Tracking Control Problem Research Articles

Approximation-based adaptive two-bit-triggered bipartite tracking control for nonlinear networked MASs subject to periodic disturbances

Purpose This paper aims to investigate the problem of adaptive bipartite tracking control in nonlinear networked multi-agent systems (MASs) under the influence of periodic disturbances. It considers both cooperative and competitive relationships among agents within the MASs. Design/methodology/approach In response to the inherent limitations of practical systems regarding transmission resources, this paper introduces a novel approach. It addresses both control signal transmission and triggering conditions, presenting a two-bit-triggered control method aimed at conserving system transmission resources. Additionally, a command filter is incorporated to address the problem of complexity explosion. Furthermore, to model the uncertain nonlinear dynamics affected by time-varying periodic disturbances, this paper combines Fourier series expansion and radial basis function neural networks. Finally, the effectiveness of the proposed methodology is demonstrated through simulation results. Findings Based on neural networks and command filter control method, an adaptive two-bit-triggered bipartite control strategy for nonlinear networked MASs is proposed. Originality/value The proposed control strategy effectively addresses the challenges of limited transmission resources, nonlinear dynamics and periodic disturbances in networked MASs. It guarantees the boundedness of all signals within the closed-loop system while also ensuring effective bipartite tracking performance.

Voltage and Fuel Utilization Control Strategy for Solid Oxide Fuel Cell Based on Active Disturbance Rejection Control

ABSTRACTSolid oxide fuel cell (SOFC) systems have become a research focus because of their clean and high‐efficiency properties. Control of output voltage and fuel utilization is critical to the energy management for multi‐energy systems incorporating SOFC energy supply. However, maintaining precise control of the system's voltage in the presence of perturbations can be challenging. Moreover, the system's voltage control process can lead to fuel utilization fluctuations, which may affect the economy and safety. The design of the controller must meet both of these requirements. The stringent control requirements lead to poor parameter adaptability of existing controllers. This paper designs a nonlinear function and adopts a nonlinear/linear active disturbance rejection controller (ADRC) based on state switching to solve the output voltage tracking control problem of SOFC and maintain the fuel utilization rate in the ideal range. The simulation experimental results show that the proposed method has the advantages of strong and superior parameter adaptability with less control effort, which provides theoretical guidance for the design of the output voltage controller of the actual SOFC system.

Optimized trajectory tracking control with disturbance resistance for wheeled mobile robot

When unavoidable disturbances exist in practical applications, the unicycle wheeled mobile robot (WMR) with non-holonomic constraint is challenging to be accurately controlled in finite time. An optimized dual closed-loop strategy is proposed in this paper to solve the trajectory tracking control problem of the unicycle WMR. The control strategy with fast time convergence and anti-disturbance properties consists of kinematic and dynamics controllers and an optimization algorithm. The kinematic controller is designed with an improved backstepping method to eliminate the non-holonomic constraints. The robust sliding mode control (SMC) method with fixed-time convergence is used to construct the dynamics controller. The optimization algorithm enhances the performance of the strategy and achieves accurate control. The global convergence and robustness of the strategy are theoretically demonstrated. The effectiveness of the strategy is verified by comparison in simulations.

Fixed-time second-order sliding mode output feedback trajectory tracking control for an autonomous surface vehicle with model uncertainties and prescribed performance

This paper investigates the fixed-time trajectory tracking control problem of autonomous surface vehicle system with asymmetric performance constraints. The external disturbances, model uncertainties and the difficulty of velocity measurement are all taken into account in the controller design. Asymmetric performance constraints are firstly studied to improve the transient and steady-state performance of the tracking error system. Next, a fixed-time extended state observer is developed to estimate the unknown velocity and external disturbances. Both the fixed-time first-order and the second-order PID-type sliding surfaces are designed. Further, two continuous output feedback controllers are built to achieve high control accuracy and low energy consumption and to achieve fixed-time stability of the closed-loop system. Finally, abundant simulations for CyberShip II demonstrate the effectiveness of the proposed algorithms.

