Nonlinear Time-varying Systems Research Articles

Prescribed-time control for time-varying nonlinear systems: A temporal scaling based robust adaptive approach

Prescribed-time control for time-varying nonlinear systems: A temporal scaling based robust adaptive approach

Global asymptotic fault-tolerant tracking for time-varying nonlinear complex systems with prescribed performance

This paper investigates the global adaptive asymptotic fault-tolerant control of time-varying complex nonlinear systems with prescribed performance. The considered system simultaneously involves both mismatched intrinsic unknown time-varying parameters and nonvanishing external disturbances as well as possible actuator faults, which make the underlying problem challenging. By introducing a special kind of funnel functions, together with fusing a barrier Lyapunov function technique and a bound estimation approach, a novel prescribed performance fault-tolerant control scheme is proposed, which, as compared with the existing results, exhibits the following appealing features: (1) it is capable of dealing with nonlinear systems with high relative degree and serious unmatched time-varying uncertainties; (2) it can guarantee a global prescribed transient performance such that the performance specifications in terms of settling time and the tracking accuracy can be off-line preassigned according to task requirements, without dependence on initial conditions and any design parameters; (3) it can realize asymptotic output tracking, where no knowledge about the high-order derivatives of the reference trajectory is required. In the end, a simulation example is provided to attest the efficiency of the designed scheme.

Deep Koopman learning of nonlinear time-varying systems

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Absolute Exponential Stability Criteria for Some Classes of Nonlinear Time-Varying Systems with Delays and Sector Nonlinearities

Absolute Exponential Stability Criteria for Some Classes of Nonlinear Time-Varying Systems with Delays and Sector Nonlinearities

Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples.

Finite time stability of time-varying stochastic nonlinear systems with random impulses

ABSTRACT This article studies the finite time stability (FNTS) of time-varying nonlinear stochastic systems with random impulses. We provide sufficient conditions for the FNTS or even fixed time stability (FXTS) for time-varying stochastic systems under two cases: (1) The impulse time is deterministic; (2) The impulse time is random. For case (1), we use the reverse average dwell time to investigate FNTS, but for case (2), we employ the Poisson process theory to solve the stability problem. In addition, the stability criteria capture the stabilising effect of stochastic noise in the FNTS problem. Finally, the correctness of the theoretical results is verified with two numerical examples. As far as the author knows, no one has studied the FNTS of time-varying stochastic systems with random impulses.

A resilient method to nonlinear distributed filtering for multi-rate systems with integral measurements under memory-event-triggered mechanism

In this paper, the resilient distributed filtering problem is studied for time-varying nonlinear multi-rate systems (TVNMRSs) with integral measurements over sensor networks, where the lifting technology is utilized during the analysis of the TVNMRSs. In order to reduce unnecessary data transmissions, the memory-event-triggered communication mechanism (METCM) is adopted to determine whether the sensor nodes communicate with each other. The purpose of this paper is to design a resilient distributed filtering method such that, for all multi-rate sampling, integral measurements, filter gain fluctuations and METCM, an upper bound on the filtering error covariance is guaranteed and minimized subsequently by choosing the appropriate filter gains. Besides, a sufficient condition with rigorous theoretical proof is provided to discuss the uniform boundedness of the upper bound on the filtering error covariance. In the end, the simulations with comparative experiments are made to demonstrate the effectiveness of proposed resilient distributed filtering algorithm based on METCM.

Stability analysis of optimal control problems with time-dependent costs

We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general attractors are established. This work covers and generalizes the related results on discounted optimal control problems to more general systems and cost functions.

