Unknown Nonlinear Uncertainties Research Articles

Disturbance attenuation for neutral Markovian jump systems with multiple delays

The work explores the study of a neutral Markovian jump system that contains multiple delays, external disturbances, and unknown non-linear uncertainties. To overcome the tracking problem, a modified repetitive controller infused with the higher equivalent-input-disturbance approach and the extended Smith predictor approach is suggested. To guarantee the mean-square asymptotic stability of the system, an appropriate mode-dependent loop-based Lyapunov–Krasovskii functional is used. The proposed controller explicitly forces the system output and accurately follows any supplied periodic reference signal. Subsequently, the efficiency of the recommended technique is demonstrated with the simulations that validate the outcomes by comparing them to the existing results.

ESO-Based Model-Free Adaptive Iterative Learning Energy-Efficient Control for Subway Train With Disturbances and Over-Speed Protection

An extended state observer based model-free adaptive iterative learning energy-efficient control (ESO-based MFAILEEC) scheme for subway train speed tracking with external disturbances and over-speed protection under the constraint on traction/braking force is proposed. Firstly, the continuous-time train motion dynamics is formulated into a discrete-time data model with consideration of external disturbances by applying the iterative dynamic linearization. Meanwhile, the external disturbances and the unknown nonlinear uncertainties of the train are transformed into a new state, which is estimated by an ESO designed in the iteration domain. Then, the ESO-based energy-efficient controller with learning ability is designed, which enables the train to achieve the purpose of energy efficiency by reducing the input force. Further, over-speed protection with trigger mechanism is developed to ensure the train operates within safe speed range. All the control strategies are designed under the constraint on traction/braking force by considering the practical limitation of the train system. No model information is involved in the whole design processes and it is a pure data-driven iterative learning approach. Rigorous mathematical analysis proves the feasibility and the robustness of the proposed method, which can guarantee the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm.

Secure Adaptive Trajectory Tracking Control for Nonlinear Robot Systems Under Multiple Dynamic Obstacles: Safety Barrier Certificates

This article studies the problem of obstacle-avoidance tracking control for a class of uncertain nonlinear robot systems in multiple-dynamic-obstacles environment. The main challenge focuses on how to simultaneously ensure tracking performance and obstacle avoidance. The existing collision-avoidance tracking control schemes cannot guarantee the tracking performance inside the obstacle detection region, since the use of additive Lyapunov-barrier function (LBF) generates the dynamic mismatching. To overcome this difficulty, a novel integral-multiplicative LBF is constructed. The adaptive mechanism is designed to compensate for the mismatching uncertainties. By incorporating the barrier function into backstepping procedure, a secure adaptive tracking control scheme is proposed. Compared with the existing results, the proposed control scheme can simultaneously achieve the obstacle avoidance and tracking performance regardless of being inside the obstacle sensing region and unknown nonlinear uncertainties.

Finite time adaptive neural tracking control for non-strict-feedback uncertain non-linear systems with disturbance and input delay

In this paper, based on neural networks (NNs), we consider finite time adaptive tracking control scheme for non-strict-feedback uncertain non-linear systems with time-variant external disturbance and input delay. A novel auxiliary system has been introduced to degrade the design difficulty caused by input delay. For the unknown non-linear functions and uncertainties in each step, radial basis function NNs are introduced to approximate them such that the control objective can be obtained. Furthermore, based on the idea of backstepping technique, an effective finite time adaptive neural tracking controller has been obtained in the presence of finite time Lyapunov theory, and the singularity problem that may occur in the design process has been overcome using the piecewise functions method. Using the Lyapunov stability theorem, which shows that all the signals of the closed-loop systems are finite time bounded, and the tracking error fluctuates around the origin. Consequently, the proposed scheme not only solves the tracking problem of non-strict-feedback systems with input delay but also realizes the finite time stability performance constraint. Finally, the simulations of two examples show the superiority of the proposed scheme.

