Backstepping-based Control Research Articles

Unit prediction horizon [formula omitted] based model predictive control for the fuel cell based plug-in hybrid electric vehicle with rule-based energy management system

Plug-in hybrid electric vehicles (PHEVs) provide a good alternative in achieving better performance and in the reduction of harmful gas emissions. The hybrid energy storage system (HESS) and the integrated charging unit constitute the PHEV under consideration. To meet the load demands, the proposed HESS is a coupled system comprising a fuel cell, high energy density battery, and high-power density super-capacitor. On-board charging involves the utilization of a DC–DC buck converter and an uncontrolled rectifier and two buck-boost converters are utilized to facilitate a smooth transfer of energy. A rule-based supervisory controller has been implemented for different load conditions which takes into account the state of charge of energy sources and also the total power inflow of the power sources. A model predictive control (MPC) technique is implemented to ensure that PHEVs function smoothly in terms of regulation of DC bus voltage and tracking of current. Unit prediction horizon i.e. only one step ahead looking into the future is considered for the MPC to make it computationally less expensive. MPC is designed in such a way that its performance is close to our favorite linear controller which in our case is the H∞ controller. The inverse optimal control technique is used for determining the weight matrices of the cost function. The proposed controller has been simulated using MATLAB. Also, the performance comparison is made between the designed MPC and the non-linear control approach i.e. integral sliding mode control and integral backstepping-based control to show that it achieves comparable or superior performance to the non-linear controller. The real-time performance of H∞ based MPC is verified using controller hardware in the loop experimental setup.

Adaptive Position Control of Electrohydraulic Servo Systems with Parameter Uncertainty using Artificial Bee Colony Optimization Algorithm

In this paper, we present a robust adaptive backstepping-based controller for precise positioning of the spool valve in an Electro-Hydraulic Servo System (EHSS) under conditions of parameter fluctuations. Classical control strategies, such as PID and linear controllers, often struggle with the nonlinearities and parameter uncertainties inherent in EHSS, leading to poor tracking performance and instability. To overcome these limitations, we employ the Artificial Bee Colony (ABC) algorithm to optimize the controller parameters, minimizing both the tracking error and control signal. The proposed controller ensures uniform ultimate boundedness of the error and control signal by utilizing a Lyapunov-based stability criterion, which guarantees that errors do not exceed a predefined bound despite uncertainties and disturbances. Simulation results validate the robustness and effectiveness of the control scheme, even in the presence of parameter variations. Additionally, a comparative analysis with sliding mode control highlights the superior performance of the proposed method, particularly in providing smoother control signals and reducing chattering while ensuring stability.

Distributed Neurodynamics-Based Backstepping Optimal Control for Robust Constrained Consensus of Underactuated Underwater Vehicles Fleet.

Robust constrained formation tracking control of underactuated underwater vehicles (UUVs) fleet in 3-D space is a challenging but practical problem. To address this problem, this article develops a novel consensus-based optimal coordination protocol and a robust controller, which adopts a hierarchical architecture. On the top layer, the spherical coordinate transform is introduced to tackle the nonholonomic constraint, and then a distributed optimal motion coordination strategy is developed. As a result, the optimal formation tracking of UUVs fleet can be achieved, and the constraints are fulfilled. To realize the generated optimal commands better and, meanwhile, deal with the underactuation, at the lower-level control loop a neurodynamics-based robust backstepping controller is designed, and in particular, the issue of "explosion of terms" appearing in conventional backstepping-based controllers is avoided and control activities are improved. The stability of the overall UUVs formation system is established to ensure that all the states of the UUVs are uniformly ultimately bounded in the presence of unknown disturbances. Finally, extensive simulation comparisons are made to illustrate the superiority and effectiveness of the derived optimal formation tracking protocol.

Output-Feedback-Based Adaptive Leaderless Consensus for Heterogenous Nonlinear Multiagent Systems With Switching Topologies.

