Class Of Unknown Nonlinear Systems Research Articles

Time-Varying Delay Compensation for a Class of Nonlinear Control Systems Over Network via $H_{\infty }$ Adaptive Fuzzy Controller

This paper introduces a robust ${H}_{{\infty }}$ adaptive fuzzy controller for a class of unknown nonlinear systems over network. There are two main problems in the networked control systems, the time-varying networked-induced delay and the data packet dropouts. The time-varying networked-induced delays cause degradation for the system performance that controlled over network and also the system can be unstable. Moreover, the delay problem is aggravated when packet losses occur during the transmission of data. The proposed controller has a filtered error to handle the networked-induced delays. Furthermore, it is robust to overcome some packet losses. The unknown nonlinear functions of the system are approximated using fuzzy logic systems. The robustness of the proposed controller is achieved by combining the adaptive fuzzy controller with ${H}_{{\infty }}$ control technique. The Lyapunov stability analysis is used to prove that the proposed controller is asymptotically stable. Stability of the whole closed loop system is guaranteed via the proposed controller in the presence of bounded external disturbance, data packet dropouts and time-varying networked-induced delays. An extensive example of an inverted pendulum system is studied in detail to verify the effectiveness of the proposed controller based on TrueTime toolbox with comparative results.

A minmax extremum-seeking controller design technique

This paper considers the solution of a minmax optimization problem for a class of unknown nonlinear systems using a perturbation-based proportional-integral extremum seeking control design technique. It is assumed that the equations describing the dynamics of the maximizing and minimizing players are unknown and the cost function to be minimized is unknown but available for measurement to both players. The proposed control system is shown to stabilize the minimizing player in the presence of destabilizing attacks. A simulation example is used to illustrate the effectiveness of the proposed technique.

Design of Adaptive Fuzzy Control for a Class of Networked Nonlinear Systems

This paper presents an adaptive fuzzy controller for a class of unknown nonlinear systems over network. The network-induced delays can degrade the performance of the networked control systems (NCSs) and also can destabilize the system. Moreover, the seriousness of the delay problem is aggravated when packet losses occur during a transmission of data. The proposed controller uses a filtered tracking error to cope the time-varying network-induced delays. It is also robust enough to cope some packet losses in the system. Fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions that appear in the tracking controller. Based on Lyapunov stability theory, the constructed controller is proved to be asymptotically stable. Stability of the adaptive fuzzy controller is guaranteed in the presence of bounded external disturbance, time-varying delays, and data packet dropouts. Simulated application of the inverted pendulum tracking illustrates the effectiveness of the proposed technique with comparative results.

Robust adaptive multiple models based fuzzy control of nonlinear systems

A new robust adaptive multiple models based fuzzy control scheme for a class of unknown nonlinear systems is proposed in this paper. The nonlinear system is expressed by using the Takagi–Sugeno (T–S) method, and some identification adaptive T–S models along with their corresponding controllers, are used in order to control efficiently the unknown system. The modeling error that is produced due to the use of the T–S plant model can cause instability problems if it is not taken into account in the adaptation rules. In this paper, in order to solve this problem, we design a control scheme that is based on updating rules that utilize the σ-modification method. Every T–S controller is updated indirectly by using the robust updating rules and the final control signal is determined by using a performance index and a switching rule. By using the Lyapunov stability theory it is shown that σ-modification based rules can ensure the robustness of the system and define a bound for the steady state identification error. The main objectives of the robust controller are: (i) to ensure that the real plant system will remain stable despite the existence of modeling errors and (ii) to ensure that the real plant will track with a high accuracy the state trajectory of a given reference model. The effectiveness of the proposed method is demonstrated by computer simulations on a well known benchmark problem.

Continuous reinforcement learning to robust fault tolerant control for a class of unknown nonlinear systems

This paper proposes two strategies to design robust adaptive fault tolerant control (FTC) systems for a class of unknown n-order nonlinear systems in presence of actuator and sensor faults versus bounded unknown external disturbances. It is based on machine learning approaches which are continuous reinforcement learning (RL) and neural networks (NNs). In the first FTC strategy, an intelligent observer is designed for unknown nonlinear systems when faults occur or not. In the second strategy, a robust reinforcement learning FTC is proposed through combining reinforcement learning to treat the unknown nonlinear faulty system and nonlinear control theory to guarantee the stability and robustness of the system. Critic and actor of continuous RL are adopted based on the behavior of the defined Lyapunov function. In both strategies, to generate the residual a Gaussian radial basis function is used for an online estimation of the unknown dynamic function of the normal system. The adaptation law of the online estimator is derived in the sense of Lyapunov function which is defined based on adjustable parameters of the estimator and switching surfaces containing dynamic errors and residuals. Simulation results demonstrate the validity and feasibility of proposed FTC systems.

