System Output Tracking Error Research Articles

Novel quantized iterative learning control based on spherical polar coordinates

AbstractThis study investigates the iterative learning control method for discrete‐time systems with data quantization, and it employs a quantizer based on spherical polar coordinates. The quantizer uses spherical polar coordinates to transform an unquantized signal into one with a predetermined quantization level. The quantization capability is dependent on the size of the support sphere, which is dynamically adjustable. In the scenarios of system output quantization, general quantization, and tracking error quantization, the learning control schemes are developed with consideration of the smallest sphere quantization features. The radii of the support spheres are designed independently based on the characteristics of the quantized signals (system output, control input, tracking error). The findings suggest that the system can achieve a bounded error convergence in the scenarios of system output and general quantization. In the context of quantization in tracking error, it is achievable to attain tracking performance with zero error. The example of a permanent magnet synchronous motor is provided to illustrate the findings of the study.

Segmented hybrid event‐triggered control for underactuated autonomous underwater vehicles with an asymmetrical prescribed performance constraint

AbstractIn this technical article, the trajectory‐tracking problem of event‐based adaptive prescribed performance control for underactuated autonomous underwater vehicles (AUVs) is considered. The primary innovation of this article is the proposal of a segmented event‐triggered mechanism (SETM) that incorporates preselected convergence time. This mechanism allows for the regulation of communication frequency in the control channel (controller‐to‐actuator) according to the dynamic characteristics of the AUV system at different stages. In addition to presenting new design scheme based on SETM, an enhanced vision known as segmented hybrid event‐triggered mechanism (SHETM) is introduced. Notably, the minimum and maximum triggering intervals (MITI and MATI) for these two ETMs can be calculated from the corresponding resettable dynamic variables presented in the trigger conditions. Subsequently, by utilizing the proposed asymmetrical prescribed performance control (APPC) strategy, the system's output tracking error behaviors in both transient and steady‐state stages can be qualitatively predetermined through design parameters within the boundary function. Moreover, the minimum learning parameter (MLP) based RBFNN adaptive control law is developed to counteract the effects of model uncertainties and ocean current perturbations. Finally, rigorous theoretical analysis and simulation results confirm the viability of the proposed scheme.

Monotonically convergent iterative learning control by time varying learning gain revisited

This note considers the problem whether we can design a time-varying learning gain to ensure the monotone convergence of system output tracking errors (SOTEs) in the sense of unweighted 1/2/∞-norm for iterative learning control systems. Firstly, it points that the iterative learning control update law with the exponentially decaying learning factor considered in Moore et al. (2005) cannot ensure the monotonic convergence of SOTEs in the sense of unweighted 1-norm, 2-norm or ∞-norm. Secondly, it is strictly proven that there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted ∞-norm and there is no time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 1-norm. Finally, this paper presents a sufficient condition under which there exists a time-varying learning gain to ensure the monotone convergence of SOTEs in the sense of unweighted 2-norm.

Robust model‐free adaptive longitudinal flight control for a flapping wing micro air vehicle with wind disturbances

AbstractIn this paper, two robust model‐free adaptive control (RMFAC) methods are proposed for a nonlinear flapping wing micro air vehicle (FWMAV) subject to measurable and unmeasurable wind disturbances. Firstly, a novel disturbance‐related full‐form dynamic linearization technique (DFFDL) is developed to transform the FWMAV with measurable disturbances into a dynamic linearization data model. Then, a DFFDL based RMFAC method is designed based on the obtained data model for the FWMAV to suppress the wind disturbances. Next, the stability analysis shows that the system output tracking error converges into a bounded range. And the above result is extended to the case of unmeasurable disturbances. Finally, the simulation comparison results demonstrate the effectiveness of two proposed RMFAC methods.

Predefined‐time control for Euler–Lagrange systems with model uncertainties and actuator faults

SummaryA novel adaptive predefined‐time tracking control algorithm is proposed for the Euler–Lagrange systems (ELSs) with model uncertainties and actuator faults. Compared with traditional finite‐time and fixed‐time studies, the system output tracking error under the proposed predefined‐time controller converges to a small neighborhood of zero in finite time, whose upper bound is exactly a design parameter in the control algorithm. For the uncertain model, radial‐based function neural network (RBFNN) is utilized to approximate the continuous uncertain dynamics. To deal with the actuator faults, an adaptive control law is involved in the fault‐tolerant controller. In order to achieve the predefined‐time bounded, a novel predefined‐time sliding mode surface is designed. It is proved that the tracking error vector trajectory of closed‐loop system is semi‐globally uniformly ultimately predefined‐time bounded, and the upper bounds of both the system settling time and the corresponding output tracking error can be adjusted with a simple parameter. Simulation examples finally demonstrate the effectiveness of the proposed control algorithm.

