Tracking Error Constraints Research Articles

Event-triggered finite-time adaptive neural network control for quadrotor UAV with input saturation and tracking error constraints

In this article, an event-triggered finite-time adaptive neural network control tracking strategy is proposed for quadrotor unmanned aerial vehicle (UAV) with input saturation and error constraints. Firstly, the radial basis function neural networks (RBFNNs) are adopted to identify the unknown uncertainty of quadrotor UAV model from the installation errors, gyroscope errors and so on. An auxiliary equation is constructed to deal with input physical saturation from the actuator motors. Additionally, by combining the performance function and error transformation, the issue of error constraint is solved. Based on the Lyapunov stability theory and event-triggered mechanisms, a finite-time adaptive neural network scheme is developed to ensure that the closed-loop quadrotor UAV system is semi-globally practically finite-time stable, and save the computation, resources, and transmission load. Finally, the simulation results illustrate the good tracking performance of quadrotor UAV by using the proposed control strategy.

Bounded Containment Maneuvering Protocols for Marine Surface Vehicles With Quantized Communications and Tracking Errors Constrained Guidance: Theory and Experiment.

A new type of containment maneuvering protocols for multiple marine surface vehicles (MSVs) is developed to follow a parameterized path in this work, where the tracking errors are constrained within finite time and the information needed to be transmitted is quantized during coordination. To achieve containment maneuvering of multiple MSVs, a two-objective coordinated control framework is proposed. For the geometric objective, by developing tan-type barrier Lyapunov functions (BLFs) and extended Lyapunov condition-based finite-time guidance laws, the performance of the parameterized line-of-sight guidance framework, including convergence speed and tracking error constraints, is improved. For the dynamic objective, based on quantized control strategy and smooth saturation functions, novel bounded containment maneuvering protocols are proposed to dramatically alleviate the burden of communications among MSVs and ensure more faster dynamic behavior on tracking the path updating speed. Both theoretical analysis and experimental tests with comparative studies illustrate the validity of the proposed containment maneuvering strategy.

Practical prescribed time tracking control for a class of nonlinear systems with event triggering and output constraints

AbstractThis paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples.

Nonsingular finite-time heading tracking control of marine vehicles with tracking error constraints

This brief copes with the finite-time heading tracking control for marine vehicles. The tracking error constraints, stochastic disturbance and dead-zone output are simultaneously taken into consideration in the controlled systems. To manage the dead-zone output issue, a smooth approximation model is brought in to offset the nondifferentiable phenomena during the control, besides, the adaptive technique and the Nussbaum function are simultaneously integrated into the design. For the tracking error constraints, the prescribed performance functions (PPF) with error transformations are designed, and novel stochastic Barrier Lyapunov functions are constructed accordingly depending on the newly tracking errors to deal with the constrained tracking control issue. To avert the “differential explosion” issue in the backstepping, the improved first-order filter technique is invoked. The proposed finite-time heading tracking control tactic renders that all variables are bounded, meanwhile, the tracking errors are kept in the pregiven boundaries. The effectiveness of theory results is substantiated via simulations.

Prescribed-time event-triggered fault-tolerant formation control of multiple UAVs under tracking error constraints

This paper studies an event-triggered fault-tolerant tracking control strategy design of multiple quadrotor UAVs (MQUAVs) formation subject to the composite influence of external disturbance, tracking error constraints and actuator faults. A prescribed time prescribed performance function is employed to solve tracking error constraints and it ensures the tracking error enters into the constraint boundary in the prescribed time. A first-order filter is designed to solve the problem of computational explosion caused by reference trajectory and unknown external disturbance. The adaptive method is used to deal with the unknown parameters and the comprehensive uncertainty which contains actuator faults and external disturbance. Furthermore, the event-triggered controller is designed to achieve the formation tracking with the reduction of update number of controller to save resources. The bounded stability of the tracking error is proved via the Lyapunov theory. At last, the effectiveness of the control strategy is verified by simulation.

