Nonlinear Time-varying Systems Research Articles

Event-based adaptive asymptotic tracking control of nonlinear time-varying systems with prescribed performance

This paper is concerned with the adaptive tracking control problem of nonlinear time-varying systems. Based on the backstepping technology, an event-based prescribed performance control scheme is developed. And the time-varying uncertainties of the system are handled by utilising bound estimation method. The proposed controller not only ensures the prescribed tracking performance, but also reduces the communication burden. By using Lyapunov stability analysis, it is proven that all of the closed-loop signals are bounded, and the tracking error can converge to zero. Simultaneously, Zeno behaviour is excluded. Finally, the simulation results are utilised to illustrate the effectiveness of the proposed adaptive control scheme.

A SDNN-MPC method for power distribution of COGAG propulsion system

In order to solve the problems of power distribution taking a long time and large fluctuation of propeller speed in the process of COGAG propulsion system switching operating patterns, model predictive control (MPC) is introduced to control power distribution and a SDNN-MPC method is proposed. Discrete incremental LPV model is established as the prediction model and MPC for power distribution process is designed. In order to make MPC suitable for COGAG, which is a nonlinear time-varying system with short sampling period, a simplified dual neural network (SDNN) with simplified constraints is used to solve the quadratic programming in MPC. A large number of simulation results show that the established LPV model has high prediction accuracy and SDNN is helpful to shorten the execution time of MPC. The softening factor and weight factors in MPC can affect the performance of power distribution control. Two principles are summarized to choose weight factors and the recommended range of the softening factor is 0.026–0.034. Compared with the PI controller, based on the SDNN-MPC the time of power distribution process is shortened and the fluctuation of propeller speed is reduced. The maneuverability and stability of the vessel are improved.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.

Recursive Fault Estimation With Energy Harvesting Sensors and Uniform Quantization Effects

In this letter, the recursive fault estimation issue is considered for nonlinear time-varying systems subject to the effects induced by energy harvesting sensors and uniform quantization. Based on the energy harvesting mechanism and stochastic distribution of the absorbed energy, the real-time occurrence probability of missing measurements is calculated recursively. This research intends to develop a recursive estimator for the considered nonlinear time-varying system with energy harvesting sensors, such that, under uniform quantization effects, the state and fault can be jointly estimated. By adopting the induction approach, an upper bound is firstly calculated for the estimation error covariances (EECs) of the state and fault. Then, the value of the time-varying estimator parameter is computed through minimizing such calculated upper bound. In the end, an illustrative example is presented to verify the availability of the developed fault estimation method.

A Data-Driven Dynamic Obstacle Avoidance Method for Liquid-Carrying Plant Protection UAVs

Autonomous sprayer UAVs are one of the most used aerial machines in modern agriculture. During flight missions, some common narrow obstacles appear in the flying zone. These are non-detectable from satellite images and one of the biggest challenges for autonomous sprayer UAVs in farmland. This work introduces an obstacle avoidance architecture specifically for sprayer UAVs. This architecture has generality in the spraying UAV problem, and it reduces the reliance on the global mapping of farmland. This approach computes the avoiding path based on the onboard sensor fusion system in real-time. Moreover, it autonomously determines the transition of several maneuver states using the current spraying liquid data and the UAV dynamics data obtained by offline system identification. This approach accurately tracks the avoidance path for the nonlinear time-variant spraying UAV systems. To verify the performance of the approach, we performed multiple simulations with different spraying missions, and the method demonstrated a high spraying coverage of more than 98% while successfully avoiding all vertical obstacles. We also demonstrated the adaptability of our control architecture; the safe distance between the UAV and obstacles can be changed by specifying the value of a high-level parameter on the controller. The proposed method adds value to precision agriculture, reduces mission time, and maximizes the spraying area coverage.

Quasi-Consensus of Time-Varying Multi-Agent Systems with External Inputs under Deception Attacks.

