Adaptive Backstepping Control Design Research Articles

Design and analysis of novel Chebyshev neural adaptive backstepping controller for boost converter fed PMDC motor

An adaptive backstepping Chebyshev neural network controller (ABCNNC) is proposed for the boost converter fed PMDC motor to track the angular velocity. The computational complexity of the neural network is avoided by the use of Chebyshev polynomials as the basis function. The online weight update of the Chebyshev neural network (CNN) is designed for the closed loop system based on the Lyapunov stability analysis to obtain the asymptotically stable system. A detailed analysis of the steady state and transient performance is performed and results are compared with that of conventional PI controller and radial basis function neural network controller (RBFNNC). To ensure the robustness of the proposed ABCNNC, it is being analysed for a wide range of variations in load torque and the set point changes and it is validated by comparing with the conventional PI control approach and RBFNNC. Comparison of results validates that the proposed ABCNNC shows the enhanced transient and steady state responses for the uncertainties caused by disturbances, than conventional PI controller and RBFNNC.

Design and analysis of novel Chebyshev neural adaptive backstepping controller for boost converter fed PMDC motor

Design and analysis of novel Chebyshev neural adaptive backstepping controller for boost converter fed PMDC motor

Asymptotic tracking control for time-delay nonlinear systems with parametric uncertainties and full state constraints

This article concentrates on an adaptive backstepping control design of time-delay strict-feedback uncertain nonlinear systems subject to full state constraints. The tan-type barrier Lyapunov functions (tBLFs) and Lyapunov–Krasovskii function are united together, which successfully get over the difficulties of system design in which the first function is involved to ensure full state constraints satisfaction and the second is established to eliminate the effect of delayed states. By employing a new control scheme, asymptotic tracking performance is arrived, and all the states remain in the desirable regions for all the system running time. Meanwhile, the boundedness of all signals of the closed-loop system is guaranteed. The performance of the control scheme is illustrated through a class of single degree of freedom (1-DOF) time-delay electrostatic microactuator systems.

Adaptive Neural Backstepping Control Design for A Class of Nonsmooth Nonlinear Systems

This paper investigates the problems of backstepping control for a class of nonsmooth nonlinear systems. With the help of set-valued functions (or maps) and set-valued derivatives, a new Lyapunov criterion is developed for nonsmooth systems. The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is, for the first time, applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design. Then, two types of continuous controllers are designed based on the backstepping technique and adaptive neural network (NN) algorithm. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. Then, the first type of controller can be efficiently designed by using the traditional backstepping technique. On the other hand, when the unknown uncertainty is taken into account in the equivalent systems, another type of controller is designed based on adaptive NN control strategy. It is proved that in both cases, all the closed-loop signals are SGUUB by using our proposed controllers. Finally, a numerical example with two types of controllers is supplied to show the availability of the provided control schemes.

Adaptive Fuzzy Prescribed Performance Control of Nontriangular Structure Nonlinear Systems

In this article, a new n -step fuzzy adaptive output tracking prescribed performance control problem is investigated for a class of nontriangular structure nonlinear systems. In the control design process, the mean value theorem is used to separate the virtual state variables needed for the control design, and the implicit function theorem is exploited to assert the existence of the desired continuous control. The fuzzy logic systems are used to identify the unknown nonlinear functions and ideal controller, respectively. By constructing a novel iterative Lyapunov function, a new n -step adaptive backstepping control design algorithm is established. The prominent characteristics of the proposed adaptive fuzzy backstepping control design algorithm are as follows: one is that it can ensure the closed-loop control system is the semiglobally uniformly ultimately bounded and the tracking error can converge within the prescribed performance bounds. The other is that it solves the controller design problem for the nontriangular nonlinear systems that the previous adaptive backstepping design techniques cannot deal with. Two examples are provided to show the effectiveness of the presented control method.

TABLF-based adaptive control for uncertain nonlinear systems with time-varying asymmetric full-state constraints

ABSTRACT In this paper, we investigate the tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and time-varying asymmetric full-state constraints. By introducing novel tan-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design, the boundedness of the fictitious state tracking errors are ensured. A novel adaptive backstepping control design based on tuning function is given, which successfully eliminates the effect of uncertainties. In addition, only one parameter needs to be adjusted online in the control design, which greatly alleviates the computation burden. Based on the proposed control scheme the asymptotic convergence of system output tracking error is realised and the time-varying full-state constraints are not violated for all the time. A numerical example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive output feedback control for fractional-order multi-agent systems

This study investigates the leader-following consensus problem in fractional-order multi-agent systems (MAS). First, a distributed observer is presented to estimate the state variables by using only the output information of MAS. Second, to overcome the difficulty of selecting an appropriate Lyapunov function for fractional order MAS, we propose a new state transformation technique to reconstruct the observer dynamic model. Then a new distributed frequency-dependent Lyapunov function is introduced in accordance with this model. Based on this new Lyapunov function, an adaptive vector backstepping controller design procedure is presented. Lastly, a series of virtual signals is generated to compensate for input nonlinearities including dead zones, quantization, and saturation by the fractional order auxiliary systems. Simulation results confirm the validity of the theoretical analysis.