Neural Feedback Passivity of Unknown Nonlinear Systems via Sliding Mode Technique.

Passivity method is very effective to analyze large-scale nonlinear systems with strong nonlinearities. However, when most parts of the nonlinear system are unknown, the published neural passivity methods are not suitable for feedback stability. In this brief, we propose a novel sliding mode learning algorithm and sliding mode feedback passivity control. We prove that for a wide class of unknown nonlinear systems, this neural sliding mode control can passify and stabilize them. This passivity method is validated with a simulation and real experiment tests.

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults

This article develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modelled as both loss of effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining the backstepping technique with the nonlinear tolerant-fault control theory, a novel adaptive fuzzy faults-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighbourhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.

Neural-network-based approach to finite-time optimal control for a class of unknown nonlinear systems

This paper proposes a novel finite-time optimal control method based on input---output data for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. In this method, the single-hidden layer feed-forward network (SLFN) with extreme learning machine (ELM) is used to construct the data-based identifier of the unknown system dynamics. Based on the data-based identifier, the finite-time optimal control method is established by ADP algorithm. Two other SLFNs with ELM are used in ADP method to facilitate the implementation of the iterative algorithm, which aim to approximate the performance index function and the optimal control law at each iteration, respectively. A simulation example is provided to demonstrate the effectiveness of the proposed control scheme.

Adaptive Neural Network Generalized Predictive Control for Unknown Nonlinear System

This paper presents an adaptive neural control design for a class of unknown nonlinear systems. Novel state variables and the corresponding transform are introduced, such that the state-feedback control of a pure-feedback system can be viewed as the output-feedback control of a canonical system. An adaptive predictor incorporated with a neural network observer is proposed to obtain the future system states predictions, which are used in the control design to circumvent the input delay and nonlinearities. The proposed predictor, observer and controller are all online implemented, and the closed-loop system stability is guaranteed. The conventional backstepping design and analysis for pure-feedback systems are avoided, which renders the developed scheme simpler in its synthesis and application. Practical guidelines on the control implementation and the parameter design are provided. The applicability in nonlinear system is demonstrated by simulation experiments. DOI: http://dx.doi.org/10.11591/telkomnika.v11i7.2804 Full Text: PDF

Multi-objective optimal control for a class of unknown nonlinear systems based on finite-approximation-error ADP algorithm

In this paper, an optimal control method for a class of unknown discrete-time nonlinear systems with general multi-objective performance indices is proposed. In the design of the optimal controller, only available input–output data are required instead of known system dynamics, and the data-based identifier is established with stability proof. By the weighted sum technology, the multi-objective optimal control problem is transformed into the single objective optimization. To obtain the solution of the HJB equation, the novel finite-approximation-error adaptive dynamic programming (ADP) algorithm is presented with convergence proof. The detailed theoretic analyses for the relationship of the approximation accuracy and the algorithm convergence are given. It is shown that, as convergence conditions are satisfied, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions. Neural networks are used to approximate the performance index function and compute the optimal control policy, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the proposed method.

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults based on dynamic surface technique

This article develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining the backstepping technique with the dynamic surface control (DSC) approach, a novel adaptive fuzzy faults-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighborhood of zero by appropriate choice of the design parameters. The simulation example and comparisons with the previous method are provided to show the effectiveness of the control approach.

Hierarchical fuzzy CMAC control for nonlinear systems

In this study, a novel indirect adaptive controller is introduced for a class of unknown nonlinear systems. The proposed method provides a simple control architecture that merges from the cerebellar model articulation controller (CMAC) network and hierarchical fuzzy logic; therefore, the complicated CMAC structure can be simplified. The overall adaptive scheme guarantees the uniform stability of the closed-loop system. A simulation is presented to demonstrate the performance of the proposed methodology.

Observer-based adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults

This paper develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modeled as lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown nonlinear functions, and K-filters are designed to estimate the unmeasured states. Combining the backstepping technique with the nonlinear fault-tolerant control theory, a novel adaptive fuzzy faults-tolerant control (FTC) approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.

DIRECT ADAPTIVE FUZZY SLIDING OBSERVATION AND CONTROL

In this paper, a new direct adaptive fuzzy sliding observation and control (AFSOC) method is proposed. The method can be applied to a class of unknown nonlinear systems. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering phenomenon is overcome by using a boundary layer around the sliding surface. The stability of the AFSOC method is proved using the Lyapunov stability theory. Numerical simulation on a benchmark chaotic system depicts the effectiveness of the proposed algorithm.