The quasi-consensus of a class of nonlinear time-varying multi-agent systems suffering from both external inputs and deception attacks is studied in this paper. This is different from a time-varying matrix, which is assumed to be bounded; further reasonable assumptions are supposed. In addition, impulsive deception attacks modeled with Bernoulli variables are considered. Sufficient conditions to achieve quasi-consensus are given, and the upper bounds of the error state related to the deception attacks is derived. Finally, a numerical simulation example is provided to show the validity of the obtained results.

Introducing a Novel Model-Free Multivariable Adaptive Neural Network Controller for Square MIMO Systems.

In this study, a novel Multivariable Adaptive Neural Network Controller (MANNC) is developed for coupled model-free n-input n-output systems. The learning algorithm of the proposed controller does not rely on the model of a system and uses only the history of the system inputs and outputs. The system is considered as a ‘black box’ with no pre-knowledge of its internal structure. By online monitoring and possessing the system inputs and outputs, the parameters of the controller are adjusted. Using the accumulated gradient of the system error along with the Lyapunov stability analysis, the weights’ adjustment convergence of the controller can be observed, and an optimal training number of the controller can be selected. The Lyapunov stability of the system is checked during the entire weight training process to enable the controller to handle any possible nonlinearities of the system. The effectiveness of the MANNC in controlling nonlinear square multiple-input multiple-output (MIMO) systems is demonstrated via three simulation studies covering the cases of a time-invariant nonlinear MIMO system, a time-variant nonlinear MIMO system, and a hybrid MIMO system, respectively. In each case, the performance of the MANNC is compared with that of a properly selected existing counterpart. Simulation results demonstrate that the proposed MANNC is capable of controlling various types of square MIMO systems with much improved performance over its existing counterpart. The unique properties of the MANNC will make it a suitable candidate for many industrial applications.

Finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance

In this paper, the problem of finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance is studied for the first time. By exploiting an approach presented in positive systems which is different from the Lyapunov–Krasovskii functional technique, an explicit criterion is formulated for the existence of a special ball such that all the state trajectories of homogeneous nonlinear positive systems with degree 0<α<1 converge within it in finite time. We then extend the main result to the general nonlinear time variant systems. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results.

Exponential stability analysis for a class of switched nonlinear time-varying functional differential systems

This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global exponential stability are established for this class of systems under arbitrary switching which satisfies some assumptions on the average dwell time. The obtained criteria are shown to cover and improve many previously known results, including, in particular, sufficient conditions for absolute exponential stability of switched time-delay systems with sector nonlinearities. Some simple examples are given to illustrate the proposed method.

Effect of mass variation on vibration properties of the tooth in drilling operation

Dental cavity represent one of the widespread illness of the tooth. Method for treating of the tooth is to drill the cavity and to fill the hole with suitable material. Measurements show that during drilling the tooth vibrates with increasing mass that causes unpleasant feeling for patient. The aim of the paper is to give the theoretical explanation for this phenomena and to give suggestion for vibration elimination. During drilling, mass of the tooth is decreasing and the so called ‘reactive force’ occurs. Drilling and reactive force cause tooth vibration. The system is modeled as a nonlinear time variable system. An analytical procedure for solving of the equation of vibration is developed. The solution is assumed in the form of the generalized trigonometric function with time variable amplitude and phase. It is obtained that not only the amplitude but also the frequency of tooth vibration in drilling are increased. In addition to reactive force the drilling velocity, diameter of the drill tool and spindle speed affect the vibration level. The appropriate values of these parameters would eliminate or decrease the patient bad feeling.

Reachable set estimation for continuous-time impulsive switched nonlinear time-varying systems with delay and disturbance

This note is concerned with the problem of reachable set estimation for switched nonlinear time-varying systems with mixed time-varying delay, delayed impulse and disturbance. Based on a novel method which does not involve the usual Lyapunov-Krasovskii functional approach, sufficient conditions, under the designed average dwell time switching, are provided for the characterization of a special sphere such that all the states of the system converge exponentially within it. Moreover, an extension is available to the result of linear time-varying systems. Finally, two simulation results are illustrated by examples to show the validity.