Finite-Time Event-Triggered Containment Maneuvering of Marine Surface Vehicles With Tracking Error Constraints: Theory and Experiment

Finite-Time Event-Triggered Containment Maneuvering of Marine Surface Vehicles With Tracking Error Constraints: Theory and Experiment

Event-Triggered Adaptive Tracking With Guaranteed Transient Performance for Switched Nonlinear Systems Under Asynchronous Switching.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

Quantized Communications in Containment Maneuvering for Output Constrained Marine Surface Vehicles: Theory and Experiment

The aim of this paper is to derive a containment maneuvering coordination strategy for a team of marine surface vehicles (MSVs) to track one parameterized path guided by two virtual leaders, where the tracking errors are constrained and the communications among MSVs are quantized. A two-level coordinated framework for containment maneuvering is proposed. For the kinematic level, to obtain the performance of tracking error constraints, guidance laws are derived by developing parameterized line-of-sight (LOS)-based symmetrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ln$</tex-math></inline-formula> -type Lyapunov functions, where the control functions are injected into the guidance laws to prevent constraint violations. For the coordination level, a communication protocol is proposed to reduce the amount of communication data by developing a quantized control strategy. Compared with the current containment maneuvering strategy, the whole design can bind the along-track and cross-track errors into the user-defined regions, increase the convergence speed of tracking errors, save bandwidth of the whole network and reduce the sensitivity of the initial positions of MSVs. Theoretical analysis shows that all signals are bounded. Experimental examples are also provided to verify the proposed containment maneuvering strategy.

Event-Triggered Tracking Control for a Class of Nonlinear Systems: A Dynamic Gain Approach

This note presents a dynamic gain approach to the event-triggered tracking control for a class of strict-feedback nonlinear systems. A novel shifting function is designed to make the initial tracking error arbitrarily bounded, which significantly relaxes the requirement on the initial tracking error. To achieve the objective that the tracking error does not exceed the constraint after the pre-specified finite time, a barrier Lyapunov function and a new reduced-order observer are constructed by using the shifting function and the desired tracking signal. Based on the proposed dynamic gain approach, an event-triggered output feedback tracking controller is designed. It is proved that the developed control scheme guarantees that all the closed-loop signals are bounded and the tracking error constraint is strictly obeyed after a specified finite time. Compared with the celebrated backstepping method, the dynamic gain approach does not involve any virtual control variables, which avoids the complicated iterative procedure. The effectiveness of the proposed approach is verified by an example.

Enhanced reduced-order extended state observers-based position tracking error constraint control of a pump-controlled hydraulic system via multiparameter singular perturbation theory

In this paper, the position tracking error constraint control is investigated for a pump-controlled hydraulic system (PHS) subject to an unmeasurable velocity signal and disturbances. A barrier Lyapunov function (BLF)-based backstepping controller is designed, and a set of enhanced reduced-order extended state observers (RESOs) is proposed to estimate the velocity and disturbances. Dynamic surface control (DSC) is used to avoid a repeated calculation of the derivatives of virtual control inputs. Multiparameter singular perturbation theory is utilized to clarify the working mechanism of the enhanced RESOs and the closed-loop system stability properties. Theoretical analysis results reveal that the closed-loop system is uniformly ultimately bounded and the position tracking error is always constrained within a prescribed bound by a proper selection of the perturbation parameters. Moreover, the final position tracking error can be arbitrarily small by further tuning these parameters. In addition, the enhanced RESOs are proven capable of improving the convergence performance of the closed-loop system. Experiments are conducted on an actual PHS to validate the superiority of the proposed control strategy.

ADAPTIVE NEURAL TRACKING CONTROL FOR SURFACE SHIP WITH COMPENSATED TRACKING ERROR-CONSTRAINS AND DELAY INPUT BASED ON COMMAND-FILTER

The article proposes an algorithm for trajectory tracking control problem of full actuated surface ships in the presence of state constraints, the delay of the input signal, and uncertain model parameters. During the design process, radial basis function neural networks are used to approximate the nonlinear components of uncertainty and a symmetric barrier Lyapunov function is incorporated to cope with the constraints of compensated tracking error. In particular, an auxiliary system is employed to eliminate the delay of the input signals, which often makes the control performance worse, even unstable. The adaptive controller that the article proposes is built based on the backstepping method using a command filter to avoid derivative explosion and reduce the computational burden on the controller. The article shows that tracking errors of surface ship can converge to a small neighborhood of zero, the compensated tracking error constraints of the system are not violated, the system is still stable when the input signal is delayed.

