trace) by appropriately designing the filter gains. A numerical simulation is provided to verify the validity of the developed filter design scheme.