This article investigates the leaderless output consensus control problem for a class of nonlinear multiagent systems with heterogenous system orders and unmatched unknown parameters via output-feedback control. The interaction topology among the agents is undirected and jointly connected. Due to the heterogenous system orders and switching topology among the agents, the classical distributed adaptive backstepping-based control technique cannot be applied to solve the problem considered in this article. To solve this issue, a novel distributed reference system is first proposed for each agent, by using only relative outputs of the neighboring agents. Subsequently, a fully distributed reference system-based adaptive leaderless output consensus control scheme is designed via output-feedback control. A remarkable merit of the proposed control scheme lies in that precisely known nonlinear dynamics, system states, distributed parameter estimates, and the states of virtual reference system are no longer needed to be shared with neighbors. This implies that the communication burden can be effectively alleviated, and even the communication network can be replaced by some perception sensors. Finally, two illustrative examples are provided to verify the effectiveness of the proposed control scheme.

Backstepping-Based Fuzzy Adaptive Stabilization of Reaction-Diffusion Equation With State Constraints.

This article proposes a stabilization scheme for a cascaded parabolic partial differential equation (PDE)-ordinary differential equation (ODE) system with state constraints. To begin, by employing the fuzzy-logic system (FLS) technique for the unknown nonlinear functions in the ODE subsystem, the influence of the nonlinearities is successfully eliminated. Then, the infinite and finite-dimensional backstepping methods are skillfully applied to the design of control schemes. Specifically, the infinite-dimensional backstepping transformation and its inverse are utilized to obtain a new PDE subsystem, which is convenient for control design. Next, based on the new target PDE-ODE cascade system, a novel first-order filter is subtly introduced into each step of the finite-dimensional backstepping-based controller design procedure to avoid the issue of "explosion of complexity." Furthermore, a novel barrier Lyapunov function (BLF) is constructed to guarantee that the states of the ODE subsystem do not violate the constraints. The controller designed in this article ensures that all signals in the closed-loop system are bounded and the states can converge to zero. Finally, a simulation example verifies that the proposed scheme can achieve satisfactory performance.

Nonlinear Fractional Uncertain Systems With Quantized Input: Adaptive Backstepping-Based Controller Design

Nonlinear Fractional Uncertain Systems With Quantized Input: Adaptive Backstepping-Based Controller Design

Barrier Lyapunov function and adaptive backstepping-based control of a quadrotor UAV

AbstractThis paper presents backstepping control and backstepping constraint control approaches for a quadrotor unmanned aerial vehicle (UAV) control system. The proposed methods are applied to a Parrot Mambo drone model to control rotational motion along the $x$ , $y$ , and $z$ axes during hovering and trajectory tracking. In the backstepping control approach, each state of the system controls the previous state and is called “virtual control.” The last state is controlled by the real control input. The idea is to compute, in several steps, a control law that ensures the asymptotic stability of the system. The backstepping constraint control method, based on barrier Lyapunov functions (BLFs), is designed not only to track the desired trajectory but also to guarantee no violation of the position and angle constraints. Symmetric BLFs are introduced in the design of the controller. A nonlinear mathematical model is considered in this study. Based on Lyapunov stability theory, it can be concluded that the proposed controllers can guarantee the stability of the UAV system and the state converges asymptotically to the desired trajectory. To make the control robust, an adaptation law is applied to the backstepping control that estimates the unknown parameters and ensures their convergence to their respective values. Validation of the proposed controllers was performed by simulation on a flying UAV system.

Backstepping-based control for a new semi-passive biped model

In this work, we propose a new Semi-Passive Biped (SPB) Model and a Center of Gravity Shift (CGS) control method of this model. The passing friction between the swing leg and the ground of passive robots locomotion consumes robots energy, resulting in the model cant walk passively. In order to analyze this problem in a more practical way, we propose a new SPB Model and analyze its energy consumption. Also, we suggest a CGS control method, which can make the proposed new SPB model walk stable. Finally, an illustrative experiment is presented to verify the SPB model and the effectiveness of the CGS control method.

