Output Tracking Research Articles

Performance-Based Distributed Control of Multiagent Systems: A Dual Phase Approach.

In this article, we investigate the distributed tracking control problem for networked uncertain nonlinear strict-feedback systems with unknown time-varying gains under a directed interaction topology. A dual phase performance-guaranteed approach is established. In the first phase, a fully distributed robust filter is constructed for each agent to estimate the desired trajectory with prescribed performance such that the control directions of all agents are allowed to be nonidentical. In the second phase, by establishing a novel lemma regarding Nussbaum function, a new adaptive control protocol is developed for each agent based on backstepping technique, which not only steers the output to track the corresponding estimated signal asymptotically with arbitrarily prescribed transient response but also extends the application scope of the proposed control scheme largely since the unknown control gains are allowed to be time-varying and even state-dependent. In such a way, the underlying problem is tackled with the output tracking error converging into an arbitrarily preassigned residual set exhibiting an arbitrarily predefined convergence rate. Besides, all the internal signals are ensured to be semi-globally ultimately uniformly bounded (SGUUB). Finally, two examples are provided to illustrate the effectiveness of the co-designed scheme.

Robust predictive fault-tolerant control under actuator random failures

A robust predictive fault-tolerant switching control method is presented for a class of industrial processes that are prone to random actuator failures. The primary contribution is the combination of stochastic control theory with robust predictive control to represent the occurrence of system failure in the form of probability, thus significantly enhancing the conventional fault-tolerant control approach. First, a state-space model of the system is established, which is then transformed into an enhanced form that includes state deviations and output tracking errors. This augmented model enables the formulation of fault-tolerant switching control laws with fault probabilities, ensuring system convergence and tracking capabilities. Subsequently, linear matrix inequality constraints are given to find the switching controller gains under recovery and fault probabilities. Under certain probabilities, failure triggers fault-tolerant control, while recovery prompts a shift back to conventional control. Final, we validate the feasibility of our approach with a case study involving pressure regulation.

Adaptive fuzzy tracking control for multiple‐input multiple‐output nonlinear systems with sensor faults and experiment in the flexible‐joint robot

AbstractThis paper is centered on the adaptive asymptotic tracking control of multi‐input multi‐output uncertain strict‐feedback nonlinear systems in the presence of both multiplicative and additive sensor faults. Through adaptive accommodation techniques, the proposed control scheme can dynamically compensate for sensor faults, thereby ensuring precise and stable control. The control scheme is devised using the backstepping design that incorporates positive integrable time‐varying functions, thereby ensuring the boundedness of all signals in the closed‐loop system and guaranteeing that the output tracking error asymptotically converges to zero. Additionally, extensive simulations and experimental evaluations conducted on the Quanser platform with 2‐link flexible‐joint robots demonstrate the efficacy of the proposed control scheme in mitigating the impact of sensor faults and achieving accurate tracking performance.

Infinite-time robust optimal output tracking of continuous-time linear systems using undiscounted reinforcement learning

This research paper focuses on addressing the challenge of infinite-time linear quadratic tracking control (LQT) for linear systems with parametric uncertainty. Traditional solutions to the LQT problem often involve using a discount factor to prevent the cost function from growing unbounded over time. However, this approach can introduce instability in the closed-loop system. To overcome this issue, this paper proposes an alternative approach using an undiscounted cost function that ensures the asymptotic stability of the uncertain closed-loop system. To design a control scheme without requiring precise knowledge of the system dynamics, reinforcement learning (RL) algorithms are employed. However, for systems with uncertain parameters that may lead to instability, the convergence of RL algorithms to a stabilising solution is not guaranteed. To address this limitation, a robust optimal control structure is developed using on-policy and off-policy reinforcement learning algorithms, resulting in a model-free controller. The effectiveness of the proposed robust optimal controller is validated through comparative simulations on an uncertain model of a DC–DC buck converter connected to a constant power load. These simulations demonstrate the advantages and benefits of the robust optimal controller in handling parametric uncertainty and ensuring stability in the control system.

Robust Output Feedback Stabilization and Tracking for an Uncertain Nonholonomic Systems with Application to a Mobile Robot.

