Nonlinear Transformation Function Research Articles

Virtual cleaning of sooty mural hyperspectral images using the LIME model and improved dark channel prior

Murals, as important carriers of cultural heritage and historical records, showcase artistic, aesthetic, social, and political significance. In ancient times, religious activities such as burning incense and candles in temples led to many murals being polluted by soot, causing them to darken, lose details, and, in severe cases, completely blacken. As a result, the development of efficient virtual cleaning methods has become a key strategy for addressing this issue. In this study, we use synthetic true colour and false colour images in different bands of the hyperspectral spectrum, and use a guided filter fusion technique to fuse these two images into a new image of the sooty mural. Through analyzing the histograms and colour distribution scatterplots of the synthetic sooty mural images, we observed significant similarities to low-luminance images. To enhance the synthesized murals, we applied the LIME model. In addition, comparisons of the histograms and colour distribution scatterplots of the enhanced sooty mural images with those of haze images revealed notable similarities. Therefore, we applied the dark channel prior algorithm to remove soot from the mural images. Considering that soot particles are larger than haze particles, we introduced guided filtering to refine the transmission map and created a nonlinear transformation function to enhance its details. In terms of both visual perception and quantitative analysis, the proposed method significantly outperforms previous methods in the virtual cleaning of sooty murals. This technology can not only restore the colours and details of murals but also provide new clues for subsequent mural studies, allowing people to once again appreciate the true beauty of the murals.

Robust adaptive asymmetric state constraint control of brush DC motor systems driving a one-link robot manipulator: A feasibility-condition-free method

In this paper, we investigate the tracking control problem for a class of brush direct current (DC) motor systems driving a one-link robot manipulator subject to asymmetric full-state constraints. By constructing a state-dependent nonlinear transformation function (NTF), we present an adaptive robust dynamic surface control (DSC) strategy that can directly address both symmetric and asymmetric state constraints, so that there is no need to convert the problem of state constraint into the constraints on tracking errors as necessitated by the Barrier Lyapunov Function (BLF)-based existing works. Furthermore, by employing the first-order filter and constructing a new coordinate transformation, the demanding feasibility condition imposed on the BLF methods is removed, allowing the designer more freedom to select design parameters. Moreover, it is worth mentioning that under the proposed nonlinear transformation function the extra condition on the constraining function is not required. The effectiveness of the proposed control is verified via the Simulation results.

Adaptive event-triggered finite-time prescribed performance control of PMSM stochastic system considering time-varying delays

This paper investigates the finite-time prescribed performance tracking control problem of permanent magnet synchronous motor (PMSM) considering stochastic disturbances and time-varying delays under event-triggered mechanism. A quintuple polynomial finite-time prescribed performance function (FPPF) is introduced to ensure the transient and steady-state performance of the system output, and a nonlinear transformation function is employed to convert the constrained error into an unconstrained one. The Lyapunov-Krasovskii function is constructed to address time delays. And the system uncertainties are approximated by the radial basis function neural networks (RBFNN). For the “explosion of complexity” caused by backstepping method, a tracking differentiator (TD) is employed. By combining finite time control, command filtering backstepping control, and event-triggered mechanism, the effect of the filter errors is decreased, and the update frequency of the control signals are reduced. It is shown that the proposed controller can guarantee finite time convergence bounded of all signals in the closed-loop system, and the tracking error can converge in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

Dynamical analysis and event-triggered adaptive finite-time prescribed performance control of the FO coupled MEMS resonators

This paper explores the dynamic behaviors and control method of weakly coupled micro-electro-mechanical system (MEMS) resonators with fractional-order (FO) dynamics. In the dynamics analysis session, Lyapunov exponents, bifurcation theory, and phase diagrams are used to analyze the effects of system parameters, coupling stiffness, and FO on the complex dynamical behaviors such as periodicity, pseudo-periodicity, and chaos oscillations. To suppress chaotic oscillations, a dynamic event-triggered finite-time prescribed performance controller is proposed. The unknown nonlinear functions are approximated through the interval type-3 fuzzy system (IT3FS) with an adaptive law. A novel finite-time prescribed performance function (finite-time PPF) is constructed to establish constrained boundaries for tracking errors. Compared with the existing PPFs, the proposed approach allows for more flexible setting of the convergence boundary before reaching steady-state. Subsequently, the constrained tracking errors are mapped to an unconstrained form using a nonlinear transformation function, whether the error constraint is symmetric or asymmetric. To circumvent the “explosion of complexity” arising from backstepping design process, a tracking differentiator (TD) is utilized. Additionally, to alleviate strain on communication resources, an event-triggered mechanism is devised to update control signals. The trigger threshold of the control signals can be adaptively adjusted based on the values of the Lyapunov function and the dynamic auxiliary variables. This control method guarantees finite-time convergence for all signals of the system. Finally, extensive simulations are performed to verify the effectiveness of the proposed algorithm.

