Nonlinear Time-varying Research Articles

Sliding Mode Control for Markovian Switching Singular Systems with Time-Varying Delays and Nonlinear Perturbations

This paper is devoted to investigating sliding mode control (SMC) for Markovian switching singular systems with time-varying delays and nonlinear perturbations. The sliding mode controller is designed to guarantee that the nonlinear singular system is stochastically admissible and its trajectory can reach the sliding surface in finite time. By using Lyapunov functional method, some criteria on stochastically admissible are established in the form of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness and efficiency of the obtained results.

Algebraic Properties of Transfer Function Matrices for Meromorphic Nonlinear Time-Varying Systems

Algebraic Properties of Transfer Function Matrices for Meromorphic Nonlinear Time-Varying Systems

Global Asymptotic Regulation via Time-Varying Output Feedback for a Class of Uncertain Nonlinear Systems

This paper is concerned with the global regulation by time-varying output feedback for a class of uncertain nonlinear systems with unmeasurable states dependent time-varying growth and unknown control coefficients. Remarkably, in this paper, the systems allow the heavily time-varying nonlinearities (see Assumption 1), and are considerably different from those in the existing closely related literature. Moreover, the unknown system control coefficients don't necessarily belong to any known finite interval (see Assumption 2), and substantially relax the restrictions on the control coefficients in the existing closely related works. These two aspects make the adaptive method technically more difficult to implement, and consequently a time-varying approach is developed in this paper. Motivated by the recent works, a new time-varying high-gain observer is first designed to rebuild the unmeasurable system states, and in addition to compensate the serious uncertainties/unknowns and time variations in control coe...

Absolute stability of Lurie direct control systems with time-varying coefficients and multiple nonlinearities

Absolute stability of Lurie direct control systems with time-varying coefficients and multiple nonlinearities is studied in this paper. Depending on the related methods, relative magnitude of the norm-unbounded coefficients was estimated. By knowledge of nonsingular M-matrix, the Lyapunov function was constructed, and some absolute stability criteria of this kind of systems were obtained. In addition, some simple and practical corollaries were derived from the theorem of Taussky. The main contribution of this paper is that the criteria which we introduced allow for the situation that the norms of coefficient matrices are unbounded. At last, the example shows the availability of the criteria.

Two New Types of Zhang Neural Networks Solving Systems of Time-Varying Nonlinear Inequalities

To solve systems of time-varying nonlinear inequalities, this paper proposes two new types of Zhang neural networks. The first new type of Zhang neural network is based on the conventional Zhang 's neural-dynamics design method, and is termed a conventional Zhang neural network (CZNN). The other one is based on a novel variant of the conventional Zhang 's neural-dynamics design method, and is termed a modified Zhang neural network (MZNN). The theoretical analysis of both CZNN and MZNN is presented to show their excellent convergence performance. Compared with CZNN for solving systems of time-varying nonlinear inequalities, it is discovered that MZNN incorporates CZNN as its special case [i.e., MZNN using linear activation functions (MZNNL) reduces to CZNN exactly]. Besides, MZNN using power-sum activation functions (MZNNP) possesses superior convergence performance to CZNN. Computer-simulation results further demonstrate and substantiate the theoretical analysis and efficacy of both CZNN and MZNN for solving systems of time-varying nonlinear inequalities.

A precise positioning actuator based on feedback-controlled magnetic shape memory alloys

This paper describes a precise positioning system based on magnetic shape memory alloys (MSMAs). This new type of material shows an interesting potential in the area of mechatronics due to its outstanding magnetically-induced strain, which is significantly larger than the one exhibited by other common active materials such as piezoelectric ceramics. However, MSMAs still have not found their way into industrial applications mainly due to their high hysteretic behavior and the strong sensitivity to temperature changes. The aim of this paper is to present the main challenges of using MSMAs for precise positioning systems by means of a simple yet effective experimental prototype. In particular, this paper examines the problem of effectively controlling the device in closed-loop. The performance of an adaptive hysteresis compensator based on the Preisach-like Krasnosel’skii–Pokrovskii model is analyzed and evaluated in the presence of temperature changes. Experiments confirm that the undesirable effects of temperature on the precision of the device can be partially addressed with an adaptive model-based algorithm devised to cope with time-varying nonlinearities.