This paper presents a novel robust output feedback control that simultaneously performs both stabilization and trajectory tracking for a class of underactuated nonholonomic systems despite model uncertainties, external disturbance, and the absence of velocity measurement. To solve this challenging problem, a generalized normal form has been successfully created by employing an input-output feedback linearization approach and a change in coordinates (diffeomorphism). This research mainly focuses on the stabilization problem of nonholonomic systems that can be transformed to a normal form and pose several challenges, including (i) a nontriangular normal form, (ii) the internal dynamics of the system are non-affine in control, and (iii) the zero dynamics of the system are not in minimum phase. The proposed scheme utilizes combined backstepping and sliding mode control (SMC) techniques. Furthermore, the full-order high gain observer (HGO) has been developed to estimate the derivative of output functions and internal dynamics. Then, full-order HGO and the backstepping SMC have been integrated to synthesize a robust output feedback controller. A differential-drive type (2,0) the wheeled mobile robot has been considered as an example to support the theoretical results. The simulation results demonstrate that the backstepping SMC exhibits robustness against bounded uncertainties.

Output Tracking Predictive Control of Uncertain Networked Control Systems

Output Tracking Predictive Control of Uncertain Networked Control Systems

Adaptive predefined-time tracking control of uncertain permanent-magnet synchronous motor drive chaotic system

A predefined-time tracking control algorithm is formulated for the Permanent Magnet Synchronous Motor(PMSM) driver system subjected to chaotic oscillations and undeterministic parameters, which can determine the upper bound of settling-time by controller gains. Radial Basis Function Neural Networks(RBFNNs) are employed to approximate the unknown nonlinear functions as universal approximators. The innovative predefined-time tracking differentiators are constructed to estimate the derivatives of the virtual inputs, resolving “the explosion of complexity” in traditional backstepping method. Then, an adaptive predefined-time controller is proposed in the backstepping framework. Lyapunov’s theoretical analysis proves that all signals in the closed-loop systems are uniformly ultimately bounded and the output tracking errors can converge to a small neighborhood of the origin within the predefined-time. Finally, simulation studies are performed to demonstrate that the proposed control scheme can quash the chaotic behaviors of the PMSM drive system and ensure fast-tracking performance even under unknown parameters.

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.

Integral reinforcement learning‐based optimal tracking control for uncertain nonlinear systems under input constraint and specified performance constraints

AbstractThis article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.

[formula omitted] output tracking control for polynomial parameter-varying systems via homogeneous Lyapunov methods

This paper investigates the H∞ output tracking control for polynomial parameter-varying systems—a class of nonlinear parameter-varying systems. Based on the homogeneous polynomial Lyapunov function (HPLF), a state feedback controller is presented to make the augmented system (composed of the original system and the tracking error system) robust exponentially stable, so that the output of the original system can track the reference signal and satisfy the H∞ output tracking performance. The conservativeness of the theoretical results is reduced due to the following facts: (1) the HPLF can depend on the full states and time-varying parameters; and (2) there are no constraints on the input coefficient matrix and the inverse of the Lyapunov matrix. In particular, when the system states and time-varying parameters are confined to a compact set, local results are obtained based on the generalized S-procedure. The solvable conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, which can be solved by sum of squares (SOS) techniques. Finally, the feasibility and effectiveness of the proposed method are verified by a numerical example and the heading control of unmanned surface vehicle.

Motion history images: a new method for tracking microswimmers in 3D

Quantitative tracking of rapidly moving micron-scale objects remains an elusive challenge in microscopy due to low signal-to-noise. This paper describes a novel method for tracking micron-sized motile organisms in off-axis Digital Holographic Microscope (DHM) raw holograms and/or reconstructions. We begin by processing the microscopic images with the previously reported Holographic Examination for Life-like Motility (HELM) software, which provides a variety of tracking outputs including motion history images (MHIs). MHIs are stills of videos where the frame-to-frame changes are indicated with color time-coding. This exposes tracks of objects that are difficult to identify in individual frames at a low signal-to-noise ratio. The visible tracks in the MHIs are superior to tracks identified by all tested automated tracking algorithms that start from object identification at the frame level, particularly in low signal-to-noise ratio data, but do not provide quantitative track data. In contrast to other tracking methods, like Kalman filter, where the recording is analyzed frame by frame, MHIs show the whole time span of particle movement at once and eliminate the need to identify objects in individual frames. This feature also enables post-tracking identification of low-SNR objects. We use these tracks, rather than object identification in individual frames, as a basis for quantitative tracking of Bacillus subtilis by first generating MHIs from X, Y, and t stacks (raw holograms or a projection over reconstructed planes), then using a region-tracking algorithm to identify and separate swimming pathways. Subsequently, we identify each object's Z plane of best focus at the corresponding X, Y, and t points, yielding ap full description of the swimming pathways in three spatial dimensions plus time. This approach offers an alternative to object-based tracking for processing large, low signal-to-noise datasets containing highly motile organisms.