Event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems

This paper is concerned with event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems. The approach of fuzzy logic systems (FLSs) approximation is extended to high-order stochastic nonlinear systems to deal with the unknown nonlinear uncertainties. A novel high-order adaptive fuzzy tracking controller is firstly presented via a backstepping approach and event-triggering mechanism which can mitigate the unnecessary waste of computation and communication resources. Based on the above techniques, frequently-used growth assumptions imposed on unknown system nonlinearities are removed and the influence for the high order is handled. The proposed high-order adaptive fuzzy tracking control method not only deals with the influence of high order, but also ensures that the tracking error converges to a small neighborhood of the origin in probability. Finally, the effectiveness of the proposed control method is illustrated by a numerical example.

Robust [formula omitted] fuzzy adaptive controller for three-phase grid-connected photovoltaic system

A robust L1 fuzzy adaptive controller is proposed in this paper for a grid-connected photovoltaic (PV) system. The latter contains a solar PV array connected to a three phase grid through a DC/AC inverter. The designed controller consists of a control law, an adaptive mechanism and a predictor. A fuzzy system is incorporated in the controller structure to achieve a good approximation of unknown nonlinear dynamics and uncertainties. Unlike conventional adaptive control strategies, the proposed control method permits fast adaptation without compromising robustness. Therefore, it can significantly improve the control performance of this type of energy conversion systems characterized by fast dynamics. Furthermore, the presented control scheme ensures the stability of the closed-loop system with bounded transient and tracking performance.

Command-filter-based adaptive neural tracking control for a class of nonlinear MIMO state-constrained systems with input delay and saturation

This paper investigates the problem of adaptive tracking control for a class of nonlinear multi-input and multi-output (MIMO) state-constrained systems with input delay and saturation. During the process of the control scheme, neural network is employed to approximate the unknown nonlinear uncertainties and the appropriate barrier Lyapunov function is introduced to prevent violation of the constraint. In addition, for the issue of input saturation with time delay, a smooth non-affine approximate function and a novel auxiliary system are utilized, respectively. Moreover, adaptive neural tracking control is developed by combining the command filtering backstepping approach, which effectively avoids the explosion of differentiation and reduces the computation burden. The introduced filtering error compensating system brings a significant improvement for the system tracking performance. Finally, the simulation result is presented to verify the feasibility of the proposed strategy.

Robust fractional‐order super‐twisting sliding mode control to accurately regulate lithium‐battery / super‐capacitor hybrid energy storage system

One of the main challenges in front of the inventors and researchers to compensate the power quality problems is the existence of an efficient and reliable electric energy source for dynamic voltage restorer (DVR). Recent advances in the technologies of lithium-battery (LB) and super-capacitor (SC) have made them possible to be used as hybrid energy storage system (HESS) for DC-power supply of DVR. But then, a robust and efficient controller must be essentially designed to compensate the intricate correlation between system components, unknown nonlinearities, parameter uncertainties related to the HESS. Hence, fractional-order super-twisting sliding mode control (FOSTSMC) is proposed for LB/SC-HESS to smoothly and accurately smoothly track the current reference and control the DC-link voltage of the asymmetric half-cascaded multilevel inverter of DVR during different compensation conditions. As the primary controller, FOSTSMC has compensated the unknown nonlinear parts and parameter uncertainties related to LB/SC-HESS through the real-time disturbance estimation using sliding mode state and disturbance observer (SMSDO). Both the battery current and DC-link voltage due to the physical measurability are chosen to design the control scheme based on the proposed FOSTSMC. The proposed controller has been compared with the proportional integral derivative and the sliding mode control under different probable scenarios to evaluate and validate its observability and controllability. To better present the effects of FOSTSMC, AHCMLI, and HESS-based DVR, they have been quantified as follows: Three real-time stability benchmarks that is, overshoot, undershoot and settling time are respectively attained for FOSTSMC: 0.6, 0.4, and 0.03; for sliding mode control: 1.1, 0.7 and 0.019; for proportional integral derivative: 0.9, 2, and 0.117. That is to say, FOSTSMC can smoothly and accurately track the current reference and control the DC-link voltage during different compensation conditions as compared with other controllers. Asymmetric half-cascaded multilevel inverter can provide 33 steps with consideration of 12 unidirectional switches, whereas binary, trinary, and other multilevel structures can provide less than 27 steps with consideration of 12 switches. The quasi-AC voltage synthesizer-based DVR can completely and accurately compensate the voltage sag and swell with THD of 2.12 and 2.35, respectively. The THD of mal-compensation voltage sag and swell using the conventional DVR are respectively 11.57 and 13.86.

PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.

Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction

For strict-feedback nonlinear systems (SFNSs) with unknown control direction, this paper synthesizes an asymptotic tracking controller by a combination of the dynamic surface control (DSC) technique, the Nussbaum gain technique (NGT) and fuzzy logic systems (FLSs). The SFNSs under study feature unknown nonlinear uncertainties and external disturbances. By utilizing the DSC technique with nonlinear filters, the issue of ‘differential explosion’ is obviated, in which the adaptive laws are constructed to conquer the effect of unknown functions. The FLSs are exploited to cope with uncertainties without any prior conditions of the ideal weight vectors and the approximation errors. In addition, by introducing the NGT, the unknown control direction problem is solved. Compared with the existing results, the proposed design procedure is able to simultaneously overcome the ‘differential explosion’ and the unknown control direction problems, and asymptotic tracking is accomplished. At the end, a second-order numerical system and a more realistic Norrbin nonlinear mathematical model are applied to confirm the feasibility of the design procedure.

Fast finite time adaptive neural network control for a class of uncertain nonlinear systems subject to unmodeled dynamics

In this paper, a fast finite time adaptive control issue is discussed for a class of uncertain nonlinear systems. The systems considered involve unmodeled dynamics as well as dynamical disturbances. First, neural networks (NNs) are introduced to deal with the difficulties caused by unknown nonlinear uncertainties, and dynamical signal functions are utilized to handle unmodeled dynamics and dynamical disturbances. Second, based on adaptive backstepping technique and a fast finite-time stability criterion, a fast finite time adaptive neural network control scheme for a class of uncertain nonlinear systems subject to unmodeled dynamics is proposed for the first time. The proposed control scheme can not only ensure that all closed-loop signals are bounded, but also has the robustness to unmodeled dynamics and dynamical disturbances. The main innovations of this work lie in the ingenious design of parameter adaptive laws and controller, and the development of fast finite-time adaptive control algorithm from a new point of view. Finally, the feasibility of the proposed control algorithm is elaborated by two simulation examples.

Partial-State-Constrained Adaptive Intelligent Tracking Control of Nonlinear Nonstrict-Feedback Systems with Unmodeled Dynamics and Its Application

In this paper, an adaptive intelligent control scheme is presented to investigate the problem of adaptive tracking control for a class of nonstrict-feedback nonlinear systems with constrained states and unmodeled dynamics. By approximating the unknown nonlinear uncertainties, utilizing Barrier Lyapunov functions (BLFs), and designing a dynamic signal to deal with the constrained states and the unmodeled dynamics, respectively, an adaptive neural network (NN) controller is developed in the frame of the backstepping design. In order to simplify the design process, the nonstrict-feedback form is treated by using the special properties of Gaussian functions. The proposed adaptive control scheme ensures that all variables involved in the closed-loop system are bounded, the corresponding state constraints are not violated. Meanwhile, the tracking error converges to a small neighborhood of the origin. In the end, the proposed intelligent design algorithm is applied to one-link manipulator to demonstrate the effectiveness of the obtained method.