Mycoses invasives chez les greffés rénaux : à propos de huit cas

This study proposes a novel framework which combines marginal probabilities of default estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology and the generalized dynamic factor model (GDFM) supplemented by a dynamic t-copula. The framework models banks’ default dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures banking systemic credit risk in the three forms categorized by the European Central Bank: (1) credit risk common to all banks; (2) credit risk in the banking system conditional on distress on a specific bank or combinations of banks; and (3) the buildup of banking system vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the banking sector short-term and conditional forward default measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. Finally, the framework produces robust out-of-sample forecasts of the banking systemic credit risk measures. This paper advances the agenda of making macroprudential policy operational.

Low complexity look up table based adaptive digital predistorter with low memory requirements

With the advent of spectrally efficient wireless communication systems employing modulation schemes with varying amplitude of the communication signal, linearization techniques for nonlinear microwave power amplifiers (PAs) have gained significant interest. In this article, a low complexity, direct-learning multilevel lookup table based adaptive digital predistortion technique has been proposed to linearize a PA. A loop delay compensation scheme has been used to achieve a significant reduction in convergence time and an improvement in linearization accuracy in the presence of an unknown loop delay. Compared with the conventional predistorters, the proposed technique shows fast adaptation speed which enables the predistorter to track time-varying PA nonlinearities.

Dynamics of a Crossed Beveloid Gear Pair with Time-Varying Mesh and Backlash Nonlinearity

A torsional time-varying vibration model of a beveloid gear pair with backlash nonlinearity is formulated. It incorpprates the load-dependant time-varying mesh characteristic vectors and backlash non-linearity. Using the proposed model, the influence of mesh damping and non-linear backlash on beveloid gear dynamics is investigated. Computational results reveal numerous interesting nonlinear characteristics, such as jump discontinuities and chaotic behaviors.

Adaptive active control of periodic vibration using maglev actuators

In this paper, active control of periodic vibration is implemented using maglev actuators which exhibit inherent nonlinear behaviors. A multi-channel feedforward control algorithm is proposed to solve these nonlinear problems, in which maglev actuators are treated as single-input–single-output systems with unknown time-varying nonlinearities. A radial basis function network is used by the algorithm as its controller, whose parameters are adapted only with the model of the linear system in the secondary path. Compared with the strategies in the conventional magnetic-levitation system control as well as nonlinear active noise/vibration control, the proposed algorithm has the advantage that the nonlinear modeling procedure of maglev actuators and the usage of displacement sensors could be both avoided. Numerical simulations and real-time experiments are carried out based on a multiple-degree-of-freedom vibration isolation system. The results show that the proposed algorithm not only could efficiently compensate for the actuators’ time-varying nonlinearities, but also has the ability to greatly attenuate the energy of periodic vibration.

Modeling and Optimization of Cement Raw Materials Blending Process

This paper focuses on modelling and solving the ingredient ratio optimization problem in cement raw material blending process. A general nonlinear time‐varying (G‐NLTV) model is established for cement raw material blending process via considering chemical composition, feed flow fluctuation, and various craft and production constraints. Different objective functions are presented to acquire optimal ingredient ratios under various production requirements. The ingredient ratio optimization problem is transformed into discrete‐time single objective or multiple objectives rolling nonlinear constraint optimization problem. A framework of grid interior point method is presented to solve the rolling nonlinear constraint optimization problem. Based on MATLAB‐GUI platform, the corresponding ingredient ratio software is devised to obtain optimal ingredient ratio. Finally, several numerical examples are presented to study and solve ingredient ratio optimization problems.

