Nonlinear Systems In Presence Research Articles

Regularization based reweighted estimation algorithms for nonlinear systems in presence of outliers

Regularization based reweighted estimation algorithms for nonlinear systems in presence of outliers

A novel finite-time leader-follower consensus control for a disturbed mechanical nonlinear system in presence of actuator saturation

This paper presents a novel leader-follower consensus control for a particular class of nonlinear multi-agent mechanical systems in the presence of control input constraints and external disturbances which includes robot system dynamics with a wide range of potential applications in industry. In this case, one of the agents is selected as the leader to direct the other agents in such a way that the whole system can reach consensus within certain prescribed performance transient bounds. Due to the presence of disturbances in most practical systems, the effect of limited disturbance in the consensus control method has been investigated, and actuator saturation is included in the design process. A terminal sliding mode control method has been adapted to ensure the stability of the overall system and fast finite-time leader-follower consensus control. The simulation results of the multi-agent nonlinear robot system in MATLAB environment, in different scenarios with simultaneous consideration of actuator saturation and external disturbance, will show the efficiency of the proposed control method.

Decentralized adaptive proportional‐integral tracking control for strong interconnected nonlinear systems subject to unmodeled dynamics and uncertain input delays

AbstractIn this paper, the problem of decentralized adaptive proportional‐integral (PI) tracking control is investigated for a class of strong interconnected nonlinear systems in presence of unmodeled dynamics and uncertain input delays. A novel compensation mechanism is proposed to deal with the considered strong interconnection functions by applying a smooth switching function to the design algorithm, and the difficulty generated by unmodeled dynamics is dominated by using a dynamic auxiliary signal. By utilizing the suitable error transformations and selecting the appropriate Lyapunov‐Krasovskii function, the effects of uncertain input delays could be surmounted. The novelty of this study is that, for the first time, a new decentralized adaptive PI tracking control scheme including a switching compensation mechanism is developed for the considered strong interconnected nonlinear systems. It is proved that all the signals in the closed‐loop systems are uniformly ultimately bounded (UUB) and the tracking errors converge to a bounded compact set. Finally, a simulation example is carried out to illustrate the effectiveness of the proposed approach.

Finite‐time tracking control for second‐order nonlinear systems with prescribed performance subject to mismatched disturbances

AbstractIn this article, a composite finite‐time control scheme with prescribed performance is investigated for a class of second‐order nonlinear system in presence of both matched and mismatched time‐varying disturbances. Under the prescribed performance control framework, asymmetric dynamic and steady performances are explicitly considered by selecting related performance functions. Then, based on the adding a power integrator technique and the finite‐time disturbance observers, a composite finite‐time prescribed performance tracking controller is designed such that the system output can track the desired reference signal in finite time even in presence of mismatched disturbances. The finite‐time stability of the closed‐loop system is analyzed rigorously. Finally, comparative numerical simulations are conducted to verify the effectiveness of the proposed control scheme.

Incremental adaptive optimal control for nonlinear systems with disturbance and input time-delay

In this paper, a model-free incremental adaptive optimal control scheme is proposed for nonlinear systems in presence of disturbance and input time-delay. The linear time-varying approximate model of the nonlinear system is obtained by incremental method, in which the relevant matrix parameters are identified by recursive least squares (RLS) estimation. A time-delay matrix function is constructed by neural network (NN) to eliminate the input time-delay, and the external disturbance of nonlinear system is dealt with by [Formula: see text] optimal control; incremental adaptive dynamic programming (IADP) algorithm is used to get the control law by solving Hamilton–Jacobi–Isaacs (HJI) equation. Convergence analysis of the proposed control scheme is provided. Simulations are given to verify the effectiveness of the proposed control scheme.

Predictor-Based Neural Dynamic Surface Control of a Nontriangular System With Unknown Disturbances

For a class of nontriangular nonlinear systems in presence of unknown disturbances, we propose a predictor-based neural dynamic surface control (PNDSC) strategy in this paper. This nontriangular system is transformed via the mean value theorem, and a predictor is then constructed. To avoid an algebraic loop problem, partial state vectors are employed as input signals of neural networks (NNs) for approximating unknown dynamics, and compensation items are designed to compensate for approximation errors from NNs. Different from the traditional NDSC, the PNDSC in this paper utilizes prediction errors to update learning parameters for improving NNs’ learning behaviors with overlarge adaptive gains. On the basis of improved NNs’ approximation behaviors, a predictor-based NNs disturbance observer (PNNDO) is constructed for compensation for external disturbances and approximation errors from NNs. Furthermore, with predictors, a normalization method of weights is developed to reduce the number of online learning parameters. On the basis of the aforementioned result, measurement noises are taken into account in our predictor-based neural control strategy. We employ predictor states, rather than measurement information paralyzed by noises, in design of our control strategy. This reduces high-frequency oscillations in control input. A Lyapunov-based stability analysis shows that all signals are ultimately bounded in the closed-loop system. Finally, the effectiveness of the proposed control strategy is verified by a numerical example and a permanent magnet brushless DC motor system.