Adaptive Backstepping Control Design for Uncertain Non-smooth Strictfeedback Nonlinear Systems with Time-varying Delays

This paper is concerned with the problem of adaptive neural tracking control for uncertain non-smooth nonlinear time-delay systems with a class of lower triangular form. Based on Filippov’s theory, the bounded stability and asymptotic stability are extended to the ones for the considered systems, which provides the theory foundation for the subsequent adaptive control design. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent system model, based on which, two types of controllers are designed by using adaptive neural network (NN) algorithm. The first designed controller can guarantee the system output to track a target signal with bounded error. In order to achieve asymptotic tracking performance, the other type of controller with proportional-integral(PI) compensator is then proposed. It is also noted that by exploring a novel Lyapunov-Krasovskii functional and designing proper controllers, the singularity problem frequently encountered in adaptive backstepping control methods developed for time-delay nonlinear systems with lower triangular form is avoided in our design approach. Finally, a numerical example is given to show the effectiveness of our proposed control schemes.

Adaptive NN Backstepping Control Design for a 3-DOF Helicopter: Theory and Experiments

This paper presents an adaptive neural network backstepping control design for an experimental helicopter with three rotational degrees of freedom. The helicopter system is described by a state-space model with unmodeled dynamics and external disturbances. By resorting to radial basis function neural networks with online gradient descent training, such unmodeled dynamics and external disturbances can be compensated in real time. With the help of Lyapunov stability criteria, it is proved that the desired trajectories can be boundedly tracked by the corresponding attitude angles of the helicopter under the proposed adaptive neural network backstepping controller. Compared with robust adaptive integral backstepping technique, our approach has smaller root mean squared error. Finally, four sets of contrastive experiment results are, respectively, given to show the effectiveness and advantages of the proposed control scheme.

Based on fuzzy-approximation adaptive backstepping control method for dual-arm of humanoid robot with trajectory tracking

In this article, a fuzzy-approximation-based adaptive backstepping control method for dual-arm of a humanoid robot was proposed. The purpose of this control system is to provide coordinated movement assistance to enable the humanoid robot’s human-like forearm to grab objects coordinately (or track any continuous desired trajectory), even in the presence of environmental disturbances and parametric uncertainties. We analyze the proposed adaptive backstepping by mathematical modeling and actually measure the robot dual-arm motion information of a number of case when they simulate the trajectory to verify the model. We design the adaptive fuzzy-approximation control strategy and combining the synthesis of the robust design, backstepping control, and Lyapunov function method, the proposed adaptive fuzzy backstepping control does not need to know the humanoid robot’s arms model precisely. In the control system proposed here, once the desired trajectories of the robot’s dual-arm positions are given, the adaptive fuzzy system was closed to any unknown functions and to the derivative of the virtual control law of the humanoid robot system. In this case, a robust design scheme was utilized to compensate for any approximation errors. With the proposed trajectory tracking, not only able to generate the coordinate motions for a humanoid robot’s two arms, but it can also control the arms to move to the desired positions. The proposed closed-loop system under the adaptive fuzzy backstepping control design was effective and that asymptotic stability was successfully achieved. The adaptive fuzzy-approximation backstepping control strategy should be more complete and intelligent and more actual test should be conducted to further evaluate the effect of the proposed trajectory tracking. The instability of dual-arm of humanoid robot system is systematically analyzed and a backstepping control strategy based on the adaptive fuzzy-approximation to improve the continuity of trajectory tracking of the robot’s arms is proposed.

