Integrator Backstepping Method Research Articles

Adaptive fixed-time stabilization for high-order uncertain nonlinear systems with unknown measurement sensitivities

This paper investigates the adaptive fixed-time stabilization problem for a class of uncertain high-order nonlinear systems with unknown measurement sensitivities and unknown control magnitude. Compared to existing practical fixed-time control approaches, our control strategy is capable of driving all states of uncertain high-order systems to the origin within a fixed time, rather than just ensuring their boundedness. Additionally, this study relaxes the restrictions on the nonlinear functions of the system, while overcoming challenges such as unknown control magnitude and unknown measurement sensitivity without prior boundaries. To achieve the control objectives, our control strategy consists of two main steps. Firstly, we divide the initial value of the high-order system into two cases, and construct adaptive controllers separately for each case by adding a power integral technique and backstepping method. Subsequently, the reliance of the stability time of the closed-loop high-order system on the initial value is eliminated by designing an appropriate controller switching mechanism. Finally, we provide a simulation example to validate the effectiveness of our control strategy.

Robust Control Design of Under-Actuated Nonlinear Systems: Quadcopter Unmanned Aerial Vehicles with Integral Backstepping Integral Terminal Fractional-Order Sliding Mode

In this paper, a novel robust finite-time control scheme is specifically designed for a class of under-actuated nonlinear systems. The proposed scheme integrates a reaching phase-free integral backstepping method with an integral terminal fractional-order sliding mode to ensure finite-time stability at the desired equilibria. The core of the algorithm is built around proportional-integral-based nonlinear virtual control laws that are systematically designed in a backstepping manner. A fractional-order integral terminal sliding mode is introduced in the final step of the design, enhancing the robustness of the overall system. The robust nonlinear control algorithm developed in this study guarantees zero steady-state errors at each step while also providing robustness against matched uncertain disturbances. The stability of the control scheme at each step is rigorously proven using the Lyapunov candidate function to ensure theoretical soundness. To demonstrate the practicality and benefits of the proposed control strategy, simulation results are provided for two systems: a cart–pendulum system and quadcopter UAV. These simulations illustrate the effectiveness of the proposed control scheme in real-world scenarios. Additionally, the results are compared with those from the standard literature to highlight the superior performance and appealing nature of the proposed approach for underactuated nonlinear systems. This comparison underscores the advantages of the proposed method in terms of achieving robust and stable control in complex systems.

Nonlinear control of a hybrid pneumo‐hydraulic mock circuit of the cardiovascular system

AbstractHybrid cardiovascular mock circuits (HMC), designed for dynamic testing of Ventricular Assist Devices (VAD), offer physiologic accuracy by sequestering model complexity in silico and ease of construction by reducing number of model elements in vitro. Despite superior response time and precision, pneumatic actuation is avoided in HMCs due to nonlinear dynamics and noise. We tested the hypothesis that a HMC consisting of a variable elastance‐driven numerical cardiovascular circuit (CVS) coupled to a pneumo‐hydraulic physical circuit can be controlled without linearizing system dynamics. Reference left ventricular and aortic pressures were generated in silico in a seventh‐order electrical analogue of the CVS and transmitted via an electro‐hydraulic interface to the physical circuit. There, they were tracked in in vitro preload and afterload pneumo‐hydraulic reservoirs, respectively. The nonlinear pneumatic dynamics in the reservoirs was controlled using the Lyapunov stability criterion. A centrifugal pump, the speed (i.e., flow) of which was adjusted manually or using PID control, was interposed between the reservoirs and mimicked the VAD under evaluation. The flow of a recirculating gear pump was controlled by an integral backstepping method to equalize reservoir fluid volumes by rejecting pressure and flow disturbances. Sensor noise was reduced with discrete‐time Kalman filtering. Our results showed that normal, failing, and assisted cardiovascular physiologies simulated in silico were commensurate with clinical data obtained from subjects with similar pathologies. The numerical pressure references were tracked with high accuracy at the physical VAD terminals. Reservoir volumes remained stable at various combinations of heart rate, pressure, and VAD flow for prolonged durations with negligible steady‐state error. The HMC described here offers a stable performance testing platform for VAD prototypes.

