Backstepping Control Method Research Articles

Research on Hover Control of AUV Uncertain Stochastic Nonlinear System Based on Constructive Backstepping Control Strategy

The paper is concerned with station keeping control problem via backstepping for an autonomous underwater vehicle (AUV) systems with nonlinear continuous function. This paper is the first time to using backstepping control method for stochastic nonlinear systems. Under nonlinear growth conditions, when the AUV motion affected the driving force, resistance of ocean and the force generated by current the difficulty arising from the underwater robot system output feedback makes the station keeping problems challenging and forward-looking. There exist two problems to research the fast response time and good station keeping, respectively. There a new control method is proposed for the first time to construct a backstepping stabilizing controller. In this paper, a concept of randomness to study the station keeping control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general function growth conditions. In order to deal with the station error of system converges to arbitrarily small domains. Under all the states of the system meet boundedness, a coordinate transformation is proposed. A useful technical theorem is proposed in the stability analysis to show that combined with the backstepping method to cleverly construct a set of Lyapunov functions, and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Finally, through the ocean library in the Simulation X simulation software and the Hardware-in-the-loop simulation, the controller design results are imported into the AUV actuator model to verify the effectiveness of the controller design.

Pareto optimum design of an adaptive robust backstepping controller for an unmanned aerial vehicle

AbstractThis research develops an adaptive robust backstepping (AR‐backstepping) controller for stabilization of an unmanned aerial vehicle (UAV) having strong coupling and highly nonlinear dynamics. At first, the backstepping control method as the basic stabilizer is utilized to determine the control efforts of the considered UAV. Next, an adaptive‐robust mechanism subject to gradient decent methods and sliding surfaces is implemented to regulate the control gains. In fact, this mechanism determines the speed of changes of the gain values of the backstepping controller to make better responses in the presence of disturbances and uncertainties. Then, the optimum values of the design parameters related to the adaptive‐robust mechanism are selected by using a multi‐objective ant‐lion optimization (MOALO) algorithm to simultaneously minimize the total error and control efforts. Finally, the results for a UAV developed in the Sirjan University of Technology, Sirjan, Iran, are given to confirm the effectiveness, robustness, and advantages of the designed AR‐backstepping controller.

A Novel Guidance Law for Intercepting a Highly Maneuvering Target

Given the resolution of the guidance for intercepting highly maneuvering targets, a novel finite-time convergent guidance law is proposed, which takes the following conditions into consideration, including the impact angle constraint, the guidance command input saturation constraint, and the autopilot second-order dynamic characteristics. Firstly, based on the nonsingular terminal sliding mode control theory, a finite-time convergent nonsingular terminal sliding mode surface is designed. On the back of the backstepping control method, the virtual control law appears. A nonlinear first-order filter is constructed so as to address the “differential expansion” problem in traditional backstepping control. By designing an adaptive auxiliary system, the guidance command input saturation problem is dealt with. The RBF neural network disturbance observer is used for estimating the unknown boundary external disturbances of the guidance system caused by the target acceleration. The parameters of the RBF neural network are adjusted online in real time, for the purpose of improving the estimation accuracy of the RBF neural network disturbance observer and accelerating its convergence characteristics. At the same time, an adaptive law is designed to compensate the estimation error of the RBF neural network disturbance observer. Then, the Lyapunov stability theory is used to prove the finite-time stability of the guidance law. Finally, numerical simulations verify the effectiveness and superiority of the proposed guidance law.

Position Output Adaptive Backstepping Control of Electro-Hydraulic Servo Closed-Pump Control System

A nonlinear adaptive backstepping control method was proposed to address the system parameter uncertainty problem in the position control process of an electro-hydraulic servo closed-pump control system. This control strategy fully considers the parameter uncertainty of the nonlinear system and establishes the adaptive rate of the uncertain parameter to adjust the parameter disturbance online in real time, thereby improving the accuracy and robustness of the control system. A pump control system experiment platform was used to verify the feasibility of the controller. The experimental results showed that the proposed control strategy provided a good control effect. The pump control system can be controlled with high precision, with a steady-state control accuracy of ±0.02 mm, which serves as a good foundation for the engineering application and promotion of the pump control system.

Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper, an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system. The considered system contains unknown nonlinear function and actuator saturation. Fuzzy logic systems (FLSs) and a smooth function are used to approximate the unknown nonlinearities and the actuator saturation, respectively. By combining the command-filter technique with the backstepping design algorithm, a novel adaptive fuzzy tracking backstepping control method is developed. It is proved that the adaptive fuzzy control scheme can guarantee that all the variables in the closed-loop system are bounded, and the system output can track the given reference signal as close as possible. Simulation results are provided to illustrate the effectiveness of the proposed approach.