Adaptive Fuzzy Backstepping Control for Stable Nonlinear Bilateral Teleoperation Manipulators With Enhanced Transparency Performance

Bilateral teleoperation technology has been widely concerned by its unique advantages in human–machine interaction-based cooperative operation systems. Communication delay, various nonlinearities, and uncertainties in teleoperation system are the main challenging issues to achieve system stability and good transparency performance. In this paper, a globally stable adaptive fuzzy backstepping control design is proposed for nonlinear bilateral teleoperation manipulators to handle the aforementioned issues. For the communication channel, instead of direct transmission of environmental torque signals, the fuzzy-based nonpower approximate environmental parameters are transmitted to the master side for environmental torque prediction, which effectively avoids the transmission of power signals in the delayed communication channel and solves the passivity problem in the traditional teleoperation system. A trajectory generator is implemented in the master side and a trajectory smoothing is applied in the slave side. Subsequently, nonlinear adaptive fuzzy backstepping controllers for master and slave are separately designed to handle the nonlinearities and uncertainties. Theoretically, the great transparency performance of both position tracking and force feedback can be achieved, and the global stability is still guaranteed under communication delay. Comparative experiments are conducted on the real platform, which verify the effectiveness and advantages of the proposed control design in some typical working scenarios.

Development of a New Adaptive Backstepping Control Design for a Non-Strict and Under-Actuated System Based on a PSO Tuner

In this work, a new adaptive block-backstepping control design algorithm was developed for an under-actuated model (represented by a ball–arc system) to enhance the transient and steady-state behaviors and to improve the robustness characteristics of the controlled system against parameter variation (load change and model uncertainty). For this system, the main mission of the proposed controller is to simultaneously hold the ball at the top of the arc and retain the cart at the required position. The stability of a controlled system based on the proposed adaptive controller was analyzed, and its globally asymptotic stability was proven based on the Lyapunov theorem. A comparative study of adaptive and non-adaptive block-backstepping controllers was conducted in relation to the transient, steady-state, and robustness characteristics. The effectiveness of the controller was verified via simulation within a MATLAB/SIMULINK environment. The simulated results show that the proposed adaptive control strategy could successfully stabilize the under-actuated ball–arc system, regardless of both the regulation problem and the tracking problem. This provides a better dynamic performance and a better load rejection capability, and it performs well in solving the uncertainty problem in the model parameter.

Interval Type-2 FNN-Based Quantized Tracking Control for Hypersonic Flight Vehicles With Prescribed Performance

This paper presents a tracking control scheme with quantization mechanism for hypersonic flight vehicles (HFVs) with prescribed performance using an interval type-2 fuzzy neural network (IT2FNN). A parameterized tracking error model of the HFV is derived with some considered uncertainties, which are approximated by an IT2FNN. The tracking control of the velocity and altitude of the HFV is designed by using a prescribed performance control technique. It allows that transient characteristics of the tracking errors can be improved and adjusted by some prescribed performance functions. According to an adaptive backstepping control design procedure, novel continuous control laws of the fuel equivalency ratio, canard deflection, and elevator deflection are designed with logarithmic quantization mechanism, for the sake of avoiding inadvertently increasing the effective gains of continuous controllers as well as reducing loads of the communication from controller unit to actuator unit. Besides, the limited tracking errors of the flight path angle and angle-of-attack can be achieved by applying the designed controllers. Finally, the presented tracking controllers with quantization mechanism are validated by comparative simulations.

Adaptive prescribed performance decentralized control for stochastic nonlinear large‐scale systems

SummaryThis paper investigates the adaptive fuzzy prescribed performance output‐feedback decentralized control problem for a class of stochastic interconnected nonlinear large‐scale systems. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a state observer is designed to estimate the unmeasured states. By combining the backstepping recursive design principle with prescribed performance theory, an adaptive fuzzy decentralized control method is presented. In order to overcome the problem of “explosion of complexity” in the adaptive backstepping control design, the first‐order filter signals are introduced into adaptive fuzzy decentralized control design algorithm and form a new simplized. The stability is proven based on the Lyapunov stability theory, which demonstrated that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded in probability and the tracking errors remain a small neighborhood of the origin within the prescribed performance bounds. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

Adaptive Heart Rate Regulation Using Implantable Pacemaker with Artificial Neural Network-Based Backstepping Controller

Implantable cardiac pacemaker is a standard medical device totreat heart rhythm disorders. In this paper, a new adaptivebackstepping controller is developed to enhance the performanceof dual-sensor pacemakers for regulating the heart rate, based onradial basis function neural networks. The robust design ofadaptive backstepping controller using Lyapunov functions allowsguaranteeing the stability and performance of the rate-adaptivepacing system for accurately accomplishing the heart rateregulation at different preset values. This developed controlsystem has been retrospectively tested on six datasets of twopatients with a pacemaker during three body activities of the rest,walking, and exercising. The resulting root mean square error(RMSE) and maximum error are less than 0.36 and 0.50 %,respectively. In addition, comparative results of this study showedthat the performance of developed backstepping controller issuperior to other pacemaker controllers in the previous studies.