Prescribed finite-time tracking control with input buffer for a manipulator system

The prescribed finite-time trajectory tracking control problem with input buffer is investigated for a linkage manipulator system. The backstepping method is used to design the prescribed finite-time trajectory tracking controller. A new prescribed finite-time performance function is proposed, which can more easily regulate control performance. With the help of this performance function, a constraint control law is designed for the tracking error, and a better transient performance than the existing prescribed finite-time performance function can be obtained under the same parameter conditions for the trajectory tracking process of the manipulator system. At the same time, a control input buffer function is designed, which solves both the overvoltage problem of control input caused by the overlarge position error of the manipulator and the problem that the manipulator system is difficult to start under heavy load. The simulation experiments verify the effectiveness and superiority of the proposed controller.

Analysis of a Dry Friction Force Law for the Covariant Optimal Control of Mechanical Systems with Revolute Joints

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control.

Adaptive output feedback command filter control based on extreme learning machine for nonaffine time delay systems with input saturation

This paper is concerned with the tracking control problem of nonlinear time delay systems. For time delay systems, we consider nonaffine pure-feedback structure. Additionally, the case where the time delay systems are subject to input saturation and unknown states is also taken into account. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the systems into an affine form. Afterwards, a state observer is developed to estimate the unknown state variables and an extreme learning machine (ELM) is used to approximate the unknown functions. The output of the command filter replaces the virtual control signal'derivative, thereby circumventing the problem of ‘explosion of complexity’. Meanwhile, compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). A Lyapunov–Krasovskii functional is designed to mitigate the unknown constant state time delay. During the controller design process, combining a prescribed performance control (PPC) with a command filter control, the tracking error can converge to a predetermined bound. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of such controller is further proved by taking an electromechanical system as an application object.

Interactive strategy of shared control vehicle and automated vehicles based on adaptive non-cooperative game

Considering the complex traffic environment in the future, an interactive strategy between human-machine shared control vehicle (HSCV) and automated vehicles (AVs) based on the adaptive non-cooperative game (NCG) theory is proposed to ensure the safety of vehicles interaction control involving drivers with different characteristics. In HSCV, first, considering the environmental risk potential field (ERPF) and the human-machine conflict coefficient, an adaptive weight distribution method is designed to realize the weight distribution between a driver and an automation system. Subsequently, the steering angle command imposed by a driver is introduced into the game solving process between HSCV and AVs, enabling adaptive dynamic game through weight adjustment. During V2V interaction, based on NCG and distributed model predictive control, a motion planning controller (MOPC) is designed to integrate the optimal solution problem of path planning and tracking control and solve the interaction problem with constraints. Two typical interactive scenarios are used to verify the feasibility of the strategy. The results demonstrate that the interaction strategy considering the different drivers’ operating commands not only realizes the interaction between a driver and an ego vehicle but also realizes the interaction between an ego vehicle and nearby vehicles to ensure the safety of vehicles.

A Finite-Time Path Tracking Control Scheme for Unmanned Vehicles Based on Multidimensional Taylor Network and Adaptive Filtering

Aiming at the path tracking control problem of unmanned vehicles under the conditions of model uncertainty and measurement noise, a finite-time path tracking control scheme based on multidimensional Taylor network (MTN) is proposed. The MTN model is used to characterize the uncertainty of the unmanned vehicle model, and the improved back propagation (BP) algorithm is used as its learning algorithm; an adaptive MTN filter is designed to filter out the measurement noise, MTN is used as a filter, and the least mean square (LMS) algorithm is used as its learning algorithm; an MTN finite-time controller is designed to perform precise path tracking control on the unmanned vehicle, which can quickly and accurately track the reference path; according to the finite-time control theory, the convergence proof verifies the effectiveness of the proposed method through unmanned vehicle simulation experiments.

Adaptive Saturated Obstacle Avoidance Trajectory Tracking Control for Euler–Lagrange Systems With Velocity Constraints

ABSTRACTThis article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy.