NESO-Based Path Following Control for Underactuated Hovercrafts with Unknown Nonlinear Uncertainties and a Safety Limit Constraint

In this brief, the path following control problem of underactuated hovercrafts subject to nonlinear time-varying uncertainties and a safety limit constraint (SLC) is addressed. A novel homogenous nonlinear extended state observer (NESO)-based safe motion controller for a path following control scenario of underactuated hovercrafts is proposed. First, a NESO is constructed to estimate and compensate the nonlinear time-varying uncertainties for the underactuated hovercraft. Then, a NESO-based backstepping sliding mode control (BSMC) law with a turning SLC is proposed to achieve the yaw control for underactuated hovercrafts, which improves both safety and maneuverability of the underactuated hovercraft during the path following control scenario. The nonlinear time-varying turning SLC is first directly taken into the control system design, which is achieved by introducing an auxiliary dynamic system to limit the virtual input control during the backstepping design process. A NESO-based backstepping surge control law is also designed to achieve the surge control for underactuated hovercrafts. Furthermore, all error signals of the proposed closed-loop control system are proven to be bounded. Finally, an application case is tested on an underactuated hovercraft to illustrate the effectiveness and superiority of the designed control scheme.

Output feedback stabilization for 1-D unstable wave equations with boundary control matched disturbance and van der Pol nonlinear boundary

In this paper we study the output feedback stabilization of a plant described by a one-dimensional wave equation with a van der Pol type nonlinear boundary condition, an unknown internal nonlinear uncertainty and an external disturbance acting at the control end (boundary). The simultaneous occurrence of nonlinear internal uncertainty, external disturbance, and van der Pol type nonlinear boundary term in the plant leads to the system is more complicated. First, we show that the open-loop system is well-posed and we design an infinite-dimensional estimator to estimate the disturbance. It is shown that the disturbance estimator can successfully estimate the total disturbance, in the sense that the estimation error signal is in L2(0,∞). Using the estimated disturbance, we propose an asymptotic state observer, and then we design an observer-based output feedback stabilizing controller. The closed-loop system is shown to be asymptotically stable. Finally, a numerical simulation is carried out to illustrate the theoretical results and effectiveness of the proposed control law.

Design of Adaptive Fuzzy Controllers for a Class of Fractional Order Nonlinear MIMO Systems With Input Saturation

This paper develops a fractional order adaptive fuzzy backstepping control scheme for an incommensurate fractional order uncertain nonlinear multiple-input multiple-output (MIMO) systems with external disturbance and input saturation. Combined with the adaptive and backstepping technique, the fuzzy logic system is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the incommensurate fractional order parameters update laws for fuzzy logic system, unknown parameters as well as the external disturbances are proposed in the controller to compensate the unknown nonlinearities, unknown parameters and disturbances. With the aids of the frequency distributed model of fractional integrator for the fractional order systems in the procedure of controller design, the stability of the closed loop system is established. At last, two simulation examples are demonstrated to verify the robustness and effectiveness of the proposed controller.

An Adaptive Control of Fractional-Order Nonlinear Uncertain Systems with Input Saturation

This paper develops a fractional-order adaptive fuzzy backstepping control scheme for incommensurate fractional-order nonlinear uncertain systems with external disturbances and input saturation. Based on backstepping algorithm, the fuzzy logic system is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the fractional-order parameters update laws for fuzzy logic system, unknown parameters, and the external disturbances are proposed. With the aids of the frequency distributed model of fractional integrator for the fractional-order systems in the procedure of controller design, the stability of the closed-loop system is established. To verify the effectiveness and robustness of the proposed controller, two simulation examples are demonstrated at last.