Event-Triggered Finite-Time Formation Control of Underactuated Multiple ASVs with Prescribed Performance and Collision Avoidance.

In this paper, an event-triggered finite-time controller is proposed for solving the formation control problems of underactuated multiple autonomous surface vessels (ASVs), including asymmetric mass matrix, collision avoidance, maintaining communication distances and prescribed performance. First, to not only avoid collisions between the follower and leader but also maintain an effective communication distance, a desired tracking distance is designed to be maintained. Second, an improved barrier Lyapunov function (BLF) is proposed to implement the tracking error constraint. In addition, the relative threshold event-triggering strategy effectively solves the communication pressure problem and greatly saves communication resources. Finally, based on coordinate transformation, line of sight (LOS) and dynamic surface control (DSC), a comprehensive finite-time formation control method is proposed to avoid collisions and maintain communication distance. All the signals of the proposed control system can be stabilized in finite time (PFS). The numerical simulation results verify the effectiveness of the proposed control system.

Global Composite Learning Fixed-Time Control of Robotic Systems With Asymmetric Tracking Error Constraints

Global Composite Learning Fixed-Time Control of Robotic Systems With Asymmetric Tracking Error Constraints

A Singular Perturbation Theory-Based Composite Control Design for a Pump-Controlled Hydraulic Actuator with Position Tracking Error Constraint

Pump-controlled hydraulic actuators (PHAs) contain slow mechanical and fast hydraulic dynamics, and thus singular perturbation theory can be adopted in the control strategies of PHAs. In this article, we develop a singular perturbation theory-based composite control approach for a PHA with position tracking error constraint. Disturbance observers (DOBs) are used to estimate the matched and mismatched uncertainties for online compensation. A sliding surface-like error variable is proposed to transform the second-order mechanical subsystem into a first-order error subsystem. Consequently, the position tracking error constraint of the PHA is decomposed into the output constraint of the first-order error subsystem and the stabilizing of the first-order hydraulic subsystem. Slow and fast control laws can be easily designed without using the backstepping technique, thus simplifying the control design and reducing the computational burden to a large extent. Theoretical analysis verifies that desired stability properties can be achieved by an appropriate selection of the control parameters. Simulations and experiments are performed to confirm the efficacy and practicability of the proposed control strategy.

Performance-based model-free adaptive finite-time control for shape memory alloy actuated swing platform

Shape memory alloy (SMA), a kind of smart material, can be used as an actuator in many fields; however, its strong nonlinearity and parameter uncertainty hinders its application in high-tracking accuracy tasks. This paper addresses the tracking control problem of the SMA actuated swing platform suffering from completely unknown nonlinear model information and prescribed finite-time error constraints. First, the equivalent dynamic linearization model of the swing platform is established, and the unknown disturbance is estimated and compensated by the extended state observer. Meanwhile, a novel discrete-time performance function is proposed, and the prescribed finite-time tracking error constraints are transformed into a new equivalent unconstrained task. Second, the model-free adaptive sliding mode controller is designed using the unconstrained error, and the complete control law, including sliding mode control law and equivalent control law, is derived. Third, the stability of the closed-up swing platform is guaranteed by employing the Lyapunov method. Finally, experiments reveal that the proposed method is preferable.

Adaptive practical prescribed-time fault-tolerant control for autonomous underwater vehicles trajectory tracking

This article investigates the practical prescribed-time trajectory tracking control problem for AUVs with parametric uncertainties under tracking error constraints and velocity constraints. A settling time regulator is combined to construct the performance function, with which we build a new adaptive fault-tolerant control scheme upon the transferred error, ensuring that the tracking error converges to an adjustably small residual set within the prescribed time with a continuous control action. Furthermore, with the specific velocity transformation techniques, the problem of velocity constraints is transformed into the boundedness of new variables, thus the feasibility conditions are eliminated, and the requirements of constrained boundary functions are relaxed. Theoretical analysis shows that the proposed control method is an effective way to achieve pre-given tracking precision within the prescribed time, while avoiding the issue of explosion of complexity. The prescribed time is independent of system initial conditions and other parameters, and the tracking error will converge asymptotically. Simulation results further demonstrate the effectiveness of the proposed approach.

