Adaptive Backstepping Control Research Articles

Adaptive control of LTV systems with uncertain periodic coefficients

The paper considers the control problem for a class of uncertain linear time-varying systems. The time-varying (TV) parameters are represented by multisinusoidal functions with a priori unknown amplitudes, phases, and frequencies of harmonics. The maximum numbers of the harmonics are known. To compensate the influence of the TV parameters on the closed-loop system, based on internal model principle, TV parameters observers are designed, and the plant model is represented in the parameterized form with constant unknown parameters. This form is used for design of adaptive backstepping controller with modular identifiers with improved parameters tuning.

Transients Improvement in the Output-Feedback Adaptive Backstepping Control of Nonlinear Systems with Input Constraints

The paper addresses the problem of transient performance improvement in the output-feedback adaptive backstepping control of parametrically uncertain nonlinear system represented in the cascaded output-feedback form. The system state is inaccessible for measurement, the system input is constrained, and the control gain is assumed unknown (its sign is known). The problem is solved by applying specially modified K-filters with adjustable parameter, using the backstepping procedure taking into account the input constraints, and involving the Kreisselmeier-like adaptation algorithm with a modified swapping scheme. The algorithm enables us to improve the closed-loop transient performance without increasing initial “swings” in the control error transients. The latter property is achieved by including the high-order time derivatives of the adjustable parameters, calculated by the adaptation algorithm, in the control law. The properties of the closed-loop system are illustrated via simulation.

A novel adaptive variable speed control strategy for wound rotor induction motors

A new approach is proposed for the design of an adaptive variable speed controller for an induction motor. This design approach is based on a new model for induction motors in the (α/β) reference frame. The model state variables are constant in steady state and therefore enable the application of adaptive backstepping control design techniques to find controller equations and adaptation laws that ensure that the rotor speed and flux track their reference values despite significant changes in machine resistances and inductances due to temperature and magnetic saturation. The proposed controller is tested in simulation. Results show robust steady state and transient performances.

Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints.

This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

Command-filtered adaptive containment control of fractional-order multi-agent systems via event-triggered mechanism

In this paper, the containment control problem of a class of fractional-order nonlinear multi-agent systems is studied, in which the multi-agent system contains unmeasured states and system nonlinearity. An adaptive neural network backstepping controller combined with event-triggered mechanism is proposed to ensure all followers can converge to the convex hull spanned by the leaders. The command filter is introduced into the proposed fractional-order control system to obtain fractional derivatives for virtual control functions continuously and avoid “explosion of complexity.” From the Lyapunov stability theory, all the signals can remain semi-global uniformly ultimately bounded in the closed-loop system. Numerical example and simulation results confirm the feasibility of the proposed control method.

Composite observer‐based adaptive event‐triggered backstepping control for fractional‐order nonlinear systems with input constraints

An event‐triggered neural adaptive backstepping controller via a state and a disturbance observers is proposed for uncertain fractional‐order nonlinear systems with time‐varying external disturbances and unavailable states. The radial basis function neural network (RBFNN) is utilized to approximate uncertain nonlinear terms, and a coupled observer including both state observer and disturbance observer is developed in view of the output of the RBFNN to obtain the dynamic information of unmeasured states and unknown compounded disturbances. Then, to tackle with the impact of input constraints, an auxiliary system is constructed, and an event‐triggered approach is developed to cut down communication burden between the controller and the actuator. Moreover, a dynamic surface control strategy is developed to cope with the tedious analytic computation of time derivatives of virtual controllers. The stability analysis demonstrates that the involved signals remain bounded, and tracking and observering errors can converge to a diminutive neighborhood around the origin. At last, the effectiveness of the developed control method is verified by two numerical examples.

Adaptive finite-time backstepping control tracker for quadrotor UAV with model uncertainty and external disturbance

In this study, for the purpose of finite-time tracking control of quad-rotor Unmanned Aerial Vehicle (UAV) system under modeling uncertainties and external disturbances, an adaptive command-filtered backstepping sliding mode control scheme is presented. At first, a state-space model of quad-rotor's system is considered in the existence of bounded model uncertainties and exterior perturbations. Then, a command-filter according to the virtual control input is planned to reduce the computing complications. Subsequently, the output of command filter is considered instead of high-order derivative of virtual input. Besides, in order to remove the differential signals which are obtained during design of command-filter, the compensation error is used. Afterward, the sliding surfaces are designed according to tracking errors which are defined between actual states of the quad-rotor, desired values and compensation error system. Furthermore, backstepping control procedure combined with Lyapunov stability theory is used for finite-time convergence of switching surface. Besides, the adaptive control strategy is applied to estimate the upper bound of uncertainty and disturbance which is unknown in advance. At last, in order to validate the high efficacy of the designed control scheme, simulation results based on the actual parameters of quadrotor are provided. In addition, the comparison outcomes are provided to show proficiency and validity of the recommended technique compared with the existing method.

Adaptive inverse optimal backstepping control strategy for longitudinal vibration of high-speed elevator system based on fuzzy observer

To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller.