Harmonic internal models for structurally robust periodic output regulation

This note deals with the problem of output regulation for nonlinear systems in presence of periodic exogenous signals. We investigate the asymptotic properties of a controller given by an internal model designed by adding harmonics on the regulation error, and a static state feedback stabilizing the augmented system of the plant and of the internal model. The solution mimics internal model-based structures adopted for linear systems by showing the asymptotic properties that are guaranteed in the nonlinear case in presence of “generic” plant variations. Forwarding technique is adopted in the design of the stabilizer. We shed also light on the linear case by presenting a new easy-to-check condition under which the regulator equations admit a robust solution.

Model-free high-order terminal sliding mode controller for Lipschitz nonlinear systems. Implemented on Exoped® exoskeleton robot

In this paper, a model-free high-order terminal sliding mode controller (TSMC) is developed for single input–single output Lipschitz nonlinear systems in presence of external disturbances. The proposed method is data-driven, i.e. it is based on online input and output information. In another word, the method is not model-based and can be applied to systems with unknown dynamics. The proposed method employs a high-order switching surface to mitigate the chattering problem. The disturbance estimation technique is also applied to overcome external disturbances. Rigorous theoretical analysis is carried out to verify convergence of states to the switching surface. To demonstrate the effectiveness and applicability of the proposed approach in different situations, several simulations are provided in addition to experimental studies. Experimental tests are implemented on an exoskeleton robot which follows the human gait trajectory in normal and uncertain conditions. In all studies, the results of the proposed method are compared with model free Linear Sliding Mode Control. It is shown that the proposed method has a better performance.

Robust Control of a Class of Nonlinear Systems in Presence of Uncertain Time-Varying Parameters Associated with Diagonal Terms via Output Feedback

Robust Control of a Class of Nonlinear Systems in Presence of Uncertain Time-Varying Parameters Associated with Diagonal Terms via Output Feedback

An Ito–Taylor weak 3.0 method for stochastic dynamics of nonlinear systems

A new framework for development of order 3.0 weak Taylor scheme towards stochastic modeling and dynamics of coupled nonlinear systems is presented. The proposed method is derived by including third order multiple stochastic integral terms of Ito–Taylor expansion and developing them for a wide class of stochastic nonlinear systems. For computing the system responses of linear and a wide class of nonlinear structural systems, the use of lower order integration schemes is sufficient. But for highly non-linear stochastically driven systems like base isolated hysteretic systems and degrading stochastic systems the evaluation of higher order terms is necessary. Additionally, the use of higher order integration schemes for stochastic dynamics of higher dimensional nonlinear systems remains a challenge due to the arising mathematical complexities with the increase in the number of DOFs (degrees-of-freedom) which really necessitates the development of the proposed algorithm. The proposed algorithm is verified using a representative class of coupled nonlinear system in presence and absence of nonlinear degradation and hysteretic oscillators. The efficiency of the proposed numerical scheme over classical integration schemes is demonstrated through a practical engineering problem. Finally, an automated extension of the proposed algorithm is presented by generalizing it for a system of N-DOFs.

Stabilization of nonlinear systems in presence of filtered output via extended high-gain observers

We consider the problem of stabilizing a nonlinear system with filtered output. Given an output feedback control law which satisfies a stability requirement, we consider the case in which the necessary output cannot be measured. The measure is rather the output of an auxiliary stable dynamics in cascade with the system. In place of fully redesign the control architecture, we slightly modify the original control law design by adding a disturbance observer and we recover the desired stability property for the system. The disturbance observer is designed as an extended high-gain observer.

Inverse optimal neural control via passivity approach for nonlinear anaerobic bioprocesses with biofuels production

SummaryThis paper proposes an inverse optimal neural control method of a nonlinear anaerobic bioprocesses model for simultaneous hydrogen and methane production in presence of disturbances. Based on the fundamental properties of the system, a passivity approach is designed such that asymptotic stability is guaranteed. A recurrent high‐order neural network for unknown nonlinear systems in presence of unknown bounded disturbances and parameter uncertainties is proposed to identify nonmeasurable state variables of the system, which are directly related to biofuels production. Optimal control laws based on the neural model are proposed so that the passivation of the entire plant is preserved. The neural control strategy performance for trajectory tracking in presence of disturbances is proven. Results via simulation show the optimal control methodology efficiency to stabilize the H2 and CH4 productions along desired trajectories even in presence of disturbances.