Physics-Informed Machine Learning for Surrogate Modeling of Heat Transfer Phenomena

Abstract In this paper, we propose a sparse modeling method for automatically creating a surrogate model for nonlinear time-variant systems from a very small number of time series data with nonconstant time steps. We developed three machine learning methods, namely, (1) a data preprocessing method for considering the correlation between errors, (2) a sequential thresholded non-negative least-squares method based on term size criteria, and (3) a solution space search method involving similarity model classification—to apply sparse identification of nonlinear dynamical systems, as first proposed in 2016, to temperature prediction simulations. The proposed method has the potential for wide application to fields where the concept of equivalent circuits can be applied. The effectiveness of the proposed method was verified using time series data obtained by thermofluid analysis of a power module. Two types of cooling systems were verified: forced air cooling and natural air cooling. The model created from the thermofluid analysis results with fewer than the number of input parameters, predicted multiple test data, including extrapolation, with a mean error of less than 1 K. Because the proposed method can be applied using a very small number of data, has a high extrapolation accuracy, and is easy to interpret, it is expected not only that design parameter can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance can be realized through real-time simulation.

A Novel Approach to Study the Time-Varying Additive Activity during the Electrorefining of Copper

Electrodeposition additives are key components to enhance the electrochemical deposition of metals, either in pure plating applications or during the electrorefining of metals. Many different additives, either organic or inorganic, are applied in industry, depending on the type of process. This work focusses on thiourea and chloride as common additives used for copper electrorefining. This electrochemical industrial process consumes an impure copper anode and produces a pure (99.995 %) copper cathode, while the anode impurities remain in the electrolyte. Additives assist the electroreduction process to produce smooth copper deposits, essential to avoid short circuits and the formation of unwanted cathode morphologies which can entrap impurities.Thiourea is a crucial but complex additive in copper refining. It is known to degenerate into formamidine disulfide (FDS) and both thiourea as FDS can undergo interactions with either copper ions in the solution or the cathode surface. Time dependent additive studies and fundamental knowledge of the effect of aged electrolyte on the cathodic part of the electrorefining process are scarce.The approach applied in this work enables the investigation of the time dependent effect of additives, in this case thiourea and chlorides, assisting the electroplating of copper. Fundamental knowledge of the assisted plating process is extended to create a corner stone for applied research, subsequently, semi-industrial circumstances are used to describe the additive behaviour in industrial relevant conditions. Operando Odd Random Phase Electrochemical Impedance Spectroscopy (ORP-EIS) is used to study the electrochemistry of the additive system [1,2]. Hereby, a multisine input signal is added to the DC current to perform the ORP-EIS experiment simultaneously with the plating process. This measurement technique allows an in situ monitoring of the electrochemical system for hour-long electrodeposition processes. The ORP-EIS technique enables a quantification of the nonlinearities and non-stationarities during the EIS experiment [3]. Additionally, the present non-stationarities are modelled and the nonlinearities are considered as nuisance factor to result in a best linear time-varying approximation [4,5]. An equivalent electrical circuit is used as model to extract the relevant physical parameters from the impedance data. The EIS study is complemented with an ex situ analysis of the thiourea concentration, through ion chromatography, as a function of plating time. Correlations could be made between electrochemical parameters and actual thiourea concentrations [2].[1] T. Collet, et al., An operando ORP-EIS study of the copper reduction reaction supported by thiourea and chlorides as electrorefining additives, Electrochimica Acta (2021) 138762. [2] T. Collet, et al., The time-varying effect of thiourea on the copper electroplating process with industrial copper concentrations, Electrochimica Acta (2022) 141412. [3] Van Gheem, et al., Electrochemical impedance spectroscopy in the presence of non-linear distortions and non-stationary behaviour part i: Theory and validation, Electrochimica Acta 49 (2004) 4753–4762. [4] N. Hallemans, et al., Detection, Classification, and Quantification of Nonlinear Distortions in Time-Varying Frequency Response Function Measurements, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6500814. [5] N. Hallemans, et al., Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systems, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6503814.

Event-trigger-based composite adaptive fuzzy control for nonlinear time-varying state constraint systems with asymmetric input saturation

In this paper, a novel composite adaptive fuzzy control (AFC) based on the command filtered backstepping and event-triggered mechanism is proposed for nonstrict-feedback nonlinear systems with input saturation and time-varying full-state constraints. A fuzzy observer is designed to estimate the unmeasured states. Simultaneously, by introducing a serial-parallel estimation model, a fuzzy control tactic with the composite adaptive law of parameters is established which greatly increases the precision of unknown term estimation. In addition, the command filtering technique is employed to solve the issue of “explosion of complexity” and compensate for the errors caused by the command filters. The event-triggered mechanism is utilized to effectively decrease the data redundancy. By using the time-varying barrier Lyapunov functions (BLFs), all the states can remain within a prescribed time-varying interval. The designed controller can guarantee the convergence of the tracking error at the origin and the boundedness of all closed-loop signals. Finally, two simulation examples are carried out to validate the effectiveness of the proposed control scheme.

Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms

We study the exponential stability and boundedness problem for perturbed nonlinear time-varying systems using Lyapunov Functions with indefinite derivatives. As the limiting function for the perturbation term, we use different forms and give stability and boundedness conditions in terms of the coefficients in these bounds. Contrary to most of the available conditions, we allow the coefficients to be unbounded. But instead, we put forward a condition that requires a series produced by coefficients to be limited and exponentially decaying. We perform our results on Linear time-varying systems and generalize many of the available results.

Characterization of Integral Input-to-State Stability for Nonlinear Time-Varying Systems of Infinite Dimension

Characterization of Integral Input-to-State Stability for Nonlinear Time-Varying Systems of Infinite Dimension

Exponential stability for nonlinear time-varying systems on time scales

In this paper, some less conservative sufficient conditions for uniform exponential stability, local uniform exponential stability and uniform practical exponential stability of nonlinear time-varying systems on time scales are proposed. Compared with the traditional exponential stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. The main tools used are some Gronwall's inequalities on time scales. Two examples are also included to verify the effectiveness of the results obtained.

Mathematical Model for Fault Handling of Singular Nonlinear Time-Varying Delay Systems Based on T-S Fuzzy Model

In this paper, a mathematical model based on the T-S fuzzy model is proposed to solve the fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD is is extremely difficult to solve and the Laplace transform is devised to build an equal system free of TVD. Additionally, the sensor fault is changed to actuator fault by the developed coordinate transformation. A fuzzy learning fault estimator is first built to estimate the detailed sensor fault information. Then, a PI FTC scheme is suggested aiming at minimizing the damage caused by the fault. Simulation results from multiple faults reveal that the FE and FTC algorithms are able to estimate the fault and guarantee the system performance properly.

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

This paper investigates the problem of unknown input observer (UIO) design for Takagi–Sugeno (TS) fuzzy systems with time-varying delay. For observer design, all the unmeasured nonlinearities are isolated in the nonlinear consequent parts of TS fuzzy systems. This allows dealing with the well-known issue related to unmeasured premise variables for TS fuzzy observer design in a more effective fashion via the mean value theorem. Using the unknown input (UI) decoupling technique, no a priori information on the UI is needed for the proposed TS fuzzy observer design, which can guarantee the asymptotic estimations of both the system state and the unknown input. Employing a fuzzy Lyapunov–Krasovskii functional with a suitable augmented vector, the effect of time-varying delay on the estimation error dynamics is taken into account in the observer design. Numerical examples are presented to demonstrate the effectiveness of the proposed fuzzy UIO design method for nonlinear time-varying delay systems.

Finite-Horizon $H_{\infty }$ Filtering via a High-Rate Network With the FlexRay Protocol

This paper addresses the finite-horizon <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> filtering problem for a class of discrete time-varying nonlinear systems over high-rate networks whose signal exchanges are scheduled by the FlexRay protocol. To improve the efficiency of the data transmission, a high-rate network is deployed for the measurement signals to be broadcasted from the sensors to the filter. The FlexRay protocol is embedded into the high-rate network to orchestrate the transmission rule of the signals with different attributes, thereby further enhancing the transmission flexibility. On the basis of the Round-Robin and Try-Once-Discard protocols, a novel FlexRay-protocol-based measurement model is proposed by using certain data holding strategies. A sufficient condition is provided to guarantee that the filtering error dynamics meets the desirable disturbance attenuation level against exogenous disturbances over a finite horizon. The parameterized form of the filter gain is attained by the solutions to some matrix inequalities. Numerical simulation is carried out to substantiate the proposed filter design algorithm.

Novel Discrete-Time Recurrent Neural Network for Robot Manipulator: A Direct Discretization Technical Route.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.