Optimal control for anti-lock braking system: Output feedback adaptive controller design and processor in the loop validation test

In this paper, the problem of controlling anti-lock braking system (ABS) was considered. Based on LuGre friction model, an output-feedback adaptive controller that enjoys good braking performances whatever the road conditions, was developed. Specifically, the controller tracks the optimal slip coefficient and, unlike previous work, the reference slip ratio is online estimated according to road conditions as well as longitudinal vehicle speed. The adaptive feature of the controller proves to be crucial for compensating the uncertainty on the changing road characteristics. The controller consists of: (i) a generator of the reference signal for the slip coefficient designed in the form of a neural network; (ii) a nonlinear observer for estimating the internal friction state; (iii) a backstepping adaptive control law, designed on the basis of a quarter-car model, that ensures tracking of the optimal slip value and providing estimates of the model unknown parameters. The controller stability properties are analyzed using Lyapunov stability tools. The theoretical stability results are confirmed by processor-in-the-loop (PIL) experiments in different road conditions. A comparative study, a robustness test, and a co-simulation involving CarSim and MATLAB/Simulink were made to highlight the much better performances, in terms of stability, tracking, robustness, and practicability of the new controller.

Prescribed Performance Adaptive Fuzzy Control for Affine Nonlinear Systems With State Constraints

This article considers the problem of prescribed performance control for a class of affine nonlinear systems with state constraints. Fuzzy logic systems (FLSs) are employed to cope with unknown nonlinear functions. In addition, an additive transformation and one-to-one mapping method are introduced to handle the control problem of nonlinear systems with full-state constraints. Then, based on adaptive backstepping control, we develop a new prescribed performance adaptive fuzzy control method, which not only makes the tracking error be constrained within the prescribed range but also ensures the other state variables do not violate the predefined constraints. The simulation example verify the feasibility of the control method.

Adaptive Predefined-Time Control for Lü Chaotic Systems via Backstepping Approach

This brief focuses on the adaptive predefined-time backstepping control for Lü chaotic systems with an unknown parameter. Different from the existing research on convergence-time control for chaotic systems, based on the backstepping technique, an improved predefined-time stable lemma for strict-feedback systems is proposed, which can achieve precise control about convergence time. Moreover, a predefined-time control scheme is designed using the proposed lemma to suppress the chaotic phenomenon and stabilize the Lü chaotic systems with predefined time. And, a novel adaptive updating law is designed to make the derivative of Lyapunov function satisfy the predefined-time stable form. The stability analysis proves that the signals in the Lü chaotic system are predefined-time stable and the convergence time can be specified by the user. Finally, a simulation example is provided to prove the effectiveness of the presented predefined-time control scheme.

IBLF-Based Adaptive Neural Control of State-Constrained Uncertain Stochastic Nonlinear Systems.

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

Adaptive Fuzzy Output-Feedback Decentralized Control for Fractional-Order Nonlinear Large-Scale Systems

This article studies the adaptive fuzzy output-feedback decentralized control problem for the fractional-order nonlinear large-scale systems. Since the considered strict-feedback systems contain unknown nonlinear functions and unmeasurable states, the fuzzy-logic systems (FLSs) are used to model unknown fractional-order subsystems, and a fuzzy decentralized state observer is established to obtain the unavailable states. By introducing the dynamic surface control (DSC) design technique into the adaptive backstepping control algorithm and constructing the fractional-order Lyapunov functions, an adaptive fuzzy output-feedback decentralized control scheme is developed. It is proved that the decentralized controlled system is stable and that the tracking and observer errors are able to converge to a neighborhood of zero. A simulation example is given to confirm the validity of the proposed control scheme.

Adaptive Backstepping Control of Uncertain Nonlinear Systems With Input and State Quantization

Although it is common in network control systems that the sensor and control signals are transmitted via a common communication network, no result is available in investigating the stabilization problem for uncertain nonlinear systems with both input and state quantization. The issue is solved in this article, by presenting an adaptive backstepping based control algorithm for the systems with sector bounded input/state quantizers. In addition to overcome the difficulty to proceed recursive design of virtual controls with quantized states, the relation between the input signal and error state need be well established to handle the effects due to input quantization. It is shown that all closed-loop signals are ensured uniformly bounded and all states will converge to a compact set. Experimental results are provided to validate the effectiveness of the proposed control scheme.

Lateral attitude control of solar-powered UAV with high aspect ratio

A solar-powered UAV usually has a high-aspect-ratio and flexible structural design. Its aerodynamic and mass characteristics are different from those of a conventional aircraft. This paper compares the differences in lateral aerodynamic data with those of Class I and Class III aircrafts. Based on the rigid-body dynamics theory, the effects of flexible wing deformation on the stability of the UAV are analyzed. Then, by combining the structural deformation, inertia variation and aerodynamic derivative, the solar-powered UAV's lateral stability is analyzed based on the root locus method. The variation of eigenvalues with wing deformation is also investigated. The rolling moment equation is combined with the kinematic equation to reveal the roll attitude limitation envelope constrained by the kinematic coupling and aileron effects. Taking into account the aerodynamic characteristics of the solar-powered UAV, its wing deformation and roll attitude limitation problem, this paper proposes an adaptive back-stepping control method with strong robustness to achieve the accurate control of the roll attitude of the solar-powered UAV.