Position constrained adaptive time-varying formation control of autonomous surface vessels with uncertain dynamics

This paper investigates the adaptive time-varying formation control problem of autonomous surface vessels (ASVs) with position constraints, uncertain dynamics and external disturbances under directed communication topology. Different from the existing studies, the nonlinear error transformation function is combined with formation control to achieve position constraints of ASVs. Based on dynamic surface control and backstepping method, a virtual control law is designed for each vessel. Radial basis function neural networks are employed to approximate the unknown nonlinear continuous function caused by ASVs’ model uncertainties, and the minimum learning parameter (MLP) method is applied to reduce computational complexity. Then, a time-varying formation position constrained controller and an adaptive law are proposed for each ASV. By using the Lyapunov stability theory, it is proved that all signals of the closed-loop ASV system are semi-global uniformly ultimately bounded and the position constrained objective can be achieved. Finally, simulation analyses are given to verify the effectiveness of theoretical results.

Bipartite containment control of nonlinear multi‐agent systems with unknown inputs and state constraints

SummaryThis article addresses the issue of bipartite containment tracking for nonlinear strict feedback multi‐agent systems (MASs) with disturbances and measurement uncertainties. To provides a better performance against strong disturbance, a coordination transformation is applied such that all the nonlinear functions, controller disturbances and measurement uncertainties are lumped into a single disturbance signal in the last state equation. Then, the lumped disturbance is compensated through a novel disturbance rebuilding method. Moreover, in order to get better control performance, state constraints are also considered through a nonlinear transformation function (NTF). Different from traditional methods dealing with the state constraint problems, the NTF method can avoid using any discontinuous Lyapunov function. Finally, an adaptive finite‐time distributed controller is established via the disturbance estimates, backstepping technique and fuzzy logic system (FLS). The performance of the controller is illustrated by a simulation example in which the bipartite containment formation of followers is realized in a practical finite time.

Determination of multi-UAVs formation shape: Using a requirement satisfaction and spherical fuzzy ANP based TOPSIS approach

Multiple unmanned aerial vehicles (multi-UAVs) formation shape refers to the geometric shape when multi-UAVs fly in formation and describes their relative positions. It plays a necessary role in multi-UAVs collaboration to improve performance, avoid collision, and provide reference for control. This study aims to determine the most appropriate multi-UAVs formation shape in a specific mission to meet different and even conflicting requirements. The proposed approach introduces requirement satisfaction and spherical fuzzy analytic network process (SFANP) to improve the technique for order preference by similarity to ideal solution (TOPSIS). First, multi-UAVs capability criteria and their evaluation models are constructed. Next, performance data are transformed into requirement satisfaction of capability and unified into a same scale. Qualitative judgments are made and quantified based on spherical fuzzy sets and nonlinear transformation functions are developed for benefit, cost, and interval metrics. Then, SFANP is used to handle interrelationships among criteria and determine their global weights, which takes decision vagueness and hesitancy into account and extends decision-makers’ preference domain onto a spherical surface. Finally, alternative formation shapes are ranked by their distances to the positive and negative ideal solution according to the TOPSIS. Furthermore, a case study of 9 UAVs performing a search-attack mission is set up to illustrate the proposed approach, and a comparative analysis is conducted to verify the applicability and credibility.