Quaternion-based fixed-time tracking control for an autonomous underwater vehicle with consideration of measurement bias

This article investigates trajectory and attitude tracking control problem of a 6-degree of freedom (DOF) autonomous underwater vehicle (AUV) subject to measurement bias and external disturbance. First, the model dynamics of rotational channels are established by unit-quaternion, which possesses simplicity and broader applicability compared to the Euler angle such that the maneuver signal could be uniquely determined. Meanwhile, by introducing constraint of the logarithm function and initial value, the unwinding phenomenon existing in rotation motion can be avoided tactfully. Considering the high requirement for sensor accuracy, the resulting measurement bias in position and velocity channels, making AUV into a mismatched system and bring the uncertain term in the process of controller design. Therefore, the echo state network (ESN) with online updates performance is applicable to approximate uncertain term simultaneously generated by measurement bias and unknown external disturbance. Then, by incorporating composite hyperbolic tangent function, the quasi-fast terminal sliding mode (QTSM) surface is constructed to realize the fixed-time convergence peculiarity of the AUV tracking system. Compared with the existing methods, the proposed algorithm can regulate artificially the stable schedule of the AUV tracking system and possess the capacity of bias tolerance and anti-disturbance. Finally, simulation results verify the validity and feasibility of the developed control algorithm.

Prescribed finite-time safe tracking control based on secure boundary protection method for nonlinear systems with unknown control gains

Aiming to the mutation of the actual output boundary, a prescribed finite-time safe tracking control problem is investigated for a class of nonlinear systems with unknown control gain in this paper. A secure boundary protection method (SBPM) and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can construct automatically two adjustable secure boundaries, so that the system meets both the control performance prescribed by the PFTPF and the constraint of the secure boundaries. In order to solve the problem of the excessive jitter of control input caused by the mutation of the output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed method can effectively deal with the mutation of actual output constraint, and it is not necessary to predict the system output value to adjust the desired output trajectory. Finally, the effectiveness of this proposed method is verified by simulations.

Adaptive visual servoing control for uncalibrated robot manipulator with uncertain dead-zone constraint

This paper addresses the adaptive visual tracking control problem of an uncalibrated camera robot system with unknown dead-zone inputs. The uncertainties include camera extrinsic and intrinsic parameters, robot dynamic parameters, and feature depth parameters. The control achieves a better performance by establishing a smooth inverse model of the dead-zone input, which eliminates the nonlinear effect of the actuator constraint. A novel adaptive control scheme is presented which does not require a priori knowledge of the parameter intervals of dead-zone model, to update the parameter values online. Furthermore, adaptive laws are provided to estimate the uncertainties that exist both in robot and in camera models. Meanwhile, in order to avoid the singularity of the image Jacobian matrix, a projection algorithm is also introduced. Subsequently, a novel robust adaptive controller together with dead-zone compensation is established so that the tracking error image space converges to the origin. Simulations and experimental studies are conducted to verify the effectiveness of the proposed method.

Machine learning model‐based optimal tracking control of nonlinear affine systems with safety constraints

AbstractThis work focuses on the development of a machine learning (ML) model‐based framework for safe optimal tracking control of a class of nonlinear control‐affine systems to ensure simultaneous closed‐loop stability and safety. Specifically, a novel multilayer feedforward neural network (FNN) with a control‐affine architecture is designed to model nonlinear dynamic systems. Subsequently, a model‐based reinforcement learning (RL) framework is presented, utilizing a novel cost function with Control Lyapunov‐Barrier Function (CLBF) properties, to learn both the control policy and the optimal value function for an infinite‐horizon optimal tracking control problem for nonlinear systems with safety constraints. The efficacy of the proposed methodology is demonstrated through simulations of a one‐link robot manipulator and a chemical process example.

Four-stage cascaded adaptive sliding mode control for automatic carrier landing with airwake disturbances and uncertainties

ObjectiveThis paper addresses the carrier landing affected by airwake, parametric uncertainties, and carrier deck motion, its main target being the design of a novel sliding mode based automatic carrier landing system to obtain accurate tracking of the reference trajectory, robustness in terms of disturbances and uncertainties, as well as excellent touchdown accuracy. ApproachFor an aircraft nonlinear dynamics, written under a four-stage cascaded strict feedback form, the design of the novel landing control architecture involves the design of a guidance subsystem, robust sliding mode controllers (for the control of the heading angle, attitude angles, and angular rates), an approach power compensation system, adaptive control laws suppressing the uncertainties and disturbances, a Kalman filter for deck motion prediction, a block computing the reference trajectory, a tracking differentiator block for deck motion compensation, and first-order command filters. Main resultsThe software validation process proves the effectiveness of the sliding mode based control scheme and the suppression of the uncertainties and disturbances. Also, the comparison between the performances of the sliding mode control based carrier landing system and the ones associated to other automatic carrier landing systems shows the superiority of the sliding mode based control scheme, as well as its better touchdown accuracy and landing success rate. SignificanceThis study innovatively transforms the general carrier landing problem into a time-varying tracking control problem for cascaded strict feedback dynamics with disturbances and uncertainties. The new designed automatic carrier landing system is the first control architecture in the literature employing the sliding mode control augmented by adaptive control laws for carrier landing, subjected to airwake, deck motion, and uncertainties.

