Nonlinear Time-varying Systems Research Articles

Two-dimensional identification of time-varying batch nonlinear processes with input dead-zone nonlinearity

ABSTRACT In the time dimension, the batch process with input dead-zone nonlinearity often has the characteristics of short operation time and time-varying process parameters. A two-dimensional recursive least squares (2D-RLS) identification method for time-varying nonlinear systems with input dead zone is proposed. By mining system dynamic information from the time direction of the same batch and different batch directions, the identification parameters are updated. The proposed two-dimensional identification strategy converts the time-varying parameter estimation problem of time dimension into the equivalent time-invariant parameter estimation problem of batch dimension. Sufficient production data in batch dimension ensure that the proposed identification algorithm can eliminate the influence of random measurement noise. The identification strategy with unequal length of batch data is also given. The convergence of the proposed algorithm is analysed. Finally, numerical simulation and experimental tests are used to verify the effectiveness and superiority of the proposed algorithm.

Global output feedback regulation of time-varying nonlinear systems via the dual-gain method

Global output feedback regulation of time-varying nonlinear systems via the dual-gain method

Passive observer-based controller design for a class of Lipschitz nonlinear time-varying systems with application to Hepatitis B disease

In this paper, a novel passive formulation has been developed based on LMI to design passive state-observer for a wide range of Lipschitz nonlinear systems. During this formulation, a stable and strictly passive state-observer is provided in order to have passive closed-loop system. A new interconnection between passivity of subsystems and passivity/stability of the total closed-loop system has been presented. In this regard, some theorems are defined based on virtually Euler-Lagrange form of passivation. Due to using this form and the proposed theorems, the design process will simplify and speed up. A passivity-based control based on passive state-observer has been proposed to control the hepatitis B virus infection disease. The reliability of the proposed controller/observer has been examined using MATLAB/SIMULINK, where the simulation results and the sensitivity analysis demonstrate the capability of this novel approach.

Hybrid Nonlinear Passivity-Based Control Approach to Magnetic-Impulsive Spacecraft Attitude Regulation

This paper proposes two novel passivity-based control design frameworks for hybrid nonlinear time-varying dynamical systems involving an interacting amalgam of continuous-time and discrete-time dynamics whose dynamical properties evolve periodically over time. In this regard, the hybrid Kalman–Yakubovich–Popov conditions are employed in tandem with the passivity theorem to construct a three-step control design algorithm to render closed-loop dynamics stable. The proposed control architectures are subsequently exploited to regulate the attitude motion of spacecraft with magnetic and impulsive modes of operation. Practical considerations involved in implementing the proposed hybrid algorithms are then discussed in detail. Simulation results show significant improvement in the performance of the attitude control system in terms of system response, robustness, and the required magnetic and impulsive control usage as compared to a hybrid linear approach.

Distributed Energy-Based Estimation Over Harvesting-Constrained Sensor Networks.

This article investigates the distributed joint state and fault estimation issue for a class of nonlinear time-varying systems over sensor networks constrained by energy harvesting. It is assumed that data transmission between sensors requires energy consumption, and each sensor can harvest energy from the external environment. A Poisson process models the energy harvested by each sensor, and the sensor's transmission decision depends on its current energy level. One can obtain the sensor transmission probability through a recursive calculation of the probability distribution of the energy level. Under such energy harvesting constraints, the proposed estimator only uses local and neighbor data to simultaneously estimate the system state and the fault, thereby establishing a distributed estimation framework. Moreover, the estimation error covariance is determined to possess an upper bound, which is minimized by devising energy-based filtering parameters. The convergence performance of the proposed estimator is analyzed. Finally, a practical example is presented to verify the usefulness of the main results.

Controllability of the time-varying fractional dynamical systems with a single delay in control

In this article, we explored the controllability of fractional dynamical systems with a single delay in the control function with the Caputo fractional derivative. It is the first work in which the author studies the controllability of a time-varying fractional dynamical system with a delay in the control function. We develop the necessary and sufficient criteria for the solution representation of controllability of time-varying fractional linear dynamical systems by utilizing the Grammian matrix. We use Schauder’s fixed point theorem to establish sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. With the help of successive approximation techniques, numerical examples validate the theoretical results.

Distributed State Estimation for Flapping-Wing Micro Air Vehicles with Information Fusion Correction.

In this paper, we explore a nonlinear interactive network system comprising nodalized flapping-wing micro air vehicles (FMAVs) to address the distributed H∞ state estimation problem associated with FMAVs. We enhance the model by introducing an information fusion function, leading to an information-fusionized estimator model. This model ensures both estimation accuracy and the completeness of FMAV topological information within a unified framework. To facilitate the analysis, each FMAV's received signal is individually sampled using independent and time-varying samplers. Transforming the received signals into equivalent bounded time-varying delays through the input delay method yields a more manageable and analyzable time-varying nonlinear network error system. Subsequently, we construct a Lyapunov-Krasovskii functional (LKF) and integrate it with the refined Wirtinger and relaxed integral inequalities to derive design conditions for the FMAVs' distributed H∞ state estimator, minimizing conservatism. Finally, we validate the effectiveness and superiority of the designed estimator through simulations.