Robust and Adaptive Stabilization Controllers of State-Constrained Nonholonomic Chained Systems: A Discontinuous Approach

In this paper, two systematic control design strategies are proposed for strict-feedback nonholonomic systems with full-state constraints to solve stabilization and adaptive stabilization problems. The stabilization schemes involve the introduction of state scaling, the barrier Lyapunov function (BLF), the integrator backstepping method, and the tuning function approach. In addition, a discontinuous switching control strategy is proposed to achieve the control goal if the first system state’s initial state is confined to zero. In both stabilization and adaptive stabilization control, the system states can be regulated at the origin, and meanwhile, the full-state constraints are realized. Finally, it is shown that the simulation results are consistent with the theory analysis results, which further demonstrates the effectiveness of the proposed control schemes.

Integral backstepping-ILC controller for suppressing circulating currents in parallel-connected photovoltaic inverters

In big solar plants where the use of a single inverter is neither economically or technically feasible, parallel linked photovoltaic inverters are necessary. For parallel-connected operation, the most significant issue is that even a slight variation in the output voltages of particular inverters results flow of circulating currents. A high level of circulation current causes inverter power losses to increase, which lowers the system's overall performance by decreasing its efficiency. In this paper, a novel simple and effective controller for parallel-connected inverters is proposed to ovoid the circulating currents among the inverters. Convergence efficiency and low computational cost of the suggested controller based on integral backstepping method are the primary motivations of this work. The simulation and experimental findings show that the suggested control system achieves the required power quality and reduces circulation current under various loading situations.

Adaptive Control of Rigid Multi-Degree-of-Freedom Nonlinear Mechanical Plants

The paper considers the problems of control synthesis of a rigid multi-degree-of-freedom (multi-DOF) nonlinear mechanical plant under conditions of parametric and functional uncertainty. Developed and investigated adaptive robust control systems are synthesized on the basis of three approaches: based on the method of computed torque, the method of majorizing functions, and also the method of integrator backstepping with modified adaptation algorithms with parametric projection. The results of a comparative study by modeling the designed adaptive systems for the nonlinear mathematical model of a four-degree manipulation arm described by the Lagrange equations are shown.

Robust Control of a Multi-Degree-of-Freedom Electromechanical Plant with Adaptive Disturbance Compensation

This paper considers the problem of control of a multi-degree-of-freedom (multi-DOF) nonlinear electromechanical plant with elastic properties and an external unknown disturbance. The unknown disturbance is assumed to be deterministic and is represented as an output of a linear autonomous model with unknown constant parameters. To solve the problem of adaptive disturbance compensation, an adaptive observer of an unknown deterministic disturbance is applied. A nonlinear robust control of a multi-DOF elastic electromechanical plant, synthesized on the basis of the integrator backstepping method and combined with adaptive robust disturbance compensation, is also being developed. The simulation of the designed nonlinear control of a multi-DOF plant with adaptive robust compensation of disturbances is performed using the MATLAB / Simulink software.

Application of Wireless Network Control to Course-Keeping for Ships

In view of the network security and reliability of the steering control system, redundant wired control networks are adopted in some ships. To solve the problems of redundant wired networks in ships, the paper designs a wireless network as a redundant network for a ship's control system. The paper applies wireless network control to course-keeping for ships in order to validate the effectiveness of the proposed ship wireless communication network. However, there are some problems, such as time delay and packet loss, in the wireless network control system (WiNCS). In view of the above problems, the codesign of a communication protocol and control algorithm is studied in the paper. From the aspect of communication, the design is based on the concurrent and disjoint multipath routing ZigBee network, which can ensure the effective application of the control algorithm. From the aspect of control, the design of the ship course-keeping controller combines an improved gray model with the nonlinear robust controller based on the nonlinear decoration and integrator backstepping method, which can compensate for time delay and packet loss. In this paper, a simulation platform is designed to study the application of a wireless network control to course-keeping for ships. The experimental results also prove that the scheme is feasible and effective on a simulation platform. It is a beneficial attempt to apply the WiNCS to course-keeping for ships.