An improved decentralized finite-time approach for excitation control of multi-area power systems

The complexity of modern power systems has introduced more challenging aspects for stability. These challenges are due to the increase in stressed and constraint conditions. To resolve this issue, a novel adaptive fuzzy decentralized-based finite-time excitation control scheme has been proposed. The proposed scheme is aimed to be deployed for a large scale power systems with output and input constraint requirements. To handle these constraints, the backstepping design with a tan-type barrier Lyapunov function (BLF) is presented. Also, the parametric system uncertainties that model the power system dynamics are approximated using the fuzzy logic systems. This would eventually make the design completely decentralized due to bound-free interactions and constraints. While considering the time-varying constraint requirements on the power system outputs, a finite-time convergence of the power system output tracking errors into a small set around zero is further guaranteed. The proposed control scheme is then validated on a four-area interconnected power system subject to load fluctuations. Numerical results show the efficacy of the proposed approach.

Adaptive event‐triggered synchronization control for bilateral teleoperation system subjected to fixed‐time constraint

SummaryThe time‐constrained positional synchronization control problem for a class of bilateral teleoperation systems is investigated and a novel fixed‐time event‐triggered control scheme is developed. Different from existing methods, the controller is triggered in a nonperiodic manner, which reduces considerably the triggering frequency of control devices. This not only saves communication resource, but also extends the lifespan of system devices because of the reduction of switching times. The control settling time is further considered by introducing a fixed‐time stability theorem. Theoretical analysis as well as a simulation example verifies that the proposed control method can reduce remarkably the amount of control signals transmitted between the master and slave while ensuring that the system output tracking error converges to a small neighborhood close to zero within a fixed‐time frame.

Adaptive fuzzy asymptotic control for switched nonlinear systems with state constraints

This article presents an adaptive fuzzy asymptotic tracking control method for switched nonlinear systems with state constraints. The fuzzy logic systems are employed to dispose the lumped unknown dynamics. The state constraints are addressed with the aid of the barrier Lyapunov function. Moreover, drawing support from some well-defined smooth functions, the asymptotic tracking controller is recursively constructed based on backstepping technique. Through Lyapunov analysis and the common Lyapunov function method, it is shown that the system output tracking error asymptotically converges to zero and all system signals are bounded under the switching signal. Finally, the validity of the developed scheme is elucidated by simulation example.

Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems

This paper addresses the event-triggered tracking control problem of nonlinear systems with predefined performance in a fixed-time environment. Unlike the existing event-triggered schemes, the developed triggering mechanism only compares the difference between the signal to be transmitted and the holding signal. The proposed control method also considers the response of the triggering mechanism. In order to achieve prescribed control performance under the condition of unmatched uncertainties and uncertain gain functions, a new adaptive fixed-time control strategy is proposed by introducing an error transformation scheme. The proposed control method under the event-triggered framework can reduce the amount of control signals transmitted while ensuring that the system output tracking error converges to a small neighborhood close to zero within a fixed-time frame. The results of two examples, including comparative studies and a practical application, show the effectiveness of the proposed control method.

Improved Constrained Model Predictive Tracking Control for Networked Coke Furnace Systems Over Uncertainty and Communication Loss

This paper proposes an improved constrained networked model predictive tracking control design for the chamber pressure of a coke furnace under uncertainty and packet losses. Unlike conventional constrained model predictive control (MPC) strategies that have a limitation in the consideration of both set-point tracking and the dynamic process responses, the system state variables and output tracking errors are combined and thus can be regulated simultaneously in the new MPC scheme. Based on such advantages, there are more degrees of freedom for the subsequent controller design and improved system performance can then be obtained. Case studies on the regulation of chamber pressure of a coke furnace under process uncertainties and packet losses are investigated to verify the proposed approach in comparison with typical traditional constrained MPC schemes.

Neural Network Adaptive Tracking Control of Uncertain MIMO Nonlinear Systems With Output Constraints and Event-Triggered Inputs.

This article is concerned with a neural adaptive tracking control scheme for a class of multiinput and multioutput (MIMO) nonaffine nonlinear systems with event-triggered mechanisms, which include the fixed thresholds, triggering control inputs, and decreasing functions of tracking errors. Unlike the existing results of nonaffine nonlinear controller decoupling, a novel nonlinear multiple control inputs separated design method is proposed based on the mean-value theorem and the Taylor expansion technique. By this way, a weaker condition of nonlinear decoupling is provided to instead of the previous ones. Then, introducing a prescribed performance barrier Lyapunov function (PPBLF) and using neural networks (NNs), the presented event-triggered controller can maintain better tracking performance and effectively alleviate the computation burden of the communication procedure. Furthermore, it is proved that all the closed-loop signals are bounded and the system output tracking errors are confined within the prescribed bounds. Finally, the simulation results are given to demonstrate the validity of the developed control scheme.