СПОСІБ ОЦІНКИ ЙМОВІРНІСНИХ ХАРАКТЕРИСТИК СИГНАЛІВ В УМОВАХ НЕЛІНІЙНОСТІ ВИМІРЮВАЛЬНОГО КАНАЛУ ПЕРЕТВОРЮВАЧІВ ОБЕРТАЛЬНОГО МОМЕНТУ

The paper proposes a method for calculating the probabilistic characteristics of signals for a wide class of nonlinear torque transducers. The presented approach is based on modeling the process of processing the input signal, taking into account the multiplicative error of the transducer. A methodology has been developed for estimating the probability density function and numerical characteristics of the output signal of a nonlinear torque transducer for different distribution laws of the input signal and types of nonlinear transformation functions. To achieve this goal, the following steps were performed: algorithms and computer programs were developed for numerical simulation and calculation of the characteristics of signals at the output of a nonlinear transducer for given input parameters, a series of computational experiments were conducted for different combinations of distribution laws of input signals and nonlinear transformation functions, the influence of different distribution laws of the input signal on the probability density function and numerical characteristics of the output signal was investigated, the influence of different types of nonlinear transformation functions on the probability density function and numerical characteristics of the output signal was studied, the obtained results were analyzed, and recommendations were formulated for the choice of the nonlinear transformation function and the distribution law of the input signal to achieve the desired characteristics of the output signal of the torque transducer. The paper discusses the features of the proposed algorithm, as well as the simulation results for a number of examples of transducers with different nonlinear characteristics and parameters of multiplicative disturbance. An analysis of the accuracy of the obtained estimates of probabilistic characteristics is carried out. The developed algorithm allows estimating the probabilistic characteristics of the output signals of nonlinear torque transducers at the design stage, which contributes to improving the quality of the development of control systems. This method can be useful for engineers and scientists involved in the design and analysis of automatic control systems with nonlinear elements.

Adaptive state feedback control of output‐constrained stochastic nonlinear systems with stochastic integral input‐to‐state stability inverse dynamics

AbstractThis article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method.

Event-Triggered Prescribed Settling Time Consensus Compensation Control for a Class of Uncertain Nonlinear Systems With Actuator Failures.

For a class of uncertain nonlinear systems with actuator failures, the event-triggered prescribed settling time consensus adaptive compensation control method is proposed. The unknown form of actuator failures may occur in practical applications, resulting in system instability or even control failure. In order to effectively deal with the above problems, a neural network adaptive control method is developed to ensure that the system states rapidly converge in the event of failure and compensate for the failures of actuator. Meanwhile, a nonlinear transformation function is introduced to make sure that the tracking error converges for the predefined interval within a prescribed settling time, which makes that the convergence time can be preset. Furthermore, a finite-time event-triggered compensation control strategy is established by the backstepping technology. Under this strategy, the system not only can rapidly stabilize in finite time but also can effectively save network bandwidth. In addition, the states of the system are globally uniformly bounded. Finally, the theoretical analysis and simulation experiments validate the effectiveness of the proposed method.

Fixed-Time Distributed Adaptive Formation Control for Multiple QUAVs With Full-State Constraints

This paper devises a fixed-time distributed adaptive formation control algorithm under the event-triggered framework to guarantee the expected formation pattern for multiple quadrotor unmanned aerial vehicles (QUAVs) with full-state constraints. The multiple QUAVs subject to full-state constraints are transformed into the ones that are free from any constraints via a time-varying nonlinear transformation function (NTF), which is effective to handle the case regardless of whether there exist state constraints. The issue of “explosion of complexity” (EOC) as well as singularity problem are fully coped via the fixed-time command filter and the smooth switch function, respectively. To further improve the control performance of multiple QUAVs, the nonsmooth error compensation mechanism is constructed to compensate the filtered error resulting from command filter. The rigorous stability analysis of the developed event-trigger-based distributed formation control scheme proves that all signals of the closed-loop system are fixed-time bounded, and the states of multiple QUAVs will not violate the prescribed constraints and the formation tracking errors converge to a small region around the origin in a fixed time. Finally, simulation examples are performed to delineate the validity of the proposed distributed formation control algorithm.

Neural-Network-Based Adaptive Control of Uncertain MIMO Singularly Perturbed Systems With Full-State Constraints.

This article investigates the tracking control problem for a class of nonlinear multi-input-multi-output (MIMO) uncertain singularly perturbed systems (SPSs) with full-state constraints. The underlying issues become more challenging because two-time-scale characteristics and full state constraints are involved. To this end, first, the adaptive neural network (NN) control method is designed to handle system uncertainties in the design process. Second, the nonlinear state-dependent coordinate transformation functions are employed to avoid the violation of full-state constraints and feasibility conditions for intermediate controllers. Furthermore, by introducing an appropriate ϵ-dependent Lyapunov function, the potential ill-conditioned numerical problems in the design process of SPSs are avoided, and the stability of the nonlinear SPSs is proven. Finally, two examples are presented to illustrate the validity of the proposed adaptive NN control scheme.