Quantization-Based Adaptive Fuzzy Consensus for Multiagent Systems Under Sensor Deception Attacks: A Novel Compensation Mechanism.

This study mainly investigates the adaptive leader-following consensus tracking control problem for a class of nonlinear multiagent systems (MASs) subjected to unknown control directions, external disturbances, and sensor deception attacks. To start with, an equivalent MAS with known control directions is obtained by introducing a linear state transformation. For the purpose of estimating the unavailable system states caused by malicious attacks, a quantization-based fuzzy state observer is designed, and the fuzzy-logic system (FLS) is utilized to approximate nonlinear functions. Moreover, a dynamic uniform quantizer with scaling function is established to reduce information transmission. With the help of coordinate transformation and available compromised states, a novel compensation mechanism is designed to offset the influence of filter errors while avoiding the problem of "explosion of complexity" in the backstepping design process. In addition, the Nussbaum-type function is considered to eliminate the design obstacle of unknown control gains resulting from the attacks. Under the constructed consensus protocol, it is proved theoretically that the consensus tracking error converges to an adjustable small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the feasibility of the provided secure control scheme is verified through two simulation examples.

Practical tracking control for a class of uncertain MIMO nonlinear systems with unmatched disturbances

This paper studies the output tracking control problem for a class of uncertain MIMO nonlinear systems. The motivation comes from how to deal with unknown coupling system dynamics between subsystems and achieve the desired tracking when the system has parameter uncertainties and external disturbances. The difficulty is to guarantee that tracking errors enter an arbitrarily prescribed neighbourhood within a finite time. Based on the construction of a time-varying dynamic gain associated with tracking errors and the effective manipulation of nonlinear parametrization, a novel robust feedback controller is built up to ensure the boundedness of all closed-loop signals and the convergence of tracking errors to a small neighborhood approaching the origin in a finite time. Finally, the feasibility of control strategy is verified by numerical and practical examples.

Low-Complexity Tracking Control of Unknown Strict-Feedback Systems With Quantitative Performance Guarantees.

This article is concerned with the prescribed performance tracking control problem for the strict-feedback systems with unknown nonlinearities and unmatched disturbances. The challenge lies in the realization of a complete performance specification for trajectory tracking in the sense of quantitatively regulating the peak value, overshoot, settling time, and accuracy while ensuring that the initial condition holds naturally. To this end, an error transformation, equipped with a shifting function, is introduced and incorporated with a new-type barrier function. Then, a class of performance functions is exploited to quantify the settling times and steady-state bounds of the intermediate errors. Moreover, to improve the flexibility of formulating performance specifications for the tracking error, a pair of asymmetric performance boundaries are further designed. With their combination, a novel robust prescribed performance control (PPC) approach is proposed in this article. It not only achieves the quantitative performance guarantees but also preserves the unique simplicity of PPC, evading the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are confirmed via three simulation studies.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Output Feedback Adaptive Optimal Control of Multiple Unmanned Marine Vehicles with Unknown External Disturbance

This paper presents an optimal output-feedback tracking control problem for multiple unmanned marine vehicles (UMVs) to track a desired trajectory. To guarantee the control objective in an optimal manner, adaptive dynamic programming (ADP) with optimal compensation terms is adopted. A neural velocity observer is designed based on a neural network (NN) to estimate the unmeasured system states and the unknown system dynamics. Furthermore, a disturbance observer (DO) is proposed to go against the effect of the unknown external disturbance of the sea environment. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded. Simulation results are given to demonstrate the effectiveness of the proposed control algorithm.