Improvement of integrator backstepping control for ships with concise robust control and nonlinear decoration

Course-keeping control through normal integrator backstepping method has defects of introducing many adjustment parameters and not considering the energy cost of actuator. In order to enhance the performance of integrator backstepping controller, a control law formed by closed-loop gain-shaping algorithm is adopted to replace the linear terms in the original control law. The energy cost is reduced by nonlinear decoration of sine function to the controller output, and the steering interval is lengthened according to the analyzation of full-scale sea trail data from training vessel Yukun. To decrease overshoot, the desired course is filtered by a first-order inertial component. Then a performance index is proposed to verify the performance of each control strategy combination. Simulation results show that the proposed controller has good robustness to the perturbation of steering mechanisms and ship model in rough sea states. At the same time, mean rudder angle is decreased by 17.3%, so energy consumption is reduced. The algorithm proposed in this paper has good theoretical analysis, satisfactory robustness with less parameters, reasonable steering frequency and remarkable energy saving effect.

Inverse optimal control for unmanned aerial helicopters with disturbances

SummaryThis paper proposes an optimal control method of an unmanned aerial helicopter (UAH) with unknown disturbances. Solving the Hamilton‐Jacobi‐Bellman (HJB) equation is considered as the common approach to design an optimal controller under a meaningful cost function when facing the nonlinear optimal control problem. However, the HJB equation is hard to solve even for a simple problem. The inverse optimal control method that avoids the difficulties of solving the HJB equation has been adopted. In this inverse optimal control approach, a stabilizing optimal control law and a particular cost function that are obtained by a control Lyapunov function are required. An integrator backstepping method is used in designing the optimal control law of the UAH. Furthermore, a disturbance‐observer–based control (DOBC) approach has been adopted in the optimal control law for dealing with the unknown disturbances of the UAH system. Simulation results have been given to certify the stability of the nonlinear UAH system and the validity of this developed control method.

Underactuated Stratospheric Airship Trajectory Control Using an Adaptive Integral Backstepping Approach

This paper deals with trajectory tracking control for an underactuated stratospheric airship in the presence of model uncertainties and external disturbances. An adaptive integral backstepping trajectory control is designed from the underactuated airship nonlinear dynamics model. The proposed controller has a two-level structure. A low-level controller based on nonlinear adaptive integral backstepping method stabilizes the attitude and velocity of the airship, whereas a high-level controller performs guidance and trajectory tracking task. Two underactuated cases of zero lateral control force and zero roll moment input are studied. Meanwhile a control allocation component based on active set with weight least square algorithm is put into the low-level controller, to find the optimal control surfaces and thrust inputs under constraints of actuator saturation. By using Lyapunov theory the closed-loop trajectory control system is proven to be globally asymptotically stable. Finally, simulation results show that the proposed adaptive integral backstepping controller can follow the reference even in the presence of parametric uncertainties and external disturbances and time delay inputs.

Cooperative control of multiple stochastic high-order nonlinear systems

Distributed cooperative control of multiple stochastic high-order nonlinear systems has not been addressed in literature. This paper presents an approach to design of distributed cooperative controllers for multiple stochastic high-order nonlinear systems under directed leader–followers type network topology via the so-called distributed integrator backstepping method. By using the algebraic graph theory and stochastic analysis method, it is shown that the output tracking errors between the followers and the leader can be tuned arbitrarily small while all the states of the closed-loop system remain bounded in probability. Finally, the effectiveness of the proposed control approach is illustrated on a stochastic underactuated mechanical system.