Adaptive Neural Network Control of a Class of Fractional Order Uncertain Nonlinear MIMO Systems with Input Constraints

An adaptive backstepping control scheme for a class of incommensurate fractional order uncertain nonlinear multiple-input multiple-output (MIMO) systems subjected to constraints is discussed in this paper, which ensures the convergence of tracking errors even with dead-zone and saturation nonlinearities in the controller input. Combined with backstepping and adaptive technique, the unknown nonlinear uncertainties are approximated by the radial basis function neural network (RBF NN) in each step of the backstepping procedure. Frequency distributed model of a fractional integrator and Lyapunov stability theory are used for ensuring asymptotic stability of the overall closed-loop system under input dead-zone and saturation. Moreover, the parameter update laws with incommensurate fractional order are used in the controller to compensate unknown nonlinearities. Two simulation results are presented at the end to ensure the efficacy of the proposed scheme.

An innovative optimal RPO-FOSMC based on multi-objective grasshopper optimization algorithm for DFIG-based wind turbine to augment MPPT and FRT capabilities

Abstract Doubly Fed Induction Generator (DFIG) with consideration of its exceptional capabilities, i.e.: variable speed operation, low mechanical stresses, and excellent power quality in limited-range speed applications is a famous kind of wind turbines. Even so, there is a challenge due to its nonlinear dynamic features and several uncertainties like unknown non-linear disturbances and parameter uncertainties. Hence, this paper proposes a novel Robust Perturbation Observer based Fractional Order Sliding Mode Controller (RPO-FOSMC) for DFIG to extract the maximum power and improve the Fault Ride-Through (FRT) capability. The strong nonlinear aerodynamics of wind turbine, the uncertain dynamic parameters of induction generator and the stochastic characteristics of wind waves are constructed in perturbation term which is estimated using the proposed RPO-FOSMC. Accordingly, the perturbation compensator provides an appropriate robustness concerning different uncertain models and attains an exceptional control capability during stochastic wind waves. Considering the inherent multi-objective nature of the nonlinear control design problem, Multi-Objective Grasshopper Optimization Algorithm (MOGOA) has been implemented to augment the robustness and dynamic performance of RPO-FOSMC. Three distinct conditions are considered to compare and analyse the fast and robust dynamic performance of optimal RPO-FOSMC against other conventional approaches. Eventually, the comprehensive simulation results have revealed and validated the exceptional dynamic capability of the suggested control strategy.

Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems

Convergence rate is an important performance index in consensus control. Yet, most of the existing results can only achieve asymptotic consensus, or finite-time consensus whose settling time is contingent on initial conditions. This paper studies the robust fixed-time consensus tracking control problem for high-order nonholonomic chained-form systems subject to unknown parameters and nonlinear uncertainties. By using the modified power integrator method, we propose a new robust fixed-time consensus tracking algorithm, with which the consensus tracking can be achieved in a fixed time independent of initial conditions even in the presence of uncertainties. An observer-based fixed-time consensus tracking algorithm is also developed as an alternative method to overcome the communication loop problem. Lyapunov analysis shows the fixed-time stability of the closed-loop system. An application to multiple wheeled mobile robots is presented.

Multiple model-based event-triggered adaptive control of a class of discrete-time nonlinear systems

ABSTRACTIn this study, the problem of event-triggered-based adaptive control (ETAC) for a class of discrete-time nonlinear systems with unknown parameters and nonlinear uncertainties is considered. Both neural network (NN) based and linear identifiers are used to approximate the unknown system dynamics. The feedback output signals are transmitted, and the parameters and the NN weights of the identifiers are tuned in an aperiodic manner at the event sample instants. A switching mechanism is provided to evaluate the approximate performance of each identifier and decide which estimated output is utilised for the event-triggered controller design, during any two events. The linear identifier with an auxiliary output and an improved adaptive law is introduced so that the nonlinear uncertainties are no longer assumed to be Lipschitz. The number of transmission times are significantly reduced by incorporating multiple model schemes into ETAC. The boundedness of both the parameters of identifiers and the system outputs is demonstrated though the Lyapunov approach. Simulation results demonstrate the effectiveness of the proposed method.