Nonlinear Time-varying Research Articles

A Composite Control Method Based on Model Predictive Control and a Disturbance Observer for the Acquisition, Tracking, and Pointing System

Nonlinear disturbances, such as friction, backlash, and base vibration, are the main factors restricting the further improvement of the dynamic performance of the Acquisition, Tracking and Pointing (ATP) system. However, the modeling and compensation of the time-varying nonlinearities are still challenging. In this paper, a compound control algorithm based on model predictive control (MPC) and a Proportional Multiple-Integral State-Augmented Kalman Filter (PMISAKF) disturbance observer is proposed to improve the disturbance rejection performance. Specifically, a PMISAKF is used to estimate the system’s state and external disturbances in real-time. These observed disturbances are then treated as known external inputs at the current or future time points and incorporated into the predictive model of MPC. This allows the optimization process to take these external factors into consideration, enabling the calculation of an optimal control strategy and achieving high pointing and tracking accuracy for nonlinear time-varying disturbances. Experimental results show that the proposed method can effectively improve the system’s anti-interference ability and tracking accuracy.

Decentralized Adaptive Secure Control of Uncertain Nonlinear Time-Varying Interconnected Systems Against Sensor and Actuator Attacks.

In this article, the decentralized adaptive secure control problem for cyber-physical systems (CPSs) against deception attacks is investigated. The CPSs are formed as a type of nonlinear interconnected strict-feedback systems with uncertain time-varying parameters. The attack affects the information transmission between sensor and actuator in a multiplicative manner. A novel decentralized adaptive backstepping secure control strategy is established by exploiting a particular kind of Nussbaum functions and a flat-zone Lyapunov function analysis approach. It is shown that all of closed-loop signals remain globally bounded, and each output signal eventually converges into a small neighborhood of the origin. Simulation results on an illustrative example are provided to display the effectiveness of the proposed control scheme.

Global regulation for uncertain feedforward nonlinear systems based on event-triggered impulsive control: a time-varying gain scaling approach

This paper addresses the problem of global regulation for uncertain feedforward nonlinear systems using event-triggered impulsive control. By constructing a state transformation with a time-varying scaling gain, both the state-feedback and output-feedback event-triggered impulsive control strategies are established. It is proven that the proposed impulsive controllers ensure the global regulation of the concerned systems while avoiding the Zeno behaviour. Furthermore, the derived results of this work are generalised to a broader class of uncertain feedforward nonlinear systems incorporating time-varying nonlinearities, as well as to a class of uncertain strict-feedback nonlinear systems. It is noteworthy that this paper is the first attempt to design an impulsive regulating controller for feedforward nonlinear systems. Finally, a simulation example is presented to verify the effectiveness of our theoretical results.

An Adaptive Smooth Event-Triggered Approach to Recursive Estimation for Nonlinear Time-Varying Systems With Uncertain Communication Topologies

An Adaptive Smooth Event-Triggered Approach to Recursive Estimation for Nonlinear Time-Varying Systems With Uncertain Communication Topologies

A Temperature Control Method of Lysozyme Fermentation Based on LRWOA-LSTM-PID

In order to overcome the difficulty of parameter tuning caused by the large lag and time-varying nonlinearity of the tank for lysozyme fermentation, a temperature control method based on LRWOA-LSTM-PID is proposed in this paper. Firstly, according to the intrinsic mechanism of the fermenter, a temperature mechanism model based on a dynamic equation is designed, which can better reflect the temperature changes in the fermenter. Secondly, a Proportional Integral Derivative (PID) parameter tuning method based on a Long-Short Term Memory Network (LSTM) is proposed, which takes advantage of the ability of LSTM to learn time sequence information and obtains the variation trend between error sequences under continuous time sampling, thereby adjusting network weights more reasonably and accelerating PID parameter tuning. Finally, a Whale Optimization Algorithm (WOA) based on the Lévy flight and random walk strategy (LRWOA) is proposed for the initialization of LSTM parameters; this algorithm has excellent optimization capabilities and overcomes the problem of LSTM falling into local optimal solutions prematurely during parameter randomization. The results show that the method proposed in this paper can achieve rapid tuning of PID parameters, thereby improving the convergence speed of the system and reducing system overshoot.