Backstepping-Based Tracking Control of Underactuated Aquatic Robots

Increased interest in the use of autonomous aquatic robots in a variety of applications has led to the need for efficient and precise control of these robots. In particular, accurate trajectory control has become of importance in many of these applications. However, the highly nonlinear and underactuated dynamics of many aquatic robots present significant challenges in control. In this work, we propose a trajectory-tracking control approach for a general class of underactuated aquatic robotic systems undergoing planar motion. We demonstrate how a backstepping-based control scheme can be synthesized to ultimately bound three tracking errors (2-D position and orientation), despite the underactuated nature of the system. Via multi-time-scale analysis of singularly perturbed systems, we prove how the control scheme achieves boundedness and convergence of the tracking errors to a neighborhood of the origin. Finally, we implement the proposed scheme on a robotic fish and demonstrate its efficacy via experimental results. This article is complemented with a video: https://youtu.be/7007tUQd3KI.

Path-following and collision-avoidance guidance of unmanned sailboats based on beetle antennae search optimization

AbstractThere are few studies on the intelligent guidance of unmanned sailboats, which should coordinate pluralistic tasks at sea in the nature of its maneuvring intractability. To ensure the algorithmic practicability, this paper proposes a path-following and collision-avoidance guidance approach of unmanned sailboats with total formulaic description. The risk-detecting mechanism is fabricated by setting a circular detecting zone and using the time to the closest point of approach. Then, the risk of collision, the path deviation, the speed loss, and the course loss can be judged by constructing the cost functions and applying the distance to closest point of approach. The optimized heading angle is deemed as the one minimizing the aggregate cost functions, which is sought by applying and improving the beetle antennae search (BAS) algorithm. In the proposed modified BAS, the searching step is redesigned to enhance the searching efficiency. To ensure the convergence of the real heading angle to the reference, the backstepping-based control law is fabricated for the high-order sailboat model and in the linear form. The control parameters are offline optimized through the modified BAS. Compared with the adaptive control, this controller can guarantee more computation simplicity and the optimized control performance. Finally, simulation corroborates that the sailboat can successfully complete path following and collision avoidance while encountering multiple static and moving obstacles under the proposed schemes.

Backstepping control of gliding robotic fish for pitch and 3D trajectory tracking

Underwater gliders are known for their energy-efficiency and long-duration operations, with demonstrated applications in ocean exploration, fish tracking, and environmental sampling. Many applications such as exploring a large area of underwater ruins would benefit from accurate trajectory tracking. Trajectory tracking is particularly challenging for underwater gliders due to their under-actuated, highly nonlinear dynamics. Taking gliding robotic fish as an example, a backstepping-based controller is proposed to track the desired pitch angle and reference position in the 3D space. In particular, under-actuation is addressed by exploiting the coupled dynamics and introducing a modified error term that combines pitch and horizontal position tracking errors. Two-time-scale analysis of singularly perturbed systems is used to establish the convergence of all tracking errors to a neighborhood around zero. The effectiveness of the proposed control scheme is demonstrated via simulation and experimental results, and its advantages are shown via comparison with a PID controller and a baseline backstepping controller that does not use the modified error. This paper is accompanied by a video available at: https://youtu.be/D8Vej3weeGc.

State observer-based model reference adaptive balance control for one-leg stance

PurposeHumanoid robots have been utilized in many fields such as medical, construction, and disaster response. While humanoid robots nowadays can achieve great capabilities, the one-leg balancing task still poses a challenging problem. This paper aims to propose a novel approach to solve the problem.Design/methodology/approachTo aid the balance of one leg in humanoid robot, an external balance mechanism is inserted to the back of the humanoid robot. First, a dynamic model of the humanoid robot with balance mechanism and its simplified model are introduced. Second, a backstepping-based control method is utilized to build the proposed controller for one-leg stance system through two steps. For the first step, a minimum observer-based controller with a virtual control input is used to control the first sub-system reaching the desired reference input. For the second step, a virtual control input is considered as a reference input of a second sub-system, then a model reference adaptive controller (MRAC) is employed to control the second sub-system reaching the virtual control input in presence of uncertainties. By using the external balance mechanism, the sideway balancing task is separated from normal walking function. Furthermore, the utilization of the balance mechanism ensures the humanoid robot's hip adduction does not exceed the threshold of a human when walking. Finally, a simulation study is carried out to evaluate the effectiveness of the proposed method.FindingsThis paper proposes a model reference adaptive control using state observer for balancing one leg of humanoid robot in stance phase that extends our previous research (Tran et al., 2021).Originality/valueThe main research contents have been introduced.