Adaptive backstepping control design for MEMS gyroscope based on function approximation techniques with input saturation and output constraints

An efficient adaptive backstepping control method is presented in the current study for controlling the micro-electro-mechanical system (MEMS) triaxial gyroscope. In this approach, practical considerations, including output constraints and input saturation, are taken into account. A Barrier Lyapunov Function (BLF) is used so that non-transgression of the constraints is ensured. In the suggested control method, for approximating the lumped uncertainties and addressing the problem of explosion of complexity, Hermite polynomials are used as a simple but effective function approximation approach as a universal approximator. Therefore, the resulting control approach is much simpler with minimal learning parameters. The Lyapunov stability theory is used so that the semiglobally uniformly ultimately boundedness of the closed-loop signals with proper tracking error convergence is guaranteed. According to the results of the comparative simulation, the superiority of this approach is confirmed.

Disturbance observer-based backstepping formation control of multiple quadrotors with asymmetric output error constraints

This paper presents a distributed formation tracking control strategy which acts on multiple quadrotor unmanned aerial vehicles (QUAVs) formation control under external disturbance and asymmetric output error constraints. An asymmetric barrier Lyapunov function (BLF) is applied to ensure the constraint of output error. Based on graph theory and backstepping control method, a distributed formation controller is designed to achieve the formation and maintenance of formations, where external disturbance is handled by disturbance observer (DO). In the framework of Lyapunov theory, the bounded stability of the closed-loop system is proved, and the output error is remained within the constraint range. The superiority and effectiveness of the designed control strategy is verified by the compared simulation.

Concise leader-follower formation control of underactuated unmanned surface vehicle with output error constraints

In this paper, a concise leader-follower formation control approach is presented for a group of underactuated unmanned surface vehicle with dynamic system uncertainties and external environment disturbances, where the output errors are required to be within constraints. To settle the output error constraints, a standard barrier Lyapunov function (BLF) is incorporated into the backstepping control method. Furthermore, the “differential explosion” problem of virtual control laws is avoided by introducing the dynamic surface control. To estimate the unknown dynamic terms, an adaptive neural network is designed and a nonlinear disturbance observer is adopted to compensate for the approximation errors of neural network and ocean environment disturbances. Under the constraint of output error, the presented controller based on standard BLF has simpler structure and better control performance than depended on tan-type BLF. The presented controller can ensure that the formation errors converge to a small range around zero, while the output error constraint requirements are met. All signals in the closed-loop system are bounded, and the numerical simulation further shows the effectiveness of the presented control scheme.

Time-varying formation control with smooth switching communication

This paper studies the communication smooth switching problem of time-varying formation control. When the formation system performs topology switching, sudden changes in communication will cause communication failure and affect formation control. To avoid this adverse impact, we introduce a smooth transition function of communication topology. At the same time, for the formation system with unknown nonlinear dynamics, an adaptive backstepping controller combining the backstepping control method and the fuzzy logic system is designed. Then, based on Lyapunov stability theory, we prove the stability of the designed controller. The results of the simulation experiments can verify the effectiveness of the designed controller.

Actor Critic Neural Network-Based Adaptive Control for MEMS Gyroscopes Suffering from Multiresource Disturbances

In this paper, an actor critic neural network-based adaptive control scheme for micro-electro-mechanical system (MEMS) gyroscopes suffering from multiresource disturbances is proposed. Faced with multiresource interferences consisting of parametric uncertainties, strong couplings between axes, Coriolis forces, and variable external disturbances, an actor critic neural network is introduced, where the actor neural network is employed to estimate the packaged disturbances and the critic neural network is utilized to supervise the system performance. Hence, strong robustness against uncertainties and better tracking properties can be derived for MEMS gyroscopes. Aiming at handling the nonlinearities inherent in gyroscopes without analytically differentiating the virtual control signals, dynamic surface control (DSC) rather than backstepping control method is employed to divide the 2nd order system into two 1st order systems and design the actual control policy. Moreover, theoretical analyses along with simulation experiments are conducted with a view to validate the effectiveness of the proposed control approach.