다양한 이유에서 오는 알 수 없는 오차들의 추정 보상을 위한 오차 기반 RBF 신경망 적응 백스테핑 제어기 설계

The servomechanism of the dual axis pan tilt system is used across a wide range of fields. Hence, it requires a robust controller that can control it under any circumstance. In this paper, a dynamic modeling of the dual axis pan tilt system is presented in a strict feedback form, and a backstepping controller is designed. Moreover, an adaptive backstepping controller is designed in a strict feedback form using error state-based radial basis function (RBF) neural networks (NN). The proposed controller prevent any unknown errors due to modeling errors, disturbances, uncertain parameters, or input saturation from undermining control performance. The activation function of the hidden layer was changed. As a result, minimum inputs decrease learning time, thereby allowing the fast estimation and compensation of unknown errors, improving the control performance by change activation function.

Output-feedback control design for switched nonlinear systems: Adaptive neural backstepping approach

The tracking control is addressed for switched nonlinear systems with arbitrary switchings by adaptive neural approach via output feedback. The switched systems under consideration are composed of some subsystems in non-strict -feedback form. It is assumed that all the system state variables are unavailable, but the output variable is measurable. A switched nonlinear observer is set up to estimate those unmeasurable state variables. Convex combination method is utilized to determine the observer gain matrix so that the effect from those nonlinear terms can be well compensated for. By the feature of the basis vector functions of radial basis neural networks (RBF NN), a new observer-based adaptive neural backstepping control design scheme is presented for the switched nonlinear non-strict feedback systems. The multiple Lyapunov method is used to show the stability of the adaptive closed-loop systems. It is also proven that the tracking error converges to a small neighborhood around the original point under the action of the suggested controllers. Finally, a simulation example is studied to test the efficacy of the suggested control strategies.

Adaptive Command-Filtered Backstepping Control of Robot Arms With Compliant Actuators

Compliant actuators are significant for safe physical human-robot interaction. Series elastic actuator (SEA) is the most popular type of compliant actuators, which possesses several attractive features, such as low output impedance, back drivability, shock tolerance, smooth force transmission, and energy efficiency. This brief focuses on the adaptive command-filtered backstepping control (CFBC) design for robot arms driven by SEAs. The CFBC alleviates the complexity problem in integrator backstepping control and has attracted great attention. However, experimental results of adaptive CFBC have not been reported. In this brief, a simplified adaptive CFBC framework is developed for robot arms driven by SEAs, where discontinuous friction is compensated for by an adaptive mechanism. Closed-loop stability is rigorously established by the Lyapunov synthesis and time-scales separation. Experimental results based on a single-link SEA-driven robot arm have been provided to verify the effectiveness of the proposed control strategy.

Nonlinear Adaptive Backstepping Controller Design for Islanded DC Microgrids

In this paper, a nonlinear adaptive backstepping controller is designed to control the common dc-bus voltage for different components in a dc microgrid under various operating conditions. The dc microgrid in this paper comprises a solar photovoltaic (PV) unit, a battery energy storage system (BESS), a backup diesel generator, and loads (both critical and noncritical). The controllers are designed for all components except loads where the main control objective for all controllers is to maintain a constant voltage at the dc-bus where all components are connected. This paper considers solar PV systems as the renewable energy source, whereas a diesel generator equipped with a rectifier is used as a backup supply to maintain the continuity of power supply in the case of emergency situations. The proposed controller is designed recursively based on the Lyapunov control theory, where all parameters within the model of different components are considered unknown. Adaptation laws are used to estimate these unknown parameters while the stability of the dc microgrid, with these adaptation laws, is ensured through the formulation of suitable control Lyapunov functions (CLFs) at different stages of the design process. The negative definiteness or semidefiniteness of these CLFs guarantees the stability of the dc microgrid. Finally, the performance of the proposed controllers is verified using both simulations and experiments on a test dc microgrid under different operating conditions. The proposed controller ensures the regulation of the dc-bus voltage within the acceptable limits under different operating conditions.

Robust Adaptive Backstepping Controller Design for Aircraft Autonomous Short Landing in the Presence of Uncertain Aerodynamics

AbstractTo achieve tracking performance and robustness simultaneously during an aircraft’s autonomous short landing phase, a three-dimensional automatic landing system designed using robust adaptiv...