Quadrotor Obstacle Avoidance Based on Integral Backstepping

This paper addressed obstacle avoidance problem of a quadrotor in outdoor environment. Path planning was finished by employing classical Dijkstra algorithm and the controller of the quadrotor adopted integral backstepping method. In order to get a smooth trajectory with time optimal and acceleration constraints properties, quantic polynomials were utilized to generate trajectory file. The scheme is particularly practical and useful because of its small computation burden and feasibility. Simulations have been done to verify the performance of the whole system. As a result, the quadrotor successfully tracked the path without any collision with obstacles except that there are some small error in the final part of position tracking performance (±1m) and some small delay in the attitude tracking about 0.3 ms. In conclusion, the proposed method showed acceptable performance for quadrotor obstacle avoidance.

Feedback control for spacecraft reorientation under attitude constraints via convex potentials

A novel guidance algorithm is proposed for the attitude reorientation of a rigid body spacecraft in the presence of multiple types of attitude-constrained zones. In this direction, two types of attitude-constrained zones are first developed using unit quaternions, namely, the attitude-forbidden and -mandatory zones. The paper then utilizes a convex parameterization of forbidden and mandatory zones for constructing a strictly convex logarithmic barrier potential that is subsequently used for the synthesis of feedback attitude control laws while the inevitable unwinding phenomenon is given a simple and effective remedy. Model-independent and model-dependent control laws are then implemented by using the Lyapunov direct method and the modified integrator backstepping method. The paper concludes with a set of simulation results to evaluate the effectiveness and demonstrate the viability of the proposed methodology.

Diagonally dominant backstepping autopilot for aircraft with unknown actuator failures and severe winds

AbstractA novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.

Modeling and Nonlinear Heading Control of Sailing Yachts

This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also includes two possible steering mechanisms: a conventional rudder and a simple moving mass system. Starting from this model, we then design, for both steering mechanisms, a nonlinear heading controller using the integrator backstepping method, which exponentially stabilizes the heading/yaw dynamics. By computing the equilibrium points of the system, the course is related to the heading angle, and course control is also achieved. A few simulation results are presented to illustrate the behavior of our control designs.

Lane Changing Trajectory Planning and Tracking Controller Design for Intelligent Vehicle Running on Curved Road

To enhance the active safety and realize the autonomy of intelligent vehicle on highway curved road, a lane changing trajectory is planned and tracked for lane changing maneuver on curved road. The kinematics model of the intelligent vehicle with nonholonomic constraint feature and the tracking error model are established firstly. The longitudinal and lateral coupling and the difference of curvature radius between the outside and inside lane are taken into account, which is helpful to enhance the authenticity of desired lane changing trajectory on curved road. Then the trajectory tracking controller of closed-loop control structure is derived using integral backstepping method to construct a new virtual variable. The Lyapunov theory is applied to analyze the stability of the proposed tracking controller. Simulation results demonstrate that this controller can guarantee the convergences of both the relative position tracking errors and the position tracking synchronization.

Tracking a process of scheduled change in the angle of attack for longitudinal dynamics of an air-to-air missile with the use of an integrator back-stepping method

Tracking a process of scheduled change in the angle of attack for longitudinal dynamics of an air-to-air missile with the use of an integrator back-stepping method

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided. </para>

Adaptive Stabilization Control of a Class of Large-scale Stochastic Nonlinear Systems with Time-delays and Unknown Virtual Control Coefficients

In this paper,the adaptive stabilization problem is investigated for a class of large-scale stochastic time-delay nonlinear systems with unknown virtual control coefficients and unknown noise covariances.First,corresponding to the unknown virtual control coefficients and unknown noise covariances,some parameters to be estimated are properly chosen. Then,in view of the effect of the time-varying delay on the stability of the closed-loop system,an suitable Lyapunov- Krasovskii functional is constructed,based on which and the well-known integrator backstepping method,a memoryless state-feedback control law is systematically designed.Under some mild conditions,it is shown that the equilibrium of the closed-loop system is globally stable in probability,and all the signals of the closed-loop system except for parameter estimates converge to zero almost surely.A simulation example is given to illustrate the effectiveness of the proposed approach.