Observer-based fuzzy tracking control of nonlinear systems with intermittent output constraints

This paper pays attention to the output tracking control problem of nonlinear systems where the output is uniquely measurable and subject to an intermittent constraint. A multiplicative transformation based on the shifting-replaying function is introduced together with barrier Lyapunov function to solve the intermittent output constraint. A state observer independent of the matching condition of control gains is designed via the non-uniform state transformation to relax the assumption of full-state measurability. By virtue of the estimated states, we propose an output feedback controller that only involves one fuzzy adaptive parameter to restrain the effect of unknown system nonlinearities. Through Lyapunov stability analysis, it is proved that the proposed controller can make all signals in the closed-loop system remain semi-globally uniformly ultimately bounded. Two simulation examples are provided to verify the effectiveness of the proposed method, and also the superiority over the existing ones.

Photovoltaic System Output Analysis and Tracking Method Based on the Surveyed Data

Photovoltaic System Output Analysis and Tracking Method Based on the Surveyed Data

Command filter based input quantized adaptive tracking control for multi‐input and multi‐output non‐strict feedback systems with unmodeled dynamics and full state time‐varying constraints

SummaryThis paper addresses the problem of adaptive tracking control for multi‐input and multi‐output (MIMO) non‐strict feedback systems with unmodeled dynamics and full state time‐varying constraints. To tackle the interference of unmodeled dynamics, the dynamic signal generated by the auxiliary system is used. Hyperbolic tangent function is used as a nonlinear mapping tool to transform the constrained system into an unconstrained one. Hysteresis quantizer is introduced to mitigate the chattering phenomenon and quantization error in the quantization signal. The derivative of virtual signal can be approximated more efficiently by command filter. Furthermore, an error compensation mechanism is established to mitigate the error introduced by the command filter. Unknown nonlinear functions are approximated by radial basis function neural networks (RBFNNs). Stability analysis of the proposed controller is performed through the Lyapunov stability theory and the output tracking error can be constrained within a specified range. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method.

Adaptive neural network finite‐time control for fractional‐order nonlinear systems with external disturbance

AbstractThis paper is concerned with the finite‐time tracking control problem of fractional‐order nonlinear systems (FONSs) with uncertainty and external disturbance. A novel design scheme of the adaptive neural network finite‐time controller (ANNFTC) is developed by utilizing the theory of finite‐time stability and fractional‐order dynamic surface control (DSC) scheme combined with backstepping method. Radial basis function neural networks (RBF NNs) are employed to estimate the unknown nonlinear function. Furthermore, an auxiliary function is introduced to approximate the unknown upper bounds of the approximation error in RBF NNs and external disturbance. The ANNFTC ensures the finite‐time boundedness of all signals in FONSs and enhances the system output's tracking performance. The effectiveness of the proposed approach is demonstrated through a simulation example, providing empirical evidence to support the theoretical framework presented in this paper.

Research on Maximum Power Control of Direct-Drive Wave Power Generation Device Based on BP Neural Network PID Method

Ocean wave energy is a new type of clean energy. To improve the power generation and wave energy conversion efficiency of the direct-drive wave power generation system, by addressing the issue of large output errors and poor system stability commonly associated with the currently used PID (proportional, integral, and derivative) control methods, this paper proposes a maximum power control method based on BP (back propagation) neural network PID control. Combined with Kalman filtering, this method not only achieves maximum power tracking but also reduces output ripple and tracking error, thereby enhancing the system’s control quality. This study uses a permanent magnet linear generator as the power generation device, establishes a system dynamics model, and predicts the main frequency of irregular waves through the Fast Fourier Transform method. It designs a desired current tracking curve that meets the maximum power strategy. On this basis, a comparative analysis of the control accuracy and stability of three control methods is conducted. The simulation results show that the BP neural network PID control method improves power generation and exhibits better accuracy and stability.

