Barrier Composite Energy Function Research Articles

Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Distributed Learning Control for High-Speed Trains Subject to Operation Safety Constraints.

Trajectory tracking problems related to high-speed trains (HSTs) are fundamental issues that affect the operation safety and ride comfort. This study proposes a distributed learning control scheme based on a multiagent system framework for trajectory tracking of HSTs subject to operation safety constraints. Two different connection modes are considered between the carriages: 1) a soft connection achieved via information exchange and 2) a hard connection enforced via couplers. Both relative displacement and speed constraints are carefully analyzed in the tracking control process. By constructing an appropriate barrier composite energy function, the convergence of the tracking error and satisfaction of the operation safety constraints are rigorously proven for the proposed scheme. The theoretical results are verified using numerical simulations.

Adaptive Iterative Learning Fault-Tolerant Control for State Constrained Nonlinear Systems With Randomly Varying Iteration Lengths.

This article presents an adaptive iterative learning fault-tolerant control algorithm for state constrained nonlinear systems with randomly varying iteration lengths subjected to actuator faults. First, the modified parameters updating laws are designed through a new defined tracking error to handle the randomly varying iteration lengths. Second, the radial basis function neural network method is used to deal with the time-iteration-dependent unknown nonlinearity, and a barrier Lyapunov function is given to cope with the state constraint. Finally, a new barrier composite energy function is used to achieve the tracking error convergence of the presented control algorithm along the iteration axis with the state constraint and then followed with the extension to the high-order case. A simulation for a single-link manipulator is given to illustrate the effectiveness of the theoretical studies.

Iterative Learning Control of Constrained Systems With Varying Trial Lengths Under Alignment Condition.

This brief is concerned with iterative learning control (ILC) of constrained multi-input multi-output (MIMO) nonlinear systems under the state alignment condition with varying trial lengths. A modified reference trajectory is constructed to meet the alignment condition by adjusting the reference trajectory to be spatially closed. Resorting to the barrier composite energy function (BCEF) approach, an adaptive ILC scheme is built to guarantee the bounded convergence of the resultant closed-loop system. Illustrative examples are presented to verify the validity of the proposed iteration scheme.

Iteration Learning Control for Uncertain Nonlinear Systems with Time-Varying Output Constraint

A novel Adaptive Iteration Learning Control (AILC) method is proposed to solve the trajectory tracking problem for a class of nonlinear uncertain systems with external disturbances. Furthermore, the output of system is required to be bounded by a time-varying function. To this end, a Barrier Lyapunov Function (BLF) term is integrated into the AILC scheme such that the impact of the uncertainties and disturbances are significantly reduced without violating the output constraints. A Barrier Composite Energy Function (BCEF) is utilized to analyze the convergence of state error and the boundedness of output. The validity of the proposed AILC scheme is verified by a numerical example. In addition, a high-fidelity simulation platform that can generate a real-life turbulent flow is utilized to demonstrate the robustness of the algorithm.

Completely distributed neuro-learning consensus with position constraints and partially unknown control directions

In this paper, we propose a new neural network-based iterative learning leader-less consensus control algorithm for the second-order uncertain time-varying nonlinear multi-agent systems, where the position of each agent is constrained in an open interval which can be pre-selected and the control direction can be non-identical and partially unknown. With the help of a novel barrier composite energy function and multiple piece-wise Nussbaum functions, the designed completely distributed learning protocols can make the positions and velocities of the agents achieve the exact consensus on a finite time interval as the iteration number increases to infinity. Meanwhile, the position trajectories of the agents at each iteration do not exceed the constraints bounds. Besides, to testify the feasibility and utility of the presented algorithm, two simulation examples are given in the end.

Disturbance observer‐based adaptive boundary iterative learning control for a rigid‐flexible manipulator with input backlash and endpoint constraint

SummaryIn this article, an observer‐based adaptive boundary iterative learning control law is developed for a class of two‐link rigid‐flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.

RBFNN-Based Adaptive Iterative Learning Fault-Tolerant Control for Subway Trains With Actuator Faults and Speed Constraint

In this article, a radial basis function neural network-based adaptive iterative learning fault-tolerant control (RBFNN-AILFTC) algorithm is developed for subway trains subject to the time-iteration-dependent actuator faults and speed constraint by using the multiple-point-mass dynamic model. First, the RBFNN is utilized to approximate the time-iteration-dependent unknown nonlinearity of the subway train system; then, the iterative learning mechanism is used to tackle the outstanding repetitive operational pattern of a subway train which runs from one station to the next strictly according to the operation timetable schedule every day within the finite time interval, and the adaptive mechanism is designed for dealing with the time and the iteration-varying factors of the subway train. Second, a barrier composite energy function technique is exploited to obtain the convergence property of the proposed RBFNN-AILFTC scheme for subway train system, which can guarantee that the tracking error is asymptotic convergence along the iteration axis, meanwhile keep the speed profile of the subway train system satisfies the constraint. Finally, a subway train simulation is shown to verify the effectiveness of the theoretical studies.

Dual-Loop Adaptive Iterative Learning Control for a Timoshenko Beam With Output Constraint and Input Backlash

In this paper, vibration control and output constraint are considered for a Timoshenko beam system with input backlash and external disturbances. By integrating iterative learning control (ILC) into adaptive control, two dual-loop adaptive ILC schemes are proposed in the presence of the input backlash. Two observers are designed to estimate two bounded terms, which are divided from the backlash inputs. Based on the defined barrier composite energy function, all the signals are proved to be bounded in each iteration. Along the iteration axis: 1) the endpoint transverse displacements and the endpoint angle displacements are restrained; 2) the transverse vibrations and the rotation vibrations are suppressed to zero; and 3) the spatiotemporally varying disturbance and the time-varying disturbances are rejected. Simulations are provided to manifest the effectiveness of the proposed control laws.