Thermal Characteristics of Spindle System Based on the Comprehensive Effect of Multiple Nonlinear Time-Varying Factors

The thermal characteristics of the spindle system for CNC machine tools are influenced by multiple factors which are nonlinear and time-varying. In this paper, a nonlinear time-varying thermal characteristics solving model for the spindle system was established based on the numerical solution method. Through theoretical deduction and data fitting, mathematical models of nonlinear time-varying factors including the friction torque generated by lubricants, convective heat transfer coefficient, and coolant and ambient temperature are constructed. The temperature and displacement of the spindle system at each time step are solved by considering the comprehensive effect of multiple nonlinear time-varying factors. And the actual temperature and axial deformation data of the spindle system are obtained through thermal characteristics detection experiments. By comparing solution results affected by multiple nonlinear time-varying factors and by non time-varying factors with experimental data, it can be concluded that the nonlinear time-varying thermal characteristics model has advantages in reflecting the trend of numerical changes and the accuracy of result solving over a method considering non time-varying factors and the solution values of temperature affected by multiple nonlinear time-varying factors are almost consistent with detection values and the relative errors are all within ±3%. The relative error of axial deformation between the value solved by the model and the detection value is close to −1%. This conclusion demonstrates the rationality and accuracy of the thermal characteristics solving model and the construction of nonlinear time-varying factors. This study is of great significance for exploring the thermal characteristics of the spindle system and improving CNC machine tool performance in depth.

Low-Complexity Control for Uncertain SbW Systems with Time-Varying Nonlinearity and Prescribed Tracking Performance

Low-Complexity Control for Uncertain SbW Systems with Time-Varying Nonlinearity and Prescribed Tracking Performance

Time-varying nonlinear parameters identification of high-speed train suspension system based on WMA

The parameters identification of suspension components provides a foundation for health assessment of the high-speed train. Considering the time-varying nonlinearity of suspension parameters caused by changing temperature, this work identifies the time-varying nonlinear parameters based on the wavelet multiresolution analysis (WMA) combined with the proposed improved Akaike information criterion (AIC). Firstly, the parameters variation law against time-temperature are fitted based on test data and the vibration responses of a two-degree-of-freedom suspension model are obtained. Secondly, the time-varying nonlinear parameters are expanded into scale coefficients using WMA. Thus, the identification of time-varying nonlinear parameters is transformed into the identification of time-invariant wavelet scale coefficients. Then the improved AIC is utilized to select the optimal basis functions and decomposition scales in noisy environments. The identified parameters vectors are used by the improved AIC as evaluation index of identification model to reduce the effect of noise. Finally, the time-varying nonlinear parameters are reconstructed based on the optimal wavelet scale coefficients. The results show that the time-varying nonlinear stiffness and damping coefficients can be accurately identified based on the WMA combined with the proposed improved AIC.

Hyperstability of Linear Feed-Forward Time-Invariant Systems Subject to Internal and External Point Delays and Impulsive Nonlinear Time-Varying Feedback Controls

This paper investigates the asymptotic hyperstability of a single-input–single-output closed-loop system whose controlled plant is time-invariant and possesses a strongly strictly positive real transfer function that is subject to internal and external point delays. There are, in general, two controls involved, namely, the internal one that stabilizes the system with linear state feedback independent of the delay sizes and the external one that belongs to an hyperstable class and satisfies a Popov’s-type time integral inequality. Such a class of hyperstable controllers under consideration combines, in general, a regular impulse-free part with an impulsive part.

Income Convergence in Southern Africa: A Nonlinear Time-Varying Framework

ABSTRACT: Convergence is considered a fundamental economic mechanism and a necessary condition for achieving industrial development and market integration as well as socio-economic cohesion in the Southern African Development (SADC) region. The former is the explicit objective of the SADC, as formulated in its Regional Indicative Strategic Development Plan (RISDP). "[A] key priority under this pillar will be ensuring macroeconomic convergence, increased cooperation, and investment". Despite convergence being a crucial ingredient for the proposed integration in the region, there has been limited research on the subject in Africa, particularly, SADC. To bridge this gap, this study sought to investigate per capita income convergence or lack thereof, in the SADC region over the period 1980 to 2017. To this end, we employed the approach proposed by Phillips and Sul (2008), which not only tests for overall convergence but for the possibility of multiple equilibria as well. Relative to the conventional approaches, this approach is superior in many respects. For instance, this technique requires no prior knowledge about possible convergence clusters, that is, the clusters are endogenously determined. Moreover, it imposes no restraints regarding trend stationarity or stochastic non-stationarity. Consequently, our findings are immune from the inefficiencies linked to unit roots or cointegration tests. The findings of the study suggested no overall convergence in the SADC region, but evidence supporting the existence of five convergence clubs, with each cluster converging to its steady-state equilibrium, and one divergent country, Angola. The first club consisted of only the high-income countries in the region, Seychelles, and Mauritius. The second convergence club had two members as well, South Africa and Botswana, whereas the third club consisted of the Kingdom of Eswatini and Namibia. In the fourth club, the identified members are Comoros, which is not included in the previous study because it was recently admitted into the bloc, Lesotho, Malawi, Mozambique, Tanzania, Zambia, and Zimbabwe, while in the fifth club, the members are the Democratic Republic of Congo and Madagascar. The findings of this study have in-depth implications for the development policies in the SADC region. These findings suggest that the region should consider adopting and implementing policies that would explicitly target low-income countries to promote convergence, and thus, create a conducive environment for the proposed monetary union in the SADC bloc.