Adaptive terminal sliding mode control of high-order nonlinear systems

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

Adaptive terminal sliding mode control of high-order nonlinear systems

In recent decades, controller design has been attracted a great deal of interest of many researchers in control community which can make the job of many other researchers in different area of research easier. The present study aims to design a finite time adaptive control input for a high-order nonlinear system in presence of a variety of mismatched uncertainties and external disturbances. Adaptive terminal sliding mode control (ATSMC) method is used to design robust controller in a finite time. Also, adaptive concept is employed in ATSMC to estimate the upper bound of mismatched uncertainties and external disturbances and their estimations are used in control input. The finite time stability proof is performed by defining a proper candidate Lyapunov function. Numerical simulation results are carried out in Simulink/MATLAB to reveal the correctness of proposed design in this research. Finally, the performance criterion, integral of the square value (ISV), is defined to provide a numerical comparison between the proposed adaptive controller and non-adaptive controller.

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller’s parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.

Practical Position Tracking Control of a Robotic Manipulator Based on Fractional Order Sliding Mode Controller

In this study, the practical position tracking control of a robotic manipulator has been performed using the proposed fractional-order sliding mode control scheme (FO-SMC). The designed control technique is composed by fractional calculus and sliding mode control (SMC) to guarantee the fast convergence of the joint positions to their desired values. The main idea behind the design of the FO-SMC control is that, the sliding mode control composed with fractional calculus contributes to reach a robust control performance of a nonlinear system in presence of uncertainties, disturbances and un-modelled dynamics without a complete dynamic model of the system. To validate and demonstrate the performance of FO-SMC method, an industrial robot manipulator with external load has been used in the real time experimental studies. The experimental outcomes demonstrate that the proposed fractional-order sliding mode control strategy has a better trajectory tracking performance in presence of the external payload for tracking tasks compared with the classical SMC.DOI: http://dx.doi.org/10.5755/j01.eie.24.5.21838

A novel intelligent fast terminal sliding mode control for a class of nonlinear systems: application to atomic force microscope

This paper addresses the problem of finite-time robust control using an intelligent fast terminal sliding mode control method for a class of nonlinear systems in presence of bounded uncertainty and disturbance. In the proposed method, adaptive neuro-fuzzy inference systems are utilized to determine some parameters in the nonlinear sliding surface based on the measured value of the sliding surface and the system error at each time and thereby variable nonlinear sliding surface is provided. Furthermore, an intelligent optimization algorithm namely honey bee algorithm is also applied to determine the optimal weights of the neuro-fuzzy network. Finite time convergence with increased speed and also chattering-free response are the main advantages of the proposed method compared with the conventional terminal sliding mode control methods. The proposed controller is applied to an atomic force microscope in attendance of uncertainty and disturbance. The simulation results demonstrate considerable success of the method, and show that the error reaches zero in a very short time without chattering.

Adaptive Neural Control of Nonlinear Systems With Unknown Control Directions and Input Dead-Zone

This paper presents an adaptive neural control approach for nonstrict-feedback nonlinear systems in presence of unmodeled dynamics, unknown control directions and input dead-zone nonlinearity. To handle the difficulty due to uncertain control directions, Nussbaum gain functions are applied. Based on the structural characteristic of radial basis function neural networks, a backstepping-based adaptive neural control algorithm is developed. The main contributions of this paper lie in the fact that a backstepping-based neural control algorithm is developed for nonstrict-feedback nonlinear systems with unmodeled dynamics, unknown control directions and actuator dead-zone, and the total number of adaptive laws is not greater than the order of control system. As a beneficial result, the controller is much easier to be implemented in practice with less computational burden. A simulation example is given to reveal the viability of the presented approach. It is demonstrated by both theoretical analysis and simulation study that the presented control strategy ensures the semiglobally uniform ultimate boundedness of all closed-loop system signals.

Adaptive Control of Quantized Uncertain Nonlinear Systems

This paper proposes a new adaptive controller for uncertain nonlinear systems in presence of quantized input signal and unknown external disturbance. A hysteresis quantizer is incorporated to reduce chattering phenomenon. By proposing a new transformation of the final control signal, using the sector-bound property of the quantizer and introducing a hyperbolic tangent function, the effects from input quantization and external disturbance are effectively compensated and the Lipschitz condition required for the nonlinear functions in the systems is removed. Besides showing global stability, tracking error performance is also established and can be adjusted by tuning certain design parameters. A numerical example is presented to demonstrate the effectiveness of the proposed adaptive control scheme.

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.