Boundedness Analysis Research Articles

Adaptive Saturated Obstacle Avoidance Trajectory Tracking Control for Euler–Lagrange Systems With Velocity Constraints

ABSTRACTThis article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy.

Distributed fusion filtering for multi-sensor nonlinear networked systems with multiple fading measurements via stochastic communication protocol

This paper studies the distributed fusion filtering (DFF) issue for a class of nonlinear delayed multi-sensor networked systems (MSNSs) subject to multiple fading measurements (MFMs) under stochastic communication protocol (SCP). The phenomenon of MFMs occurs randomly in the network communication channels and is characterized by a diagonal matrix with certain statistical information. In order to decrease the overload of communication network and save network resources, the SCP that can regulate the information transmission between sensors and estimators is adopted. The primary aim of the tackled problem is to develop the DFF method for nonlinear delayed MSNSs in the presence of MFMs and SCP based on the inverse covariance intersection fusion rule. In addition, the local upper bound (UB) of the filtering error covariance (FEC) is derived and minimized by means of suitably designing the local filter gain. Moreover, the boundedness analysis regarding the local UB is proposed with corresponding theoretical proof. Finally, two simulation examples with comparative illustrations are given to display the usefulness and feasibility of the derived theoretical results.

Uniform ultimate boundedness analysis for linear systems with asymmetric input backlash and dead-zone: A piecewise quadratic Lyapunov function approach

This paper deals with the interconnection between a linear system and a nonlinear operator consisting of asymmetric input backlash and asymmetric dead-zone. The uniform ultimate boundedness of the system is studied. A piecewise quadratic Lyapunov function, suitable with the polyhedral description of the nonlinear operator is proposed. The conservatism of existing results is therefore reduced. The effectiveness and improvement of the results are assessed using a numerical example.

Analysis of mathematical model for asthma caused by the effects of environmental pollution

Asthma is a condition in which your airways narrow and swell and may produce extra mucus. In this study, an improved mathematical model of asthma which includes infected class not detected, infected detected class and recovered (relieved) class was formulated. The model exhibits two equilibrium, namely disease free equilibrium and endemic equilibrium. The analysis of positivity and boundedness of solutions showed that the model is epidemiologically well pose d. Simulation results showed that when pollutants are discharged into the environment at a constant rate, the asthma disease cases also increase in the population due to the fact that the interaction rate of both susceptible and infected undetected with pollutants in creases.Finally, asthma can be control by restricting the smokers from the population and the rate of release of pollutants into the environment.

Distributed consensus filtering in sensor networks considering correlated estimation errors

This paper focuses on the distributed state estimation (DSE) problem in sensor networks through the application of a consensus-based methodology. In practical scenarios, the estimation errors within the sensor network exhibit inherent correlation, primarily arising from the consideration of same prior estimate and process noise in a distributed estimation system. However, prevailing distributed approaches, particularly those embedded within consensus-based DSE frameworks, simply assume independence among estimation errors or utilize a suboptimal strategy that neglect cross-covariance matrix, which may lead to a degraded estimation results. To address this limitation, we propose the fusion algorithm Weighted Average Consensus considering Correlated Estimates Errors, abbreviated as WACCEE. The algorithm improves DSE performance by integrating the correlation among local estimation errors as indicated by the cross-covariance matrix into the fusion process. Furthermore, we prove that the proposed WACCEE fusion algorithm exhibits consensus. Additionally, the stability of the WACCEE filters is guaranteed through an analysis of mean-square exponential boundedness of the estimation error using stochastic stability theory. Finally, the effectiveness of the proposed algorithm substantiated by its application to a target tracking case study and a connected undirected sensor network.

Offline analysis of the relaxed upper boundedness for online estimation ofoptimal event sequences in Partially Observable Petri Nets

Offline analysis of the relaxed upper boundedness for online estimation ofoptimal event sequences in Partially Observable Petri Nets

Analysis of a stochastic model for a prey–predator system with an indirect effect

In the current work, we develop and analyse a prey–predator model as a semi-Kolmogorov population model in which the predator has an indirect effect on the prey. The functional response of the model is investigated as Holling type (II). We construct a stochastic environment because of the parameter's random essence to study the influence of environmental fluctuations on this model and introduce a stochastic version of the prey–predator model. Then we present a dynamical analysis of solutions, including existence, uniqueness, positivity, stochastic boundedness, and stochastic extinction of all prey. Finally, some numerical simulations are carried out to validate our theoretical findings and confirm the efficiency and adaptation of our stochastic model.