Adaptive fault-tolerant control for high-order fully actuated system with full-state constraints

This paper studies the adaptive tracking control problem for a class of uncertain high-order fully actuated (HOFA) systems with actuator faults and full-state constraints. Firstly, we design a novel nonlinear transformation function (NTF) only related to state and constraint boundaries and capable of handling asymmetric time-varying constraints. With the designed function, we obtain an equivalent totally unconstrained HOFA model which is generally simpler to design controllers than first-order state-space model. Then, the adaptive fault-tolerant controller is constructed with the help of the HOFA approach. By applying the Lyapunov stability theory, it is rigorously proved that the output tracking error converges to zero asymptotically, other signals of the resulting closed-loop systems are bounded, and full-state constraints are not violated for all time. Finally, the simulation results verify the efficiency of the proposed control design method.

Few Shot Class Incremental Learning via Efficient Prototype Replay and Calibration.

Few shot class incremental learning (FSCIL) is an extremely challenging but valuable problem in real-world applications. When faced with novel few shot tasks in each incremental stage, it should take into account both catastrophic forgetting of old knowledge and overfitting of new categories with limited training data. In this paper, we propose an efficient prototype replay and calibration (EPRC) method with three stages to improve classification performance. We first perform effective pre-training with rotation and mix-up augmentations in order to obtain a strong backbone. Then a series of pseudo few shot tasks are sampled to perform meta-training, which enhances the generalization ability of both the feature extractor and projection layer and then helps mitigate the over-fitting problem of few shot learning. Furthermore, an even nonlinear transformation function is incorporated into the similarity computation to implicitly calibrate the generated prototypes of different categories and alleviate correlations among them. Finally, we replay the stored prototypes to relieve catastrophic forgetting and rectify prototypes to be more discriminative in the incremental-training stage via an explicit regularization within the loss function. The experimental results on CIFAR-100 and miniImageNet demonstrate that our EPRC significantly boosts the classification performance compared with existing mainstream FSCIL methods.

Disturbance‐observer‐based adaptive finite‐time dynamic surface control for PMSM with time‐varying asymmetric output constraint

AbstractThis article presents a disturbance‐observer‐based adaptive finite‐time dynamic surface control scheme, capable of guaranteeing transient behavior for the PMSM with arbitrary asymmetric time‐varying output constraint and unmatched external disturbance. The major challenge of this paper is devising efficient strategies to tackle the nonsymmetric output restraints with arbitrary characteristics and unmatched external perturbation for the system under the finite‐time backstepping framework. Given this, a nonlinear transformation function is adopted to coordinate from the output‐constrained dynamic model to an uncontained one, and a finite‐time disturbance observer is introduced to evaluate the unmatched external perturbation. Then, a dynamic surface control approach having adaptive properties for PMSM is conceived by combing a neural network to evaluate the nonlinear functions and a first‐order filter to handle the “explosion of complexity.” Additionally, it is proved that the signals in the closed‐loop system can narrow down to a bounded region and the tracking error can merge in a limited time to tiny vicinity of zero by employing a fast finite‐time stability principle. Eventually, simulation cases and contrast results reveal the tracking performance and immunity to the disturbance of the devised controller.

A study on data-driven identification and representation of nonlinear dynamical systems with a physics-integrated deep learning approach: Koopman operators and nonlinear normal modes

Identifying the intrinsic coordinates or modes of dynamical systems is essential to understand, analyze, and characterize the underlying complex dynamical behaviors. This is a critical challenge for nonlinear dynamical systems because the modal transformation, which is universal for linear systems, no longer applies. Koopman operators and nonlinear normal modes (NNMs) are two main frameworks aiming to provide a general representation of nonlinear dynamics. In this study, we investigate their abilities on representing nonlinear dynamical systems. Addressing the challenge that the closed-form models or equations of dynamical systems are generally unknown realistically, we first present a physics-integrated deep learning-based data-driven framework to identify the eigenfunction of Koopman operators and the nonlinear modal transformation function of NNMs, respectively. We then evaluate their representation abilities by their reconstruction and predictive accuracy of the nonlinear dynamical response using the identified Koopman modes and NNMs. We conduct numerical experiments on Duffing systems with varying nonlinearity levels and dimensions, and observe that NNMs achieve higher representation accuracy and better computational efficiency than Koopman operators using the same dimension of intrinsic coordinates or modes.