Adaptive Attitude Control of a Rigid Body With Input and Output Quantization

In this article, the adaptive attitude-tracking problem of a rigid body is investigated, where the input and output are transmitted via a network. To reduce the communication burden in a network, a quantizer is introduced in both uplink and downlink communication channels. An adaptive backstepping-based control scheme is developed for a class of multiple-input and multiple-output (MIMO) rigid body systems. The proposed control algorithm can overcome the difficulty to proceed with the recursive design of virtual controls with quantized output vector, and a new approach to stability analysis is developed by constructing a new compensation scheme for the effects of the vector output quantization and input quantization. It is shown that all closed-loop signals are ensured uniformly bounded and the tracking errors converge to a compact set containing the origin. Experiments on a 2 degrees-of-freedom helicopter system illustrate the effectiveness of the proposed control scheme.

Trajectory Tracking Control of Rowing Pectoral Fin-Actuated Robotic Fish

Robotic fish has received increasing attention in the last few decades, as they hold strong promise in a myriad of applications. Efficient and precise control of these robots, particularly accurate trajectory control, has become essential in many of these applications. This article proposes a dual-loop backstepping-based trajectory tracking control approach for a robotic fish actuated by rowing pectoral fins. While rowing pectoral fin-based locomotion is important for maneuvering, the range constraints of fin movement pose significant challenges in the control of robotic fish, including potentially preventing the robot from generating the thrust needed to maneuver in a desired direction. To overcome these challenges, we propose a dual-loop controller, designed based on an averaged dynamic model of the robot. In particular, an outer-loop backstepping-based controller finds the needed force and moment inputs for the robot to track the desired trajectory, while the inner loop determines the optimal fin-beat parameters such that the resulting fin-generated forces and moment are close to their desired values. Experimental results are presented to show the efficacy of the proposed control scheme, where the robot is commanded to track a trajectory with variable linear and angular velocities. Comparing to a well-tuned proportional–integral–derivative controller, the proposed control scheme shows a distinct advantage in tracking desired orientations in addition to tracking desired positions.

A reinforcement learning backstepping‐based control design for a full vehicle active Macpherson suspension system

This paper presents a reinforcement learning backstepping-based control scheme for the design of a full vehicle active suspension system such that both the superior ride comfort and stabilization are achieved. It is well known that the traditional backstepping control scheme is suitable to solve higher order nonlinear system based on the strict-feedback form; however, the disadvantage of the procedure requires computing the derivatives of virtual control signals, which is a very complex task. Therefore, a reinforcement learning scheme using the deep deterministic policy gradient (DDPG) control strategy is developed to replace the process of finding virtual control force in backstepping method. It not only avoids the complexity of analytically calculating the derivatives of the virtual control signals, but also retains the systems robustness when there exist random disturbances from road irregularities. To verify the performance of the proposed active suspension control scheme, the random road unevenness profiles according to ISO 8608 is considered as vertical and lateral disturbance input excitation of a full-vehicle suspension system. Compared with conventional passive suspension system and backstepping control scheme, the proposed approach can be demonstrated to not only effectively improve ride comfort under random road excitation, but also improve the transient response and robustness.

Decentralized adaptive control of uncertain interconnected systems with triggering state signals

Backstepping is a powerful technique of control design for uncertain systems and has been well received. As it involves differentiating virtual control signals recursively, the involved signals must be differentiable. However, when the measured states are only transmitted based on event-triggered conditions, such requirement will not be met, making the recursive backstepping design procedure inapplicable. Thus it is still an open problem to study how an event-triggered scheme is employed to transmit state signals in decentralized control of uncertain interconnected systems with dynamic interactions. In this paper, we present a solution by constructing a new decentralized adaptive backstepping-based control algorithm capable of coping with discontinuity caused by state-triggering. With aid of appropriately chosen Lyapunov functions, all signals in the closed-loop system are ensured globally uniformly bounded. Simulation results are presented to demonstrate the effectiveness of the proposed methodology.