Boundedness analysis of neutral stochastic systems driven by [formula omitted]-Brownian motion

This paper is concerned with exponential ultimate boundedness problem for a class of neutral stochastic differential systems driven by G-Brownian motion. By developing a method that combines the comparison principle and the reduction to absurdity, we provide sufficient conditions for exponential ultimate boundedness in the mean square of neutral stochastic differential systems driven by G-Brownian motion. The obtained results improve greatly some previous works given in the literature. Finally, some comparisons with existing results and examples are provided to show the effectiveness and superiority of the theoretical results.

Boundedness Analysis of the Fractional Maximal Operator in Grand Herz Space on the Hyperplane

The primary purpose of this work was to prove the boundedness of the Fractional Maximal Operator in Grand Herz Spaces on the Hyperplane. Here, We defined Grand Herz Space in a continuous Case. For Simplicity, We divided our Problem into two theorems by taking two subsets of Hyperplane( ) as ( ) and its complement . We proved the boundedness of the Fractional Maximal Operator in Grand Herz Space on these two subsets of Hyperplane. We also defined the continuous Case of Grand Herz Space. We proved some results to use in our proof. We represented other terms this paper uses, i.e. the Hyperplane and Fractional Maximal operator. Our proof method relied on one of the corollaries we gave in this paper. We proved the condition to apply that corollary, and then by referring to this, we confirmed both of our theorems. This paper is helpful in Harmonic analysis and delivers ways to analyse the solutions of partial differential equations. The Problem of our discussion provides methods to study the properties of very complex functions obtained from different problems from Physics, Engineering and other branches of science. Solutions of nonlinear Partial Differential equations often resulted in such functions which required deep analysis. Our work helps check the boundedness of such types of functions.

Optimized Distributed Fusion Filtering for Uncertain Nonlinear Systems With Missing Measurements: Algorithm Design and Boundedness Analysis

Optimized Distributed Fusion Filtering for Uncertain Nonlinear Systems With Missing Measurements: Algorithm Design and Boundedness Analysis

Distributed Resilient Fusion Filtering for Nonlinear Systems with Random Sensor Delays: Optimized Algorithm Design and Boundedness Analysis

Distributed Resilient Fusion Filtering for Nonlinear Systems with Random Sensor Delays: Optimized Algorithm Design and Boundedness Analysis

On the stability, integrability and boundedness analysis of systems of integro-differential equations with time-delay

On the stability, integrability and boundedness analysis of systems of integro-differential equations with time-delay

Stability and boundedness analysis for a system of two nonlinear delay differential equations

Stability and boundedness analysis for a system of two nonlinear delay differential equations

Finite-time contractive boundedness analysis and controller synthesis for interval positive linear systems under [formula omitted]-gain performance

This paper investigates the finite-time contractive boundedness (FTCB) analysis and controller synthesis problems for interval positive linear systems under L1-gain performance. Firstly, both FTCB and L1-gain FTCB definitions are extended to positive systems with disturbances. Subsequently, FTCB and L1-gain FTCB criteria are established for the considered positive systems by using the linear copositive Lyapunov function approach. Furthermore, the state feedback controller is designed to guarantee the positivity and L1-gain FTCB of the resulting closed-loop systems, and a convex optimization-based algorithm is given to derive the optimal L1-gain and controller parameter. Finally, a numerical example and an application example about pest control are used to verify the effectiveness of the proposed conditions.

Numerical Analysis of Linearly Implicit Methods for Discontinuous Nonlinear Gurtin-MacCamy Model.

In this study, we study a nonlinear age-structured population models with discontinues mortality and fertility rates, motivated by the fact that different maturation period may cause the significant difference in rates. We develop a novel numerical method with two-layer boundary conditions, the linearly implicit -methods on a special mesh. With a uniform boundedness analysis of numerical solutions, the finite time convergence is proved piecewisely according to the fundamental approach for the smooth rates. For juvenile-adult models, the existence of numerical endemic equilibrium is determined by a numerical basic reproduction function, which converges to the exact one with accuracy of order 1. Moreover, it is shown that for juvenile-adult models, the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium are approximately exhibited by the numerical processes. Finally, some numerical experiments on the Logistic models and tadpoles-frogs models illustrate the verification and the efficiency of our results.