Adaptive neural network fixed‐time control of p$$ p $$‐normal systems with asymmetric output constraints

AbstractThis paper studies the problem of fixed‐time control for a class of nonlinear ‐normal systems with asymmetric output constraints and external disturbances. Compared with the existing fixed‐time control schemes, the smooth switching functions are designed to avoid the singularity problem. Then, a time‐varying nonlinear transformation function (NTF) is introduced, blue and a unified tool to deal with the symmetric, asymmetric, and even unconstrained problems simultaneously. Moreover, by adding blue one power integration technology, the controller is designed, which can inhibit the influence of external disturbances on the system. According to Lyapunov stability analysis, the presented fixed‐time blue control method ensures that all signals are bounded in a fixed time. In the end, two simulation examples demonstrate the effectiveness of the proposed scheme.

Computer analysis of multiple measurements with the sensor's quadratic transformation function

The object of research is multiple measurements. The research aims to improve the accuracy of multiple measurements with a non-linear and unstable sensor transformation function. It is proved that the redundant measurement equation ensures the independence of the measurement result from the parameters of the transformation function and their deviations from the nominal values. It was found that the result of redundant measurements is affected by the reproduction errors of normalized temperatures T1 and T2. It is shown that the best accuracy results are obtained with a reproduction error of normalized temperature T2 within ±1.0 % and temperature T1 within ±0.1 %. This makes it possible to reduce the accuracy requirements for the source of reproduction of normalized temperature Т2. The possibility of processing the results of multiple measurements by two approaches is presented. Computer modeling using the first approach found that with a reproduction error of normalized temperature T2 within ±0.5 %, the relative measurement error is 0.003 %. When modeling the second approach, the relative error is 0.05 %. It was also found that with an increase in the reproduction error of normalized temperature T2 to ±1.0 %, the value of the relative error is 0.04 %. Due to this, when applying the second approach, it becomes possible to choose a non-high-precision source of reproduction of normalized temperature T2. In addition, the sensitivity of the second approach to the digit range of measuring devices was found, which leads to the dependence of the measurement result on their accuracy. There are reasons to assert the possibility of increasing the accuracy of multiple measurements by processing the results of intermediate measurements according to redundant measurement equations using two approaches

Low-Computation Tracking Control of Nonlinear Systems With Asymmetric Full-State Constraints and Unknown Control Directions

This article considers the tracking control problem for an uncertain feedback nonlinear system with asymmetric time-varying full-state constraints and unknown control directions. We propose a new low-computation full-state constrained robust control algorithm, that removes the feasibility conditions of virtual controllers and solves the unknown control direction problem without using the Nussbaum gain technique. By introducing nonlinear transformation functions, the original constrained systems are converted into new unconstrained tracking error systems, and the new systems eliminate the limitation of the initial conditions. Then, to seek the correct control directions, an orientation function with error conversion is constructed, which avoids introducing Nussbaum-type functions and logic switching rules. The proposed method possesses inherent robustness against model uncertainties and disturbances, and guarantees that the full-state constraints and the tracking error of systems enter into a prescribed set in a fixed time. Finally, simulation examples are presented to demonstrate the superiority and effectiveness of the developed control algorithm.

Decentralized adaptive neural safe tracking control for nonlinear systems with conflicted output constraints

The issue of decentralized adaptive safe tracking control for interconnected large-scale nonlinear systems (ILSNSs) with conflicted output constraints is discussed in this paper. By “conflicted output constraints”, we mean that the output constraint functions conflict with reference signal, i.e., the reference signal is not completely constrained within the constraint range. In existing methods, it is always assumed that the reference signal is constrained within the constraint region. In practice, the constraints may be detected during system operation and conflict with the reference signal given in advance. In this particular case, the existing methods based on barrier Lyapunov function (BLF) or nonlinear transformation function (NTF) are invalid. From a new point of view, this article designs a new safety reference signal (SRS) which is completely restricted within the constraint range by using the boundary protection approach. Meanwhile, a prescribed performance function which can arbitrarily define the convergence time and tracking accuracy is introduced so that the system output can better track the SRS. Then, combining backstepping technique and radial basis function neural network (RBFNN), a new controller is constructed, under which a desired tracking trajectory can be obtained under the premise of ensuring safety performance. Furthermore, by adding a dynamic event triggering mechanism (DETM) between the actuator and the plant, the communication burden is effectively reduced. Simulation results verify the scheme developed.