Passive Fuzzy Controller Design for the Parameter-Dependent Polynomial Fuzzy Model

This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent NTV systems. According to the Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of the PDPF model. Furthermore, the passive theory is applied to achieve performance, constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions, which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller, such that the NTV system is robustly stable and passive. Finally, two examples are applied to demonstrate the effectiveness of the proposed stability criterion.

Bright matter-wave bound soliton molecules in spin-1 Bose–Einstein condensates with non-autonomous nonlinearities

This work deals with matter-wave bright soliton molecules in spin-1 Bose–Einstein condensates described by three-component Gross–Pitaevskii equations with non-autonomous nonlinearities that can be tuned by Feshbach resonance management. Notably, it portrays the possibility to generate bright bound soliton molecules with the help of an exact analytic solution under a controlled velocity resonance mechanism. Results show that these soliton molecules experience the effects of time-varying nonlinearities and modulate themselves during propagation by keeping their stable properties. Significantly, the chosen periodic and kink-like nonlinearities expose the snaking, bending, compression, and amplification of multi-structured soliton molecules along with appreciable changes in their amplitude, velocity, width, and oscillations of the molecule profiles. The present results will add significant knowledge to a complete understanding beyond the known interaction dynamics of matter-wave bright solitons in spinor condensates.

Multivariate linear-regression variable parameter spatio-temporal zoning model for temperature prediction in steel rolling reheating furnace

In the steel industry, temperature control and prediction of billets during heating in steel rolling reheating furnace (SRRF) can guarantee product performance and save energy consumption. However, the nonlinear time-varying (NTV) and distributed of SRRF are a great challenge for the accurate temperature control of billets. It is important to predict and regulate the temperature of the SRRF online and to identify the causal variables that may lead to temperature variations. In this paper, a new multivariate linear regression variable parameter spatio-temporal (MLR-VPST) zoning model approach is proposed to predict the temperature. Firstly, a MLR-VPST zoning model method is proposed to predict the temperature of the SRRF, which can handle the distribution characteristics of the temperature field and the NTV characteristics. Secondly, a new least squares matrix block (LSMB) algorithm is proposed to obtain batch parameter solutions, which can improve the dynamic and temperature prediction accuracy. Thirdly, a zoning model approach is proposed to describe the degree of fitting of the SRRF model in each zone, and the linear correlation is gradually increasing from the reheating zone to the soaking zone. It makes the temperature of the soaking zone more accurate. Simulation results of real-time data from steel company show that it meets the requirements of the rolling process.

On Averaging Technique for Nonlinear Time-Varying Systems without Local Lipschitz Continuity

The majority of literature for averaging methods deal with a class of nonlinear time-varying (NLTV) dynamics and their time-invariant averaged systems with locally Lipschitz continuous (LLC) condition. In this work, a class of uniformly continuous NLTV systems and their uniformly continuous averaged systems are considered. The first result shows the closeness of solutions between the original NLTV system and its averaged system with a sufficiently small time-scale separation parameter ε on a subset of a time interval, in which both systems have well-defined solutions. If the averaged system is finite-time stable (FTS), the second result shows that the original NLTV system will uniformly converge to an arbitrarily small neighborhood of the origin on a finite-time interval with sufficiently small ε. Simulation results support the theoretical finding.

Model parameter identification for lithium-ion batteries using adaptive multi-context cooperatively co-evolutionary parallel differential evolution algorithm

Lithium-ion battery (LIB) has a polarization phenomenon during charging and discharging processes, and the internal chemistry of LIB is characterized by severe time-varying nonlinearity. Therefore, the equivalent circuit model (ECM) is usually used for LIB research. To address the problems of low identification accuracy and local optimization in the offline identification of battery parameters, this paper proposes a novel adaptive multi-context cooperatively co-evolutionary parallel differential evolution (AMCC-PDE) algorithm to identify parameters of LIB. Firstly, the data segment to be identified is divided into a plurality of segments according to the state of charge (SOC), and each segment is called a unit data segment (UDS). In addition, the UDS has a parameter group (PG) for the first-order RC model. Secondly, according to the differential equation of the first-order RC model, the PG (R0+,R0−, D1, R1, U1, init) of each UDS and the open-circuit voltage (UOCV) at each sampling point are considered as variables to be optimized. Then, such an optimization problem is transformed into a large-scale global optimization (LSGO) problem. In addition, to trade off the relationship between population diversity and convergence speed, a novel parallel mutation strategy is proposed. Finally, an AMCC-PDE algorithm is proposed to solve the above LSGO parameters identification model. In both of the DST and FUDS datasets, the identification error at each point obtained by AMCC-PDE is lower than 2 mV, which shows the effectiveness of AMCC-PDE and indicates that the algorithm can avoid destroying the variable-coupling relationship.