Robust Adaptive Control via Neural Linearization and Compensation

We propose a new type of neural adaptive control via dynamic neural networks. For a class of unknown nonlinear systems, a neural identifier-based feedback linearization controller is first used. Dead-zone and projection techniques are applied to assure the stability of neural identification. Then four types of compensator are addressed. The stability of closed-loop system is also proven.

Fuzzy knowledge-based model for prediction of traction force of an electric golf car

The methods of artificial intelligence are widely used in soft computing technology due to its remarkable prediction accuracy. However, artificial intelligent models are trained using large amount of data obtained from the operation of the off-road vehicle. In contrast, fuzzy knowledge-based models are developed by using the experience of the traction in order to maintain the vehicle traction as required with utilizing optimum power. The main goal of this paper is to describe fuzzy knowledge-based model to be practically applicable to a reasonably wide class of unknown nonlinear systems. Compared with conventional control approach, fuzzy logic approach is more efficient for nonlinear dynamic systems and embedding existing structured human knowledge into workable mathematics. The purpose of this study is to investigate the relationship between vehicle’s input parameters of power supply (PI) and moisture content (MC) and output parameter of traction force (TF). Experiment has been conducted in the field to investigate the vehicle traction and the result has been compared with the developed fuzzy logic system (FLS) based on Mamdani approach. Results show that the mean relative error of actual and predicted values from the FLS model on TF is found as 7%, which is less than the acceptable limit of 10%. The goodness of fit of the prediction value from FLS is found close to 1.0 as expected and hence shows the good performance of the developed system.

Adaptive Fuzzy Control for Unknown Nonlinear Systems with Perturbed Dead-zone Inputs

Abstract Adaptive fuzzy control is used to control a class of unknown nonlinear systems with perturbed dead-zone inputs in this paper. A new dead-zone actuator model which contains time-varying and perturbed actuation gain is proposed. The dead-zone nonlinearity is treated as a linear-like term, a nonlinear term, and a disturbance-like term, by which the robustness of the system can be obtained by less control effort. Backstepping technique combined with nonlinearly parameterized fuzzy approximators is employed to derive the controller, which removes the restriction that fuzzy basis functions must be well-known for control design. It is proved in theory that the proposed controller guarantees the stability and desired tracking performance of the closed-loop system. A simulation example is also included to demonstrate the effectiveness of the controller.

Adaptive Neural Control for a Class of Uncertain Nonlinear Systems in Pure-Feedback Form With Hysteresis Input

In this paper, adaptive neural control is investigated for a class of unknown nonlinear systems in pure-feedback form with the generalized Prandtl-Ishlinskii hysteresis input. To deal with the nonaffine problem in face of the nonsmooth characteristics of hysteresis, the mean-value theorem is applied successively, first to the functions in the pure-feedback plant, and then to the hysteresis input function. Unknown uncertainties are compensated for using the function approximation capability of neural networks. The unknown virtual control directions are dealt with by Nussbaum functions. By utilizing Lyapunov synthesis, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of zero. Simulation results are provided to illustrate the performance of the proposed approach.

Adaptive neural-networks-based fault detection and diagnosis using unmeasured states

Fault detection and diagnosis play important roles in modern engineering systems. A number of fault diagnosis (FD) approaches for nonlinear systems have been proposed. But, most of the achievements are based on the assumptions that the systems models are known, and states of systems are measurable. A novel FD architecture for a class of unknown nonlinear systems with unmeasured states has been investigated. A general radial basis function (RBF) neural network is used to approximate the model of unknown system, an adaptive RBF neural network with on-line updated centre, and the width vector of ‘Gaussian’ function is used to approximate the model of fault. A nonlinear state observer is designed to estimate system states that are inputs to the neural networks. The stability analysis for the system is given, and the adaptive parameter-updating laws are derived using Lyapunov theory. Simulation examples are used to illustrate the effectiveness of the proposed method.

Robust intelligent tracking control with PID-type learning algorithm

This paper proposes a robust intelligent tracking controller (RITC) for a class of unknown nonlinear systems. The proposed RITC system is comprised of a neural controller and a robust controller. The neural controller is designed to approximate an ideal controller using a proportional–integral–derivative (PID)-type learning algorithm in the sense of Lyapunov function, and the robust controller is designed to achieve L 2 tracking performance with desired attenuation level. Finally, to investigate the effectiveness of the RITC system, the proposed design methodology is applied to control two chaotic dynamical systems. The simulation results verify that the proposed RITC system using PID-type learning algorithm can achieve faster convergence of the tracking error and controller parameters than that using I-type learning algorithm.