Almost sure and mean square convergence of iterative learning control system with state feedback under random packet dropouts

This paper investigates the almost sure and mean square convergence of a state feedback-based iterative learning control scheme for a class of discrete-time multi-input–multi-output linear systems with a direct feedback term in the presence of random data dropouts. Firstly, the realisability of the control system is considered. It is shown that the realisability of the control system is only determined by the direct feedback matrix, which has nothing to do with the input–output coupling matrix, and the direct feedback matrix to be full-row rank is enough to guarantee the system realisable. Secondly, the convergence of output tracking errors is analysed in both the almost sure and mean square senses, respectively. By the contraction mapping method combined with matrix decomposition and transformation techniques, it is strictly proved that the output sequence can converge to any given desired trajectory in the sense of almost sure and mean square, respectively, if and only if the general spectral radius condition is satisfied. Finally, an example is given to show the correctness of the theoretical analysis.

Robust predictive minmax fault‐tolerant control for multi‐phase batch processes under partial actuator faults and asynchronous switching

AbstractIn view of the uncertainties, partial actuator faults, asynchronous switching as well as unknown external interference in multi‐phase batch processes, a robust predictive minmax fault‐tolerant control approach is presented. First, considering that a controller and a system state cannot switch synchronously during switching, a match‐and‐mismatch switching model is constructed. Then, an output tracking error is introduced to establish an equivalent extended switching model. In this extended model, the robust control issue is transformed into the minmax optimization issue by establishing the minmax performance index. On this basis, the control laws with control input and interference input are designed. Second, sufficient conditions are given to assure the system separately has asymptotic and exponential stabilities in each phase and batch. By calculating the given sufficient conditions online, the gains of the control laws, and the minimum and maximum operating time under match and mismatch cases are obtained. With the maximum operating time, the controller receives the switching signal beforehand to eliminate the mismatch case of switching. Additionally, a robust criterion is supplied to confirm the system's robustness. Finally, a simulation study of an injection molding process shows that the approach is valid and feasible.

ITS Efficiency Analysis for Multi-Target Tracking in a Clutter Environment

The Integrated Track Splitting (ITS) is a multi-scan algorithm for target tracking in a cluttered environment. The ITS filter models each track as a set of mutually exclusive components, usually in the form of a Gaussian Mixture. The purpose of this research is to determine the limits of the ‘endurance’ of target tracking of the known ITS algorithm by analyzing the impact of target detection probability. The state estimate and the a-posteriori probability of component existence are computed recursively from the target existence probability, which may be used as a track quality measure for false track discrimination (FTD). The target existence probability is also calculated and used for track maintenance and track output. This article investigates the limits of the effectiveness of ITS multi-target tracking using the method of theoretical determination of the dependence of the measurements likelihood ratio on reliable detection and then practical experimental testing. Numerical simulations of the practical application of the proposed model were performed in various probabilities of target detection and dense clutter environments. Additionally, the effectiveness of the proposed algorithm in combination with filters for various types of maneuvers using Interacting Multiple Model ITS (IMMITS) algorithms was comparatively analyzed. The extensive numerical simulation (which assumes both straight and maneuvering targets) has shown which target tracking limits can be performed within different target detection probabilities and clutter densities. The simulations confirmed the derived theoretical limits of the tracking efficiency of the ITS algorithm up to a detection probability of 0.6, and compared to the IMMITS algorithm up to 0.4 in the case of target maneuvers and dense clutter environments.

Gain scheduled internal model control based on the dynamic sliding mode method for the water level of nuclear steam generators

Abstract The Steam Generator (SG) is a crucial component of a nuclear power plant. Proper water level control in a nuclear steam generator is of great importance to ensure a sufficient cooling source for the nuclear reactor and to prevent damage to turbine blades. The water level control problem of steam generators has been a leading cause of unexpected shutdowns in nuclear power plants, which must be addressed for plant safety and availability. The control problem is challenging, particularly at low power levels due to shrink and swell phenomena and flow measurement errors. Furthermore, the dynamics of the steam generator vary as the power level changes. Therefore, there is a need to enhance the water level control system of the SG. In this paper, a Gain Scheduled Internal Model Control (IMC) based on the Dynamic Sliding Mode (DSMC) method is developed for the level control problem. The proposed method exhibits the desired dynamic properties throughout the entire output tracking process, independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness, and stability. The simulation results confirm the improvement in transient response achieved by using the proposed controller.