Finite-time stabilization of time-varying nonlinear systems based on a novel differential inequality approach

In this paper, the finite-time stabilization problem is investigated for a class of time-varying nonlinear systems. The classical finite-time differential inequality is extended to time-varying systems and some new lemmas are derived for global finite-time stability (FTS) and local FTS of the corresponding closed-loop systems. Then based on the hybrid control theory and the extended time-varying differential inequality, we present two control schemes including continuous control and hybrid control. It is shown that the continuous control is formulated to make the system converge in finite time, while the impulsive part involved in hybrid control accelerates the stabilization. In addition, the theoretical results are applied to the finite-time synchronization of complex networks with time-varying parametric matrices. Ultimately, two numerical examples are presented to demonstrate the distinctiveness and the effectiveness of our proposed results.

Lyapunov-Bregman functions for speed-gradient adaptive control of nonlinear time-varying systems

The paper is devoted to application of Bregman divergence to nonlinear adaptive control. Using Bregman divergence instead of quadratic function leads to a new class of Lyapunov functions in adaptive control that can be called Lyapunov-Bregman functions. An extended control algorithms design scheme is proposed and the properties of the designed control systems in presence of disturbances and time-varying parameters are studied. A special case of model reference adaptive control for nonlinear time-varying systems is studied based on the speed-gradient methodology.

Matrix measures, stability and contraction theory for dynamical systems on time scales

&lt;p style='text-indent:20px;'&gt;This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study both linear and nonlinear dynamical systems on time scales. Specifically, we start with considering linear time-varying systems and, for these, we prove a time scale analogous of an upper bound due to Coppel. We make use of this upper bound to give stability and input-to-state stability conditions for linear time-varying systems. Then, we consider nonlinear time-varying dynamical systems on time scales and establish a sufficient condition for the convergence of the solutions. Finally, after linking our results to the existence of a Lyapunov function, we make use of our approach to study certain epidemic dynamics and complex networks. For the former, we give a sufficient condition on the parameters of a SIQR model on time scales ensuring that its solutions converge to the disease-free solution. For the latter, we first give a sufficient condition for pinning synchronization of complex time scale networks and then use this condition to study certain collective opinion dynamics. The theoretical results are complemented with simulations.&lt;/p&gt;

Model Identification and Model Predictive Control of Biopharmaceutical and Biomedical Systems

This paper demonstrates the use of model predictive control (MPC) formulations for uncertain time-varying biopharmaceutical and biomedical systems implemented using measured data without prior knowledge of an accurate model. Furthermore, we demonstrate how prior knowledge can be incorporated in the identification of the model either through constraints or as regularization of the system identification procedure. We demonstrate the use of system identification to develop a model of the fed-batch Chinese hamster ovary mammalian cell bioreactor process and the implementation of model-based control to maximize therapeutic product yields. We also use a time-varying nonlinear biomedical system to demonstrate improvements due to incorporating prior information in the learning of the models and reidentification of the models when prediction accuracy deteriorates. We propose a new partial least squares algorithm that incorporates regularization from prior knowledge and can handle missing data in the independent covariates. Simulation case studies involving a biopharmaceutical production process and automated drug delivery demonstrate the capabilities of the proposed techniques.