Adaptive finite time attitude tracking control of a rigid spacecraft considering input magnitude and rate saturations

This article investigates the attitude tracking control problem of a rigid spacecraft under the modeling inaccuracy, environmental disturbance, and input magnitude and rate saturations. A robust controller is proposed based on several nonlinear control methods, including the integral terminal sliding mode control, adaptive control, backstepping control, auxiliary system, and nonlinear observer methods. Within the control framework, a new integral terminal sliding mode surface (ITSMS) is first designed which integrates the fast nonsingular terminal sliding mode surface (FNTSMS) with a first-order filter to achieve the finite time stability without the input singularity problem. And adaptive laws are employed to compensate for the modeling inaccuracy and environmental disturbance with no prior knowledge. To satisfy the input magnitude and rate saturation constraints, a dynamic model in the form of a first-order filter is built up to restrict the dynamics of the actuators, which is then associated with the auxiliary system. Meanwhile, a nonlinear observer is used to avoid calculating the derivative of the expected virtual control signal. Semi-globally uniformly ultimate bounded stability is proved for the closed-loop system, and the tracking errors can converge to small regions around the expected equilibrium in finite time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed controller.

Command filtered adaptive fuzzy control of fractional-order nonlinear systems

The standard backstepping control scheme has inherently computational complexity explosion problem, and consequently, becomes prohibitive as the order increases. This paper contributes to command filtered adaptive fuzzy control (AFC) of fractional-order nonlinear systems (FNSs) by using fractional backstepping control method. To approximate the virtual input, a fractional-order command filter (FCF) is proposed. Filtering approximation errors that affect the performance of the controller during the filtering process are solved by an error compensation mechanism (ECM). The simulation results verify the validity of the theoretical results.

Event-triggered neural adaptive backstepping control of the K chaotic PMSGs coupled system

This paper presents an event-triggered neural adaptative backstepping control method for the K chaotic permanent magnet synchronous generators (PMSGs) coupled system. The actual wind farm is usually a complex coupled system, in which there are K identical generators operating simultaneously and forming a coupled electromagnetic field through the transmission bus. By using a series of capacitors and resistors to concatenate multiple identical PMSGs forming a coupled network, we firstly establish its dynamic model based on Faraday's law of electromagnetic induction. Then we conduct its dynamic analysis and find this coupled system can generate complex nonlinear dynamics like chaos oscillation, which, if not being compensated properly, could lead to severe deterioration of system performance. Here we propose an adaptive backstepping scheme by integrating the simplified interval type-2 fuzzy neural network (SIT2FNN), Nussbaum type function, improved saturation function reaching law, cosine barrier function, event-triggered strategy and tracking differentiator (TD). In the setting, the SIT2FNN is utilized to estimate unknown terms of the system and the improved reaching law is used to improve the stability of the controller along with the Nussbaum type function to approximate unknown parameters. Meanwhile, the event-triggered strategy is exploited to save computation and communication resources along with the second-order TD to avoid the term explosion associated with backstepping. The stability of the proposed scheme is proved by the Lyapunov function. Finally, the effectiveness of our scheme is verified by simulation results.

Optimal game theoretic solution of the pursuit‐evasion intercept problem using on‐policy reinforcement learning

AbstractThis article presents a rigorous formulation for the pursuit‐evasion (PE) game when velocity constraints are imposed on agents of the game or players. The game is formulated as an infinite‐horizon problem using a non‐quadratic functional, then sufficient conditions are derived to prove capture in a finite‐time. A novel tracking Hamilton–Jacobi–Isaacs (HJI) equation associated with the non‐quadratic value function is employed, which is solved for Nash equilibrium velocity policies for each agent with arbitrary nonlinear dynamics. In contrast to the existing remedies for proof of capture in PE game, the proposed method does not assume players are moving with their maximum velocities and considers the velocity constraints a priori. Attaining the optimal actions requires the solution of HJI equations online and in real‐time. We overcome this problem by presenting the on‐policy iteration of integral reinforcement learning (IRL) technique. The persistence of excitation for IRL to work is satisfied inherently until capture occurs, at which time the game ends. Furthermore, a nonlinear backstepping control method is proposed to track desired optimal velocity trajectories for players with generalized Newtonian dynamics. Simulation results are provided to show the validity of the proposed methods.