Composite Energy Function-Based Spatial Iterative Learning Control in Motion Systems

In this brief, a novel spatial iterative learning control (ILC) method is proposed for a class of high-order nonlinear motion systems in the presence of both parametric and nonparametric uncertainties. Since the system performs the tracking task iteratively in the spatial domain and the uncertainties are functions of spatial coordinates, the traditional ILC that updates the control signals in the time domain is not applicable. The proposed spatial ILC aims at improving the system tracking performance by making full use of the spatial periodicity. First, the dynamics of the motion systems are converted from the temporal domain to the spatial domain via feedback linearization. Then, the learning law is designed to tackle the system uncertainties. By utilizing a newly defined space-based barrier composite energy function, the boundedness and the convergence of state tracking error are ensured rigorously. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC scheme.

Distributed learning consensus for heterogenous high-order nonlinear multi-agent systems with output constraints

This paper considers the learning consensus problem for heterogenous high-order nonlinear multi-agent systems with output constraints. The dynamics consisting of parameterized and lumped uncertainties is different among different agents. To solve the consensus problem under output constraints, two distributed control protocols are designed with the help of a novel barrier Lyapunov function, which drives the control updating and parameters learning. Both convergence analysis and constraint satisfaction are strictly proved by the barrier composite energy function approach. Illustrative simulations are provided to verify the effectiveness of the proposed protocols.

Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints

SummaryThis paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ‐type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively from both theoretical and practical viewpoints. These schemes include the original adaptive scheme, projection‐based scheme, smooth function‐based scheme and its alternative, and dead‐zone–like scheme. The consensus convergence and constraints guarantee are strictly proved for each control scheme by using the barrier composite energy function approach. Illustrative simulations verify the theoretical analysis.

Adaptive iterative learning control for nonlinear uncertain systems with both state and input constraints

This work proposes a new adaptive iterative learning control (AILC) scheme for nonlinear systems with both state and input constraints, where the time-varying parametric uncertainties, external disturbances, and random initial errors are also considered together. The proposed AILC consists of a learning control law and two fully projected parameter learning laws. By incorporating a barrier composite energy function into the learning control law and using a projection mechanism for the parameter learning laws, the proposed AILC can flexibly and actively manipulate the states and inputs of the system into their pre-specified and constrained ranges, respectively. It is theoretically shown that the asymptotic and pointwise convergence properties are guaranteed without violating any state and input constraints. The validity of the proposed AILC scheme is further verified with a practical train operation system.

Iterative Learning Control of a Nonlinear Aeroelastic System despite Gust Load

The development of a control strategy appropriate for the suppression of aeroelastic vibration of a two-dimensional nonlinear wing section based on iterative learning control (ILC) theory is described. Structural stiffness in pitch degree of freedom is represented by nonlinear polynomials. The uncontrolled aeroelastic model exhibits limit cycle oscillations beyond a critical value of the free-stream velocity. Using a single trailing-edge control surface as the control input, a ILC law under alignment condition is developed to ensure convergence of state tracking error. A novel Barrier Lyapunov Function (BLF) is incorporated in the proposed Barrier Composite Energy Function (BCEF) approach. Numerical simulation results clearly demonstrate the effectiveness of the control strategy toward suppressing aeroelastic vibration in the presence of parameter uncertainties and triangular, sinusoidal, and graded gust loads.

Iterative learning control for train trajectory tracking under speed constrains with iteration-varying parameter

An iterative learning control based on Automatic Train Operation is proposed for repetitively running train to deal with trajectory tracking problem under iteration-varying operation condition and certain speed constrains. Iteration-varying operation condition considered in this paper focuses on the air resistance coefficient of the train, which may be completely different at any two consecutive operation processes due to different weather conditions. To eliminate the influence of the resistance coefficient caused by the different weather conditions, data measured by the temperature sensors is used. In order to meet the speed constrains, the Barrier Composite Energy Function scheme is used to guarantee that the speed constraints are not violated. The effectiveness of the proposed method is verified by theoretical analysis and numerical simulation.

Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties

In this work, by proposing a Barrier Composite Energy Function (BCEF) method with a novel Barrier Lyapunov Function (BLF), we present a new iterative learning control (ILC) scheme for a class of single-input single-output (SISO) high order nonlinear systems to deal with output-constrained problems under alignment condition with both parametric and nonparametric system uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. Backstepping design with the newly proposed BLF is incorporated in analysis to ensure output constraint not violated. Through rigorous analysis, we show that under this new ILC scheme, uniform convergence of state tracking error is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

A barrier composite energy function approach for robot manipulators under alignment condition with position constraints

SUMMARY In this work, we propose an iterative learning control scheme with a novel barrier composite energy function approach to deal with position constrained robotic manipulators with uncertainties under alignment condition. The classical assumption of initial resetting condition is removed. Through rigorous analysis, we show that uniform convergence is guaranteed for joint position and velocity tracking error. By introducing a novel tan-type barrier Lyapunov function into barrier composite energy function and keeping it bounded in closed-loop analysis, the constraint on joint position vector will not be violated. A simulation study has further demonstrated the efficacy of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.

State-Constrained Iterative Learning Control for a Class Of MIMO Systems

In this note, we present a novel iterative learning control (ILC) method for a class of state-constrained multi-input multi-output (MIMO) nonlinear system under state alignment condition with both parametric and nonparametric uncertainties. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. Barrier Composite Energy Function (BCEF) scheme with a novel Barrier Lyapunov Function is proposed to facilitate the analysis of state tracking error convergence while satisfying the state constraints. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC method.