Prescribed time observer based trajectory tracking control of autonomous underwater vehicle with tracking error constraints

This paper addresses the trajectory tracking control problem of the autonomous underwater vehicle with tracking error constraints and prescribed time convergence. In view of the fact that underwater vehicle is inevitably influenced by unknown external disturbances and input saturation, a disturbance observer is first proposed to achieve prescribed time disturbance attenuation. By virtue of the proposed observer, the observation error will arrive and maintain at a user-defined compact set in a prescribed time, which lays the foundation for subsequent control design. Then, an auxiliary dynamic system with time varying gain is constructed to deal with the input saturation phenomenon. Finally, a robust tracking control scheme is derived by integrating the proposed observer and auxiliary dynamic system into the prescribed performance control architecture, which results in both prescribed time convergence and transient performance constraints in the presence of input saturation and disturbances. Numerical simulation studies are carried out to illustrate the superiority and benefits of the proposed algorithm.

Composite Learning Finite-Time Control of Robotic Systems With Output Constraints

In this article, for robotic systems with uncertain dynamics and time-varying asymmetric output constraints, we present a composite learning finite-time control scheme with salient features benefited from two design steps. In the first step, unlike existing composite adaptive/learning control algorithms, which result in either exponential convergence or finite-time convergence but exhibit a potential singularity issue, a modified nonsingular terminal sliding mode-based composite learning controller is adopted such that both tracking error and parameter estimation error converge to zero in finite time without singularity. The unknown parameter learning law is constructed by using online historical data and regressor extension, which gives a benefit of relaxing the typically required stringent persistent excitation with a much weaker excitation condition termed interval excitation. In the second step, a universal time-varying asymmetric barrier function (UTABF) is adopted to directly constrain the system output rather than the most commonly used barrier Lyapunov function, which indirectly converts the output constraints into the conservative tracking error constraints. Moreover, the UTABF can handle both constrained and unconstrained cases uniformly without the need for changing the control structure. Both theoretical analysis and experiments results on an industrial manipulator confirm the benefits and effectiveness of the proposed control scheme.

스마트 베타 전략에 따른 액티브 주식형 펀드의 최적 추적오차

Purpose - This study introduces a methodology for finding the optimal tracking error of active stock funds. Tracking error is commonly used in risk budgeting techniques as a concept of cost for alpha creation.&#x0D; Design/methodology/approach - This study uses a post-optimal smart beta portfolio that maximizes alpha under the given tracking error constraint.&#x0D; Findings - As a result of the analysis, the smart beta strategy that maximized alpha under the constraint of 0.15% daily tracking error shows the highest IR. This means the maximum theoretically achievable efficiency. In this regard, a fixed-effect panel regression analysis is conducted to evaluate the active efficiency of domestic stock funds. In addition to control variables based on previous studies, the effect of tracking error on alpha is analyzed. The alpha used in this model is calculated using the smart beta portfolio according to the size of the constraint of the tracking error as a benchmark. Contrary to theoretical estimates, in Korea, the alpha performance is maximized under a daily tracking error of 0.1%. This indicates that the active efficiency of domestic equity funds is lower than the theoretical maximum.&#x0D; Research implications or Originality - Based on this study, it is expected that it can be used for active risk management of pension funds and performance evaluation of active strategies.

Nonlinear filtering‐based output tracking error constraint control for permanent magnet synchronous motors with complete unknown coefficients

SummaryThis article investigates the problem of the output tracking error constraint performance for permanent magnet synchronous motors with complete unknown coefficients. First, to achieve the output tracking error constraint performance, an improved barrier Lyapunov function combined with exponent‐type performance is given. Then, to erase the effects of unknown coefficients, adaptive compensation strategy, fuzzy logic systems, and Nussbaum‐type function are utilized, which relax the assumption requirement that the partial coefficients must be known in the related results. Further, to simplify the control design, a novel nonlinear filters‐based dynamic surface control method is presented. Unlike the previous linear filters‐based ones, it can achieve better control performance. It is proved that by utilizing the proposed method, all the signals in the closed‐loop systems are bounded, and also the prescribed output tracking error constraint condition does not violate. Final, simulation example verify the effectiveness of our proposed method.