Synchronous Generator Rectification System Based on Double Closed-Loop Control of Backstepping and Sliding Mode Variable Structure

Low-voltage and high-current direct current (DC) power supplies are essential for aerospace and shipping. However, its robustness and dynamic response need to be optimized further on some special occasions. In this paper, a novel rectification system platform is built with the low-voltage and high-current permanent magnet synchronous generator (PMSG), in which the DC voltage double closed-loop control system is constructed with the backstepping control method and the sliding mode variable structure (SMVS). In the active component control structure of this system, reasonable virtual control variables are set to obtain the overall structural control variable which satisfied the stability requirements of Lyapunov stability theory. Thus, the fast-tracking and the global adjustment of the system are realized and the robustness is improved. Since the reactive component control structure is simple and no subsystem has to be constructed, the SMVS is used to stabilize the system power factor. By building a simulation model and experimental platform of the 5 V/300 A rectification module based on the PMSG, it is verified that the power factor of the system can reach about 98.5%. When the load mutation occurs, the DC output achieves stability again within 0.02 s, and the system fluctuation rate does not exceed 2%.

Nonlinear Differential Braking Control for Collision Avoidance During Lane Change

In this paper, a nonlinear differential braking control method is developed to avoid collision during lane change under driver torque. The lateral dynamics consist of lateral offset error and yaw error dynamics and can be interpreted as a semi-strict feedback form. In the differential braking control problem under the driver torque, a matching condition does not satisfy, and the system is not in the form of, the strict feedback form. Thus, a general backstepping control method cannot be applied. To overcome this problem, the proposed method is designed via the combination of the sliding mode control and backstepping. Two sliding surfaces are designed for differential braking control. One of the surfaces is designed considering the lateral offset error, and the other sliding surface is designed using the combination of the yaw and yaw rate errors as the virtual input of the lateral offset error dynamics. A brake steer force input is developed to regulate the two sliding surfaces using a backstepping procedure under the driver torque. Integral action and a super twisting algorithm are used in the lateral controller to ensure the robustness of the system. The proposed method, which is designed via the combination of the sliding mode control and backstepping, can improve the lateral control performance using differential braking. The proposed method is validated through simulations.

Optimal Adaptive Control and Backstepping Control Method with Sliding Mode Differentiator

In order to improve the success rate of space debris object capture, how to increase the resistance to interference in the space robot arm has become an issue of interest. In addition, since the space operation time is always limited, finite-time control has become another urgent requirement needed to be addressed. Considering external disturbances, two control methods are proposed in this paper to solve the control problem of space robot arm. Firstly, a linear sliding mode control method is proposed considering the model uncertainties and external disturbances. The robot arm can track the desired trajectory, while a trade-off between optimality and robustness of the solved system can be achieved. Then, in order to reduce conservativeness and relax restrictions on external disturbances, a novel backstepping control method based on a finite-time integral sliding mode disturbance observer is developed, which compensates for the effects of both model uncertainties and infinite energy-based disturbance inputs. Finally, simulation examples are given to illustrate the effectiveness of the proposed control method.

Backstepping Sliding-Mode Control of Piezoelectric Single-Piston Pump-Controlled Actuator

A piston piezoelectric (PZT) pump has many advantages for the use of light actuators. How to deal with the contradiction between the intermittent oil supplying and position control precision is essential when designing the controller. In order to accurately control the output of the actuator, a backstepping sliding-mode control method based on the Lyapunov function is introduced, and the controller is designed on the basis of establishing the mathematical model of the system. The simulation results show that, compared with fuzzy PID and ordinary sliding-mode control, backstepping sliding-mode control has a stronger anti-jamming ability and tracking performance, and improves the control accuracy and stability of the piezoelectric pump-controlled actuator system.

Unknown Dynamics Estimator-Based Output-Feedback Control for Nonlinear Pure-Feedback Systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method.

Synchronization of Rossler chaotic systems via hybrid adaptive backstepping/sliding mode control

In this paper, a hybrid control approach combining adaptive backstepping and fuzzy sliding mode control is proposed for the synchronization of two Rossler chaotic systems. The proposed approach provides fast, high accuracy chaos synchronization in presence of unknown system parameters and external disturbances. The adaptive backstepping control law is developed to stabilize the synchronization error dynamics arising from the mismatch between the drive and response systems. Both unknown system parameters and unknown external disturbance are estimated by the adaptive backstepping control approach in a way that the overall system with the controller becomes stable. As a result, the requirement to have a priori knowledge about the unknown parameters, e.g., disturbance bounds, is nullified. The fuzzy sliding mode controller is designed to accompany the adaptive backstepping to confine the synchronization error and enhance the synchronization speed between the two chaotic systems. Performance of the proposed approach is investigated for a numerical example and compared against commonly used chaos synchronization techniques including optimal control, active control, and adaptive backstepping control method. Simulation results indicate the superior performance of the hybrid control method over state-of-the-art for the synchronization of Rossler chaotic systems.