A Hybrid Multiscale Permutation Entropy-Based Fault Diagnosis and Inconsistency Evaluation Approach for Lithium Battery of E-Vehicles

Lithium battery is a complex nonlinear time-varying system with several inconsistencies. The fault diagnosis method has difficulty making an early diagnosis of battery faults without obvious abnormalities. In fact, voltage inconsistency is a representative fault response. Therefore, the monitoring of voltage inconsistency is highly important for the safe and reliable operation of lithium batteries in E-vehicles. The entropy method does not rely on an accurate analysis model and expert experience. Moreover, it does not consider the complex fault mechanism and system structure. Hence, it has gradually attracted widespread attention. Given such attention, a hybrid fault diagnosis method combining multiscale permutation entropy (MPE) and coefficient of variation (CV) is presented in this paper, and the improved MPE fault diagnosis model based on 3-sigma is emphasized. First, MPE and the 3-sigma rule are used to calculate the threshold, and the voltage inconsistency of the battery is judged by the threshold. Then, the location of the faulty cells is located by the CV. The superiority of the proposed method is proven by experimental data from the Yunzhitong platform of CRRC Electric Vehicle Co., Ltd. and a comparison of frontier methods. The proposed approach is feasible and promising in real E-vehicle applications.

Deriving a thermal model from data by machine learning based on physical laws

We propose a method for creating a reduced-order model (ROM) for temperature prediction that is applicable to nonlinear time-variant systems, able to be created using a very small amount of data, and easy to interpret. Our nonlinear time-variant ROM is an extension of sparse identification of nonlinear dynamical systems, which was first proposed in 2016. Three machine learning methods are developed for automatically deriving a thermal network model from time-series data. Link relationships between temperature nodes and parameter settings, such as thermal resistance and heat capacity, are automatically inferred by machine learning. The effectiveness of the proposed method is demonstrated using the results of thermo-fluid analysis for a natural air-cooled power module in which thermal resistance is a function of temperature. The ROM was created using the results of 15 thermo-fluid analyses, with is fewer than the 25 independent variables in the ROM. The computational efficiency of the created ROM is very high, and unknown data, including extrapolated data, were predicted with error of less than 1 K. By using the proposed method, it is expected that design parameters can be fine-tuned and actual loads can be taken into account, and also that condition-based maintenance can be realized through real-time simulation.

Signal Transmission by Sampled-time Adaptive Synchronization of Time-varying Chaotic Systems

In the paper, the adaptive synchronization problem is studied for a class of time-varying nonlinear systems. The only assumption imposed is the boundedness of the rate of change of the controlled system parameters, while the initial uncertainty can be quite large. The adaptation algorithms in the discrete-time form are derived based on adaptive control of nonlinear time-varying systems with an explicit reference model. As the result, the estimate of the limiting deviation of the solution of the closed-loop system from that of the reference model was obtained. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limiting error in the system can be made arbitrarily small despite a possibly big range of system parameter values. The systems based on a direct approach are considered. The procedure for the synthesis of a sampled-time adaptive controller and analysis of the synthesized system is illustrated by an example of the signal transmission system. The results obtained allow one to build and analyze a wide class of adaptive systems with reference models under time-varying conditions.

Finite Horizon H-Infinity Control of Nonlinear Time-Varying Systems Under WTOD Protocol

The finite horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $ </tex-math></inline-formula> control problem is investigated for a class of discrete nonlinear time-varying systems subject to Weighted Try-Once-Discard communication protocol. The equations of state and output under investigation involve both deterministic and stochastic nonlinearities. By resorting to the Taylor series expansion formula, Lyapunov stability theory and cross-amplification lemma, sufficient conditions are established for the existence of the desired observer-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> controller. The gain matrices of the controller and observer are obtained by solving a set of recursive linear matrix inequalities.

Practical partial stability of time-varying systems

&lt;p style='text-indent:20px;'&gt;In this paper we investigate the practical asymptotic and exponential partial stability of time-varying nonlinear systems. We derive some sufficient conditions that guarantee practical partial stability of perturbed systems using Lyapunov's theory where a converse theorem is presented. Therefore, we generalize some works which are already made in the literature. Furthermore, we present some illustrative examples to verify the effectiveness of the proposed methods.&lt;/p&gt;