Sliding mode differentiator-based event-triggered control for state-constrained nonlinear systems with unknown virtual control coefficients

In this paper, a novel event-triggered (ET) adaptive neural tracking control scheme is proposed for uncertain strict-feedback systems subject to asymmetric time-varying full-state constraints, unknown virtual control coefficients and external disturbances. The lower-order time-varying asymmetric barrier Lyapunov function (TVABLF) is constructed to ensure that state constraints are not transgressed. Then, a simple backstepping-based control procedure is developed to remove the existing restrictions on a high power of piecewise TVABLF and high-order differentiability of virtual laws. In particular, a novel adaptive updating law is constructed to co-design the controller and the ET scheme by the combination of the Nussbaum gain technique, thereby solving the ET controller design difficulty resulting from unknown control coefficients. The proposed scheme can guarantee all states within the time-varying constrained areas, achieve the satisfactory tracking ability and save the communication resource. Finally, the effectiveness of the proposed scheme is testified by numerical and practical examples.

Reduced-Order Observer-Based Adaptive Fuzzy Tracking Control Scheme of Stochastic Switched Nonlinear Systems

In this article, an adaptive approximation-based output-feedback tracking control scheme is presented for a class of stochastic switched lower-triangular nonlinear systems with input saturation and unmeasurable state variables. First, to overcome the design obstacle caused by the nondifferential saturation nonlinearity, a carefully selected nonlinear function of the control input signal is applied to estimate the saturation function. Then, a reduced-order state observer is designed to model the unmeasured system states, which also means the error system can be established. Furthermore, the fuzzy-logic systems are utilized to approximate the unknown system nonlinearities in the adaptive backstepping-based controller design procedure. It is ensured that all the closed-loop system variables are bounded in probability and the error signal belongs to a compact set in the mean square sense. Finally, the effectiveness and the practicability of the proposed control scheme are shown by two examples.

Indirect Fuzzy Control of Nonlinear Systems With Unknown Input and State Hysteresis Using an Alternative Adaptive Inverse

It is interesting to study the problem of adaptive fuzzy control for uncertain nonlinear systems with input and state hysteresis. However, since the hysteresis behavior, especially the state hysteresis, present at the sensors is complicated, mainly in view of its multivalues and rate-dependent features, it is a challenging task to develop the backstepping-based control design. So far, there is still no available result in addressing the problem. In this article, we will pursue this task. A novel indirect fuzzy control scheme is proposed with an alternative adaptive hysteresis inverse, which is used to cancel the unknown input hysteresis. To tackle the effects of state hysteresis, a new dynamic compensation is developed to adaptively accommodate the uncertain dynamics involved in the sensors. It is proved that in addition to system stability, the proposed scheme enables the tracking error to approach a prescribed interval asymptotically. Illustrative examples are used to verify the method developed.

Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement

This paper investigates the adaptive neural tracking control of the strict-feedback nonlinear systems, where the states are measured in an event-triggered manner so as to save the communication resources. As the neural networks (NNs) account for the unknown dynamics of the system, the minimum learning parameters (MLPs) are extracted from the weights of the NNs and the upper bounds of the disturbances. The estimates of the MLPs are updated in an event-triggered manner to ensure the approximation ability of the NNs and the stability of the closed-loop system. An adaptive neural model is established to substitute for the original strict-feedback system and direct the design of the backstepping-based control laws. The states of this adaptive model are reset to the measured states of the original system when the triggering condition is violated. The triggering condition is constructed in the compound form and with the adaptive threshold. The dead-zone operator is involved to avoid the accumulation of triggering instants. In this paper, we notice the problem of “jumps of virtual control laws” for the event-triggered control (ETC) in the backstepping frame, and a detailed formulaic definition is given in section 2.2. To solve this problem, the first-order filters are fabricated to provide the continuous substitutes for virtual control laws. In addition, the “complexity explosion” generated by direct differentiating of virtual control laws can be averted. Through the proposed scheme, the closed-loop system can be viewed as an impulsive dynamic system, and the semi-globally uniformly ultimate boundedness (SGUUB) of all the errors is proved. Finally, two examples validate the feasibility of the proposed control scheme.