Saturated Adaptive-Law-Based Backstepping and Its Applications to a Quadrotor Hover

This article presents a saturated adaptive-law-based backstepping control method for a class of uncertain nonlinear systems with external dynamic disturbances. In this approach, a novel adaptive backstepping control method with a new command filter is primarily proposed to design the feedback controllers. In order to address the system unknown nonlinearities caused by external dynamic disturbances, a method named “saturated adaptive law approach” is used to estimate the system unknown nonlinearities online. Meanwhile, a filter called “dual command filter” is applied to estimate the derivative of certain signal such that the saturated adaptive law approach can be well implemented. With the help of Lyapunov stability criteria, it is proved that the target signal can be tracked by the output of the system with small error. Finally, our control method is applied to a quadrotor hover system, and two sets of comparison experiments are given to show the effectiveness of the proposed control method.

MPPT Performance and Power Quality Improvement by Using Fractional-Order Adaptive Backstepping Control of a DFIG-Based Wind Turbine with Disturbance and Uncertain Parameters

MPPT Performance and Power Quality Improvement by Using Fractional-Order Adaptive Backstepping Control of a DFIG-Based Wind Turbine with Disturbance and Uncertain Parameters

Adaptive neural network asymptotic path-following control of underactuated ships with stochastic sea loads

This paper investigates the high-precision path following of underactuated ships suffering from stochastic sea loads, where a novel adaptive neural network asymptotic control framework is fabricated. Based on the nonlinear 3-degree-of-freedom (3-DOF) motion model of the underactuated ship, the stochastic ship motion model is established by involving both unknown deterministic and stochastic disturbances, which is chosen as the control objective. To transform path following to tracking control, a novel virtual ship guidance approach is fabricated with generating smooth reference signals. Through the control scheme, the radial-basis-function neural networks (RBF NNs) are employed to approximate the total marine uncertainties. By introducing integral-bounded functions to control laws and adaptive laws, the asymptotic convergence of positional tracking errors is guaranteed with the aid of adaptive backstepping control. To ensure the computational simplicity, the adaptive laws are fabricated with the minimum learning parameters (MLPs). Via the important inequality of the neural basis function, the “algebraic loop” problem is successfully solved, such that the control logicality is guaranteed. Finally, the numerical experiments validate the high-precision tracking performance of the proposed scheme.

Motion characteristics and gait planning methods analysis for the walkable lunar lander to optimize the performances of terrain adaptability

Lunar environmental adaptability and gait control are significant for developing a walkable lunar lander (WLL). However, gait planning for the WLL is challenging due to the optimization process required for the stable margin sequence. To overcome this concern, this study develops a new Center of Gravity (COG) trajectory planning algorithm appropriate for a WLL that will enhance walking performance. Specifically, our method designs an adaptive back-stepping controller (ABSC) based on the established kinematic model to compensate for the influence of parameter uncertainties on the single-leg motion system. Compared to the classic PID control, our method's motion trajectory accuracy on the joint drive position is improved by 3.2 times. Additionally, various experiments on the prototype device verify the foot's motion trajectory. Furthermore, a new COG trajectory planning algorithm is proposed that combines the Jacobian COG and the centroid of a support polygon, including a foot contact constraint. This strategy effectively balances optimization and search operations, improving the lander's passing ability and stability in complex terrains. Moreover, this work considers the longitudinal stability margin (LSM) method and minimum stability margin of the lander as a sequential optimization problem. Hence, the hierarchical control architecture is established to compensate for the mission and environment changes, improving computational efficiency. Finally, the developed method is applied to the simulation prototype to verify its performance in various environments. The experimental results demonstrate that the proposed method allows the WLL to move in various environments and improves its stability in simulation experiments. At the same time, compared with the foot endpoint trajectory gait control method, our method can improve the walking efficiency by 8.56% and 6.58%, respectively.

Adaptive Neural Backstepping Control Approach for Tracker Design of Wheelchair Upper-Limb Exoskeleton Robot System

In this study, the desired tracking control of the upper-limb exoskeleton robot system under model uncertainty and external disturbance is investigated. For this reason, an adaptive neural network using a backstepping control strategy is designed. The difference between the actual values of the upper-limb exoskeleton robot system and the desired values is considered as the tracking error. Afterward, the auxiliary variable based on the tracking error is defined and the virtual control input is obtained. Then, by using the backstepping control procedure and Lyapunov stability concept, the convergence of the position tracking error is proved. Moreover, for the compensation of the model uncertainty and the external disturbance that exist in the upper-limb exoskeleton robot system, an adaptive neural-network procedure is adopted. Furthermore, for the estimation of the unknown coefficient related to the parameters of the neural network, the adaptive law is designed. Finally, the simulation results are prepared for demonstration of the effectiveness of the suggested method on the upper-limb exoskeleton robot system.