Adaptive Fuzzy Tracking Control for a Class of Uncertain Switched Nonlinear Systems With Full-State Constraints and Input Saturations.

In this article, an adaptive fuzzy tracking control scheme is developed for a class of uncertain switched nonlinear systems with input saturations and full-state constraints. First to surmount the design difficulty with respect to a saturation nonlinearity controller, a nonlinear smooth function approximating the nondifferential saturation function is introduced to establish a standard switched adaptive tracking control strategy based on the mean-value theorem and the input compensation technique. Then, invoking fuzzy-logic systems (FLSs), a novel analysis method of average dwell time for switched nonlinear systems with full-state constraints is proposed by using an artful logarithmic inequality. Furthermore, the designed adaptive controller can ensure that all the states of uncertain switched nonlinear systems are not to violate the set constraint bounds by employing barrier Lyapunov functions (BLFs), and that the system output tracking error can converge to a desired neighborhood of the origin within a suitable compact set. Finally, the simulation results are given to demonstrate the validity of the presented approach.

Fuzzy Adaptive Event-Triggered Control for a Class of Uncertain Nonaffine Nonlinear Systems With Full State Constraints

This article is concerned with the fuzzy adaptive tracking control problem for a class of uncertain nonaffine nonlinear systems with full state constraints and event-triggered inputs. First, based on the mean-value theorem and the input compensation method, the control input signal of nonaffine nonlinear term is successfully decoupled, and the remained compound nonlinear function can be approximated by fuzzy logic systems. Then, an improved event-triggered control strategy including the fixed threshold, the event-trigger control input, and the decreasing function of tracking errors, is given to update the actual control input. Correspondingly, the computation burden of the communication procedure is effectively alleviated. In addition, the developed control scheme guarantees that all the states of the closed-loop systems are not to violate the predefined compact sets by constructing barrier Lyapunov functions. Also, the system output tracking error can converge to a desired neighborhood of the origin. Finally, the validity of the proposed approach is demonstrated by the simulation results.

Event-Triggered Output Feedback Control for MEMS Gyroscope With Prescribed Performance

This paper investigates an event-triggered output feedback control problem with guaranteed tracking performance for microelectromechanical system (MEMS) gyroscope subject to the lumped disturbances, including parameter uncertainties, coupling between driving mode and sensing mode, and unknown external disturbances. Firstly, to make the system output tracking errors evolve within the predetermined performance envelopes, a prescribed performance control (PPC) is employed in our controller design, such that a prescribed trajectory tracking with preselected settling time and steady-state tracking accuracy can be ensured. Besides, to simultaneously realize disturbance rejection and estimation of the immeasurable velocity state, linear extended state observers (LESOs) are designed to reconstruct the lumped disturbances and immeasurable velocity states for both MEMS gyroscope driving and sensing modes. In general, excessively energy and resource consumption are fundamentally neglected in most of the existing output feedback controllers for MEMS gyroscope, which will dramatically reduce the operational time of the close-loop system. To address this problem, we embed a fixed threshold event-triggered mechanism into the controller design procedure, such that the communication data size can be drastically reduced without sacrificing the tracking accuracy. Finally, to obtain the close-loop stability for MEMS gyroscope, robust control laws are designed to compensate for the measurement error and estimation error, meanwhile Zeno phenomena can be effectively eliminated. The simulation results and comparisons validate the effectiveness of the proposed scheme.

Robust Tracking Control of Variable Stiffness Joint Based on Feedback Linearization and Disturbance Observer With Estimation Error Compensation

The variable stiffness joint (VSJ) has the characteristics of independent and controllable position and stiffness. The variable stiffness characteristics and inherent flexibility make the VSJ suitable to be used as the actuation joint of the physical human-robot interaction application robot, so as to improve the task adaptability of the robot and physical human-robot interaction safety. The VSJ based on equivalent lever mechanism has the advantages of low energy consumption in stiffness adjustment, so there are many researches on this type of VSJ. The tracking control of output link angular position and joint output stiffness are two basic control targets of the VSJ. For the system dynamic model of the VSJ based on equivalent lever mechanism, considering the unknown parametric perturbations, the unknown friction torques acting on the drive units, the unknown external disturbance acting on the output link and the control input saturation constraints, a robust tracking controller based on feedback linearization, disturbance observer with anti-windup measures, sliding mode control and estimation error compensator is designed to improve the tracking control accuracy of the position and stiffness of the VSJ. The simultaneous tracking control of position and stiffness of the VSJ can be achieved by the designed controller, and the simulation results show the effectiveness and robustness of the proposed controller. Moreover, the simulation results show that the proposed estimation error compensator for the disturbance observer with fixed preset observation gain can effectively reduce the system output tracking error and improve the anti-disturbance characteristics of the controller.