Analysing the linkage between total factor productivity and tourism growth in Latin American countries

PurposeThe study aims to investigate the nexus between total factor productivity and tourism growth in Latin American countries for time series data from 1995 to 2017.Design/methodology/approachUsing the extension of the Granger noncausality test in the nonlinear time-varying of Ajmi et al. (2015), the study points out the interconnectedness between the variables during the period.FindingsThe study found nonlinear causality between the variables. Particularly, studying the conclusions for the time-varying Granger causality fashion, it can be noticed that the one-way causality from total factor productivity to tourism growth is obtained for Argentina, Bolivia, Brazil, Uruguay and Venezuela, while the vice versa is confirmed for Chile, Ecuador and Nicaragua. Lastly, the study dissected the plots of the curve causality.Practical implicationsIn view of the results, some crucial policy implications could be suggested, such as, under certain circumstances and as an exceptional case, the use of policy instruments such as targeted investment, marketing and the support of tourism organizations focused on driving a tourism-led-based productivity and/or tourism programs and projects.Originality/valueThe current work is distinguished from the existing body of understanding in several substantial directions. This work explores, for the first time, the linkages between the total factor productivity index and tourism growth for Latin American countries. No single attempt has been known to investigate this interaction by using nonlinear causality, and this study determines the shape of the curve between the total factor productivity index and tourism growth for each country.

Extension of the Observability Rank Condition to Time-Varying Nonlinear Systems

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors.

A Method for Controlling Series and Parallel Nonlinear Time-Varying LRC Circuits

Series and parallel LRC circuit systems are widely encountered in numerous electrical, electronics, control issues and differential equation applications. Accurate control of the current in series and voltage in parallel LRC circuit systems with nonlinear time-varying inductance, resistance and capacitance is a challenge. In this study, a novel approach proposed for control of current in nonlinear time-varying series LRC circuit and voltage in nonlinear and time-varying parallel LRC circuit. The proposed controller is characterized by a nonlinear algebraic equation and straining the tracking error converge to zero. Illustrative results confirm the proposed approach for forcing the current /voltage in series and parallel nonlinear time-varying LRC circuit to follow the targeted current /voltage trajectories efficiently. The proposed approach shows great novelty to determine the dynamics behavior of nonlinear time-varying systems. Therefore, the obtained results generalize and improve the existing conclusions. Simulations illustrate the feasibility and validity of the theoretical results.

Stability of state-delayed digital filters with overflow nonlinearities

In this work, stability of digital filters in the presence of overflow nonlinearities and time-varying delay is investigated with/without external disturbance. Two new lemmas related to characterization of overflow nonlinearities are developed. The first lemma is established with better utilization of system information which includes overflow nonlinearities, previous and current states of the digital filter. The second lemma associated with overflow nonlinearities is developed with lesser constraints. Furthermore, by utilizing the established lemmas and a new Lyapunov functional, an asymptotic stability condition is presented for the digital filter with time-varying delay and overflow nonlinearities. The developed condition is shown to be more relaxed and computationally less demanding than the existing criteria. In addition to that, a sufficient condition is derived under which the digital filter with external disturbance, overflow nonlinearities, and time-varying delay has a prescribed noise attenuation level. To show the efficacy of the proposed approach, numerical examples are presented.

Broad-RBFNN-Based Intelligence Adaptive Antidisturbance Formation Control for a Class of Cluster Aerospace Unmanned Systems with Multiple High-Dynamic Uncertainties

This paper investigates the antidisturbance formation control problem for a class of cluster aerospace unmanned systems (CAUSs) suffering from multisource high-dynamic uncertainties. Firstly, to estimate and compensate the uncertainties existing in CAUS coordinate dynamics, an adaptive antidisturbance formation control law, which is combined by a robust adaptive control law and the second order disturbance observer, has been designed. Secondly, aiming at the adverse influences caused by the nonlinear time-varying nonlinearities existing in the formation flight dynamics, the radial basis function neural network (RBFNN) is introduced. Furthermore, considering the rapidly varying characteristics of the aforementioned formation flight nonlinearities, a novel board RBFNN (B-RBFNN) has been constructed and utilized to improve the approximation and compensation performance. In virtue of the fusing of the B-RBFNN and the second-order disturbance observer-based adaptive formation control law, the rapid response rate and the higher control accuracy of the formation control system can be achieved. As a result, a novel B-RBFNN-based intelligence adaptive antidisturbance formation control algorithm has been established for CAUS trajectory coordination and formation flight. Numerical simulation results are proposed to illustrate the effectiveness and advantages of the proposed B-RBFNN-based intelligent adaptive formation control method for the CAUS.