Adaptive Fault-Tolerant Control of Hypersonic Vehicles with Unknown Model Inertia Matrix and System Induced by Centroid Shift

In this paper, the fault-tolerant control problem of hypersonic vehicle (HSV) in the presence of unexpected centroid migration, actuator failure and external interference is studied in depth. First, the proposed dynamics for HSV with the aforementioned unexpected factors are modeled to demonstrate the peculiar nature of the subject under study. The adverse effects of accidental centroid migration are mainly reflected in the following aspects: (1) the change of inertia matrix of the system, (2) the uncertainty of the system and (3) the eccentric moment, which are coupled and unknown. Subsequently, to account for the effect of unexpected centroid shifts, a sliding-mode observer and an adaptive estimator are designed to obtain unknowns useful for subsequent FTC controller designs. Later, we derived an innovative adaptive FTC scheme by employing the observer in conjunction with a specific adaptive controller consisting of a sixth-order dynamic compensator, which can guarantee the achievement of the control objective without resorting to the exact knowledge of the inertial matrix. Moreover, the analysis of boundedness with respect to the entire signal in this closed system is performed by means of the Lyapunov stability theory. Ultimately, simulation results show that the proposed FTC strategy is efficient and powerful.

Optimized Distributed Filtering for Time-Varying Saturated Stochastic Systems With Energy Harvesting Sensors Over Sensor Networks

This paper addresses the distributed filtering (DF) problem for time-varying saturated stochastic systems subject to energy harvesting (EH) sensors and time delay through sensor networks. The sufficient energy is a prerequisite for normal data transmission, so the EH technique is considered in the communication network, which can be regarded as an explicit decision, i.e., the sensors have the ability to harvest energy from surrounding environment. Particularly, the data information can be transmitted only when the sensors store nonzero units of energy, and vice versa. The specific probability distribution of EH level for individual sensor node can be computed iteratively at each sampling time by virtue of rigorous theoretical derivations. The focus is on the design of a novel DF scheme such that an optimized upper bound matrix on the filtering error covariance is obtained. Furthermore, the boundedness analysis with regard to the proposed filtering error dynamics is discussed with the help of some detailed mathematical computations. Finally, some comparative experiments are used to illustrate the validity of the developed variance-constrained optimized DF scheme under EH strategy.

A Time-Delay Approach to Extremum Seeking with Measurement Noise*

In this paper, we present a time-delay approach to extremum seeking (ES) corrupted by white noise for uncertain static quadratic maps. We first apply a time-delay approach to the ES system and arrive at a neutral type time-delay system with stochastic perturbations. Then we further present the latter system as a retarded one and employ the variation of constants formula for the mean-square exponential ultimate boundedness analysis. Under the assumption that the upper bound of the 6th moment of the estimation error is a known arbitrarily large constant L, explicit conditions in terms of simple scalar inequalities depending on the bound L, tuning parameters and the intensity of measurement noise are established to guarantee the mean-square exponential ultimate boundedness of the ES control systems. Comparatively to the existing results for ES with measurement noise via the qualitative analysis, our approach can provide a quantitative analysis and simplify the stability analysis process as well. A numerical simulation is given to illustrate the efficiency of the proposed method.

Recursive locally minimum-variance filtering for two-dimensional systems: When dynamic quantization effect meets random sensor failure

This article deals with the recursive filtering issue for an array of two-dimensional systems with random sensor failures and dynamic quantizations. The phenomenon of sensor failure is introduced whose occurrence is governed by a random variable with known statistical properties. In view of the data transmission over networks of constrained bandwidths, a dynamic quantizer is adopted to compress the raw measurements into the quantized ones. The main objective of this article is to design a recursive filter so that a locally minimal upper bound is ensured on the filtering error variance. To facilitate the filter design, states of the dynamic quantizer and the target plant are integrated into an augmented system, based on which an upper bound is first derived on the filtering error variance and subsequently minimized at each step. The expected filter gain is parameterized by solving some coupled difference equations. Moreover, the monotonicity of the resulting minimum upper bound with regard to the quantization level is discussed and the boundedness analysis is further investigated. Finally, effectiveness of the developed filtering strategy is verified via a simulation example.

Boundedness analysis of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion

The present article is devoted to discuss the pth moment exponential ultimate boundedness for a class of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion. By combining the method of proof by contradiction with Lyapunov method and graph theory, some sufficient condition for both the Lyapunov-type theorem and the coefficients-type theorem are proposed to ensure the pth moment exponential ultimate boundedness of the considered systems. As applications, the boundedness criteria are applied to stochastic distributed delay-coupled neural networks and stochastic distributed delay-coupled control systems in the framework of G-Brownian motion.