TABLF-based adaptive control for uncertain nonlinear systems with time-varying asymmetric full-state constraints

ABSTRACT In this paper, we investigate the tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and time-varying asymmetric full-state constraints. By introducing novel tan-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design, the boundedness of the fictitious state tracking errors are ensured. A novel adaptive backstepping control design based on tuning function is given, which successfully eliminates the effect of uncertainties. In addition, only one parameter needs to be adjusted online in the control design, which greatly alleviates the computation burden. Based on the proposed control scheme the asymptotic convergence of system output tracking error is realised and the time-varying full-state constraints are not violated for all the time. A numerical example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive Fixed-Time Control for MIMO Nonlinear Systems With Asymmetric Output Constraints Using Universal Barrier Functions

In this note, we propose a novel adaptive fixed-time control scheme for output tracking problems of a class of multi-input multi-output (MIMO) nonlinear systems with asymmetric output constraint requirements, using a new universal barrier function . It is universal in the sense that the proposed scheme is a general one that also works for systems with symmetric constraints or without constraint requirements, without changing the control structure. Novel adaptive estimations and analysis are introduced to address system uncertainties in the fixed-time convergence settings. We show that under the proposed novel control scheme, each element in the system output tracking error vector of the MIMO nonlinear system can converge into small sets near zero with fixed-time convergence rate, while the asymmetric output constraint requirements on each element of the output tracking error are satisfied at all time. The proposed scheme can effectively deal with unmatched system uncertainties and uncertain gain functions. In the end, a simulation example on a two-degree-of-freedom robot manipulator is presented to demonstrate the efficacy of the proposed scheme.

Robust bang-bang control of disturbed nonlinear systems based on nonlinear observers

This paper proposes a robust bang-bang controller (RBC) based on the high-gain nonlinear observer for a nonlinear system with intermittent disturbances. The intermittent disturbances are able to model the system faults and sudden changes of operating conditions of practical nonlinear systems. A bang-bang constant funnel controller (BCFC) is employed, and the largest control capabilities of the control system is explored to stabilize the nonlinear system against the disturbances. The BCFC functions with the estimates of tracking error of control target and its derivatives estimated with a high-gain state observer, which eliminates the requirement on the derivative calculations of the system output tracking error. The error convergence of the observer is verified. The closed-loop stability of the RBC is proved in a bounded-input bounded-state sense. Simulation studies are undertaken with a single-machine infinite-bus (SMIB) power system to test the performance of the RBC.

Adaptive fuzzy asymptotically tracking control of full state constrained nonlinear system based on a novel Nussbaum-type function

This study carries out the problem of adaptive backstepping fuzzy tracking control for a class of full state constrained uncertain nonlinear system with unknown control directions. Based on Nussbaum-type functions and tan-type Barrier Lyapunov functions, a novel adaptive fuzzy tracking controller is proposed to guarantee that the system output tracking error asymptotically converges to zero, while the constraints on the states of system will not be violated during operation. Compared with the existing results, a better convergence effect is obtained for this class of systems. Stability analysis of the proposed closed-loop control system is supported by the Lyapunov stability theory. Finally, a simulation example is presented to illustrate the effectiveness of the proposed control strategy.

Design of Optimal Hybrid Controller for Multi-Phase Batch Processes With Interval Time Varying Delay

Concerning two dimensional (2D) multi-phase batch processes, a delay-range-dependent optimal hybrid iterative learning control (2D-OILC) scheme is presented. Firstly, the process is converted into a 2D-FM time delay switched system in different dimensions by introduction of state errors and system output tracking errors among batches. According to this model, hybrid iterative learning control is combined with feedback control and a 2D optimal hybrid controller is designed. Secondly, the average dwell time method is adopted to give sufficient conditions for system robust stability in terms of linear matrix inequalities and the upper bound for system's optimal performance index is provided. Besides, the issue of optimal controller design is presented to draw the minimum upper limit of the closed-loop system performance index. The presented control law not only can make the closed-loop system preserving good tracking performance but also ensures its $H_{\infty }$ performance. Last but not least, the validity of the above strategies is proved by the simulation on an injection molding process.