Adaptive Fuzzy Output-Feedback Tracking Control for Nonlinear Time-Varying State-Constrained Systems Without the Feasibility Condition

Adaptive Fuzzy Output-Feedback Tracking Control for Nonlinear Time-Varying State-Constrained Systems Without the Feasibility Condition

Quasi-Consensus Control for Stochastic Multiagent Systems: When Energy Harvesting Constraints Meet Multimodal FDI Attacks.

In this article, the quasi-consensus control problem is investigated for a class of stochastic nonlinear time-varying multiagent systems (MASs). The innovation points of this research can be highlighted as follows: first of all, the dynamics of the plant are stochastic, nonlinear, and time varying, which resembles the natural systems in practice closely. Meanwhile, an energy harvesting protocol is put forward to collect adequate energy from the external environment. Second, as a generalization of the existing result, the ultimate control objective is quasi-consensus in a probabilistic sense, that is, designing a distributed control protocol in order that the probability of centering the allowable region for the states of each agent is larger than some predetermined values. Third, the MASs are subject to false data-injection (FDI) attacks, and a more general multimodal FDI model is proposed. On the basis of the probabilistic-constrained analysis technique and the recursive linear matrix inequalities (RLMIs), sufficient conditions are provided to guarantee the probabilistic quasi-consensus property. To derive the controller gains, an optimal probabilistic-constrained algorithm is designed by solving a convex optimization problem. Finally, two examples are provided to substantiate the validity of the proposed framework.

Global Stabilization of Incommensurate Real Order Time-Varying Nonlinear Uncertain Systems

Global Stabilization of Incommensurate Real Order Time-Varying Nonlinear Uncertain Systems

State estimation-based parameter identification for a class of nonlinear fractional-order systems

Parametric identification is an important part of system theory since knowledge of the parameters allows the analysis and control of the system. The aim of this paper is to propose a novel robust (against measurement noise) parameter identification method for a class of nonlinear fractional-order systems. In order to solve the parametric identification we carry out this problem to a state estimation problem, we introduce a Fractional Algebraic Identifiability (FAI) property which allows to represent the system parameters as a function of the inputs and outputs of the system, this parameter identification method provides an on-line identification process (while the system is operating), we also propose a fractional-order differentiator which allows to reduce the effect of measurement noise as well as to provide the estimation of a fractional-order derivative of the system output. Moreover, we use the Mittag–Leffler boundedness to demonstrate the convergence of this method, a different approach for this stability analysis method is given in this paper. Finally, we illustrate the accuracy and robustness of our proposed method by means of the parametric identification of two nonlinear fractional-order systems: a time-varying nonlinear fractional-order system and a nonlinear fractional-order mathematical model of a simple pendulum.

Multi-sensor information fusion filtering for delayed nonlinear stochastic singular systems with packet disorders

The fusion filtering problem is investigated for a class of time-varying nonlinear singular systems with packet disorders (PDs). The key idea is to transfer the original singular systems with multiple sensors to full-order augmented nonsingular systems by utilizing the matrix transformation method. The phenomenon of PDs accompanied with random transmission delays (RTDs) is considered, which exists in the channel from sensor to filter. A set of independent and identically distributed random variables obeying known probability distribution are introduced to model the RTDs. A centralized fusion filter is designed, which employs the rounding function of the mathematical expectation of the RTDs. Furthermore, the nonlinear function is linearized by utilizing the method of Taylor series expansion. Then, the desired upper bounds of the estimation error covariance are guaranteed and then locally minimized through appropriately designing the corresponding filter gains. Finally, a numerical example with comparisons is carried out to verify the feasibility of the proposed fusion filtering method.

Decentralized Intermittent Feedback Adaptive Control of Non-Triangular Nonlinear Time-Varying Systems

This paper investigates the decentralized stabilization problem for a class of interconnected systems in the presence of non-triangular structural uncertainties and time-varying parameters, where each subsystem exchanges information only with its neighbors and only intermittent (rather than continuous) states and input are to be utilized. Thus far to our best knowledge, no solution exists priori to this work, despite its high prevalence in practice. Two globally decentralized adaptive control schemes are presented based on the backstepping technique, the first one is developed in a continuous fashion by combining the philosophy of the modified congelation of variables based approach with the special treatment of non-triangular structural uncertainties, which avoids the derivative of time-varying parameters and eliminates the limitation of the triangular condition, thus largely broadens the scope of application. By making use of the important property that the partial derivatives of the constructed virtual controllers in each subsystem are all constants, the second scheme is developed through directly replacing the states in the preceding scheme with the triggered ones. Consequently, the non-differentiability issue of the virtual controllers stemming from intermittent state feedback is completely obviated. The internal signals under both schemes are rigorously shown to be globally uniformly bounded with the aid of several novel lemmas, while the stabilization performance can be enhanced by appropriately adjusting design parameters. Moreover, the inter-event intervals are ensured to be lower-bounded by a positive constant. Finally, numerical simulation verifies the benefits and efficiency of the proposed method.

Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems

Adaptive Event-triggered Cooperative Tracking Control Under Full-state Constraints Based on Nonlinear Time-varying Multi-agent Systems

Trajectory control of Mars probe based on fuzzy variable parameter theory

The longitudinal dynamics model of the Mars probe's entry phase is a time-varying and nonlinear model. The study of time-varying nonlinear systems is complex. When the system is processed with a T–S fuzzy system, there is a limitation that the number of fuzzy rules increases dramatically. In this paper, the dynamic model of the Mars probe in the entry phase is treated with a fuzzy variable parameter system to overcome this shortcoming. By the process of local linearisation, a fuzzy variable parameter model of the Mars probe is established according to the time-varying characteristics of atmospheric density. Next, the full-state feedback and dynamic output feedback gain-scheduling controllers are designed based on the quadratic Lyapunov stability theory. Finally, Simulink simulation verifies that the fuzzy variable parameter system of the Mars probe's entry phase can be asymptotically stabilised by the designed controllers.

Uniform asymptotic and input to state stability by indefinite Lyapunov functions

In this work, we study uniform, uniform asymptotic, and input-to-state stability conditions for nonlinear time-varying systems. We introduce an easily verifiable condition for uniform attractivity by utilizing an indefinite sign upper bound for the derivative of the Lyapunov function. With this bounding structure, we propose novel conditions that enable us to test uniform stability, uniform asymptotic stability, and ISS, easily. As a result, the constraints on the coefficients of the bound that identify uniformity for stability and attractivity, and many of the available conditions have been relaxed. The results are also used for the perturbation problem of uniformly stable and uniformly asymptotically stable linear time-varying systems. Consequently, we demonstrate that uniform asymptotic stability of nonlinear time-varying systems can be robust for perturbations, but with special time-varying coefficients.

Finite-time stabilization of nonlinear time-varying systems involving impulsive action

This article investigates the finite-time stabilization of time-varying impulsive systems by time-varying feedback control. Moreover, the stabilizing and destabilizing effects of impulses on the stability of the system are considered, where the stabilizing impulses are used to regulate the unstable continuous dynamics. In addition, it can be found that the local and global characteristics of the finite-time stability may be affected by the stabilizing impulses. By establishing the relationship among the time-varying gain functions, the system structure and impulsive time sequences, some sufficient conditions for finite-time stability of time-varying systems involving impulsive action are proposed. Furthermore, based on the results mentioned above, a new class of finite-time controllers is designed for time-varying affine systems with external noises. The effectiveness of the proposed results is illustrated by three examples.

Practical $h$-stability behavior of time-varying nonlinear systems

Practical $h$-stability behavior of time-varying nonlinear systems

Design of Functional Interval Observer for Discrete Time-Varying Nonlinear Interconnected Systems Based on Coding-Decoding Scheme

In this paper, we design a distributed functional interval observer for discrete time-varying nonlinear interconnected systems. The communication between subsystems adapts the coding-decoding scheme (CDS) to save bandwidth and avoid data conflicts. The state set is described by the ellipsoid which can improve estimation accuracy and reduce conservatism. Besides, we give the conditions for the establishment of the observer and the stability of the error dynamic system. The observer gain matrices are obtained by solving a set of linear matrix inequalities (LMI) and some given conditions. The shape matrix of the ellipsoid is determined by selecting the optimal solution. Finally, we give two simulation examples to prove the designed functional interval observer is effective.

Adaptive Control of Noncanonical Nonlinear Systems With Time-Varying Dynamics

In this paper, adaptive control designs are systematically studied for uncertain noncanonical nonlinear systems with time-varying dynamics. As a key system characterization, the relative degrees are directly defined for noncanonical nonlinear time-varying systems, and at the same time, the necessary time-varying parameter conditions are specifically derived for different system dynamics. Then, robust adaptive feedback linearization based control designs are studied for noncanonical nonlinear systems with time-varying dynamics under different relative degree conditions. The designs ensure that all closed-loop system signals are bounded and the output tracking error is small in the mean. Simulation studies are presented for a time-varying noncanonical nonlinear aircraft model to show the effectiveness of the developed adaptive control schemes.