Banking Systemic Vulnerabilities: A Tail-Risk Dynamic CIMDO Approach

This study proposes a novel framework which combines marginal probabilities of default estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology of Segoviano, and the generalized dynamic factor model (GDFM) supplemented by a dynamic t-copula. The framework models banks? default dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures banking systemic credit risk in three forms: (1) credit risk common to all banks; (2) credit risk in the banking system conditional on distress on a specific bank or combinations of banks and; (3) the buildup of banking system vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the banking sector short-term and conditional forward default measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. Finally, the framework produces robust outof-sample forecasts of the banking systemic credit risk measures. This paper advances the agenda of making macroprudential policy operational.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Digital PID Algorithm of Navigation System for Spraying Robot

Electromagnetically inductive navigation system of the spraying robot is developed to meet the requirements of automatic spraying operation. The system is composed of the mechanical part, electromagnetic inductive sensor, SCM-based control system and DC electromotor PWM drive system. The mathematical model constituted by integral element and inertia element is founded with the DC servo-motor voltage as the input variable through the structural analysis of the navigation system. The increment digital PID algorithm is applied to achieve running path control of the spraying robot. Experimental results indicate that the spraying robot navigation system based on digital PID algorithm overcomes time-varying volatility, nonlinearity and strong coupling, thus has fast response speed and good robustness.

Neural Networks-Based Adaptive Control for Nonlinear Time-Varying Delays Systems With Unknown Control Direction

This paper investigates a neural network (NN) state observer-based adaptive control for a class of time-varying delays nonlinear systems with unknown control direction. An adaptive neural memoryless observer, in which the knowledge of time-delay is not used, is designed to estimate the system states. Furthermore, by applying the property of the function tanh(2)(ϑ/ε)/ϑ (the function can be defined at ϑ = 0) and introducing a novel type appropriate Lyapunov-Krasovskii functional, an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time-delay. It is highly proven that the closed-loop systems controller designed by the NN-basis function property, new kind parameter adaptive law and Nussbaum function in detecting the control direction is able to guarantee the semi-global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero. The characteristic of the proposed approach is that it relaxes any restrictive assumptions of Lipschitz condition for the unknown nonlinear continuous functions. And the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states. Finally, two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach.

Second-Order Switching Time Optimization for Nonlinear Time-Varying Dynamic Systems

This technical note gives a method for calculating the first and second derivatives of a cost function with respect to switching times for systems with piecewise second-differentiable dynamics. Differential equations governing the linear and bilinear operators required for calculating the derivatives are presented. Example optimizations of linear and nonlinear systems are presented as evidence for the value of second-order optimization methods. One example converges in 33 iterations using second-order methods whereas the first-order algorithm requires over 30 000 iterations.

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.

Decoupling Control of Gas Mixing Based on Fuzzy-Single Neuron Adaptive PID

The gas mixing pressuring and calorific value control of gas mixing process have the characteristics of strong coupling, nonlinear, uncertainty and large time-varying. If the calorific value of mixing gas is unstable in gas pressurization station, the quality and quantity of iron and steel production will be affected. In this paper, an compound decoupling control method of fuzzy-single neuron adaptive PID is proposed according to the mixing gas pressure and calorific value decoupling control, the fuzzy decoupling controller is used to realize the initial adjustment of mixing gas and pressure, which has the characteristics of rapidity and anti-interference performance. The fine adjustment work of control process is completed by the secondary adjustment of adaptive PID controller of single neuron, the design of controller has the ability of parameter self-learning, and the simulation results show that this design scheme has a better dynamic performance than traditional PID scheme to verify the feasibility of this method.

Incremental online sparsification for model learning in real-time robot control

For many applications such as compliant, accurate robot tracking control, dynamics models learned from data can help to achieve both compliant control performance as well as high tracking quality. Online learning of these dynamics models allows the robot controller to adapt itself to changes in the dynamics (e.g., due to time-variant nonlinearities or unforeseen loads). However, online learning in real-time applications – as required in control – cannot be realized by straightforward usage of off-the-shelf machine learning methods such as Gaussian process regression or support vector regression. In this paper, we propose a framework for online, incremental sparsification with a fixed budget designed for fast real-time model learning. The proposed approach employs a sparsification method based on an independence measure. In combination with an incremental learning approach such as incremental Gaussian process regression, we obtain a model approximation method which is applicable in real-time online learning. It exhibits competitive learning accuracy when compared with standard regression techniques. Implementation on a real Barrett WAM robot demonstrates the applicability of the approach in real-time online model learning for real world systems.

On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

A nonlinear time‐varying (NLTV) dynamic model of a hypoid gear pair system with time‐dependent mesh point, line‐of‐action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high‐speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.