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Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization
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作者 Fei Liu Song-yan Wang +1 位作者 Tao Chao Ming Yang 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2023年第8期157-179,共23页
The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actua... The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actual trajectory from the reference one.One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer(ESO) and then modify the control commands.However,ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large,which reduces the guidance accuracy.This paper introduces differential inclusion(DI) and designs a controller to solve the large-range parameter uncertainties problem.When above uncertainties have large ranges,it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set.If the DI system is stabilized,all the subsets are stabilized.Different from the traditional controllers,the parameters of the designed controller are calculated by the uncertain boundaries.Therefore,the controller can solve the problem of large-range parameter uncertainties of in ascending.Firstly,the ascent deviation system is obtained by linearization along the reference trajectory.The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation,which is called DI system.A DI adaptive saturation tracking controller(DIAST) is proposed to stabilize the DI system.Secondly,an improved barrier Lyapunov function(named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations.Compared with traditional barrier Lyapunov function,it can dynamically adjust the boundary of deviation convergence,which improve the convergence rate and accuracy of altitude,velocity and LTIA deviation.In addition,the correction amplitudes of angle of attack(AOA) and angle of sideslip(AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight.In this paper,a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate,which eliminates the adverse effects caused by the saturation.Finally,it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller.Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values.The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm.Compared with Robust Gain-Scheduling Control method,the robustness to the engine parameters are greatly improved and the control variable is smoother. 展开更多
关键词 Solid launch vehicles Trajectory tracking Adaptive controller differential inclusion
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On Fractional Differential Inclusion for an EpidemicModel via L-Fuzzy Fixed Point Results
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作者 Maha Noorwali Mohammed Shehu Shagari 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第11期1937-1956,共20页
The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have ... The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19. 展开更多
关键词 Hausdorff metric L-fuzzy set L-fuzzy set-valued map Caputo fractional differential inclusion COVID-19
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CONTINUOUS SELECTIONS OF SOLUTION SETS OF FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS 被引量:3
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作者 Aurelian CERNEA 《Acta Mathematica Scientia》 SCIE CSCD 2015年第2期399-406,共8页
Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov's theorem for a fractional i... Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov's theorem for a fractional integro-differential inclusion involving Caputo's fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered. 展开更多
关键词 differential inclusion fractional derivative decomposable set
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Controllability of Neutral Impulsive Differential Inclusions with Non-Local Conditions 被引量:2
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作者 Dimplekumar N. Chalishajar Falguni S. Acharya 《Applied Mathematics》 2011年第12期1486-1496,共11页
In this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli... In this short article, we have studied the controllability result for neutral impulsive differential inclusions with nonlocal conditions by using the fixed point theorem for condensing multi-valued map due to Martelli [1]. The system considered here follows the P.D.E involving spatial partial derivatives with α-norms. 展开更多
关键词 CONTROLLABILITY NEUTRAL IMPULSIVE differential inclusionS Spatial Partial DERIVATIVE Martelli Fixed Point THEOREM
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Existence of solutions for implicit fuzzy differential inclusions 被引量:1
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作者 Chao MIN Nanjing HUANG +1 位作者 Zhibin LIU Liehui ZHANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第3期401-416,共16页
A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed s... A class of implicit fuzzy differential inclusions (IFDIs) are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions (FDIs) and fuzzy differential equations (FDEs), which might be helpful in the analysis of fuzzy dynamic systems. 展开更多
关键词 implicit fuzzy differential inclusion (IFDI) fuzzy differential equation (FDE) selection theorem stacking theorem
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On the Approximation Solvability of the Abstract Differential Inclusion 被引量:1
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作者 Xiao Jin sheng, Huang Xiang ding College of Mathematics and Statistics, Wuhan University, Wuhan 430072,China Abstract:The approximation solvability of the 《Wuhan University Journal of Natural Sciences》 EI CAS 2001年第3期626-630,共5页
The approximation solvability of the abstract differential inclusion du/dt∈f(t,u) is presented. The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued probl... The approximation solvability of the abstract differential inclusion du/dt∈f(t,u) is presented. The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued problem are discussed. 展开更多
关键词 approximation solvability differential inclusion evolution multivalued problem
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Robust Stabilization for Nonlinear Differential Inclusion Systems Subject to Disturbances 被引量:3
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作者 CAI Xiu-Shan 《自动化学报》 EI CSCD 北大核心 2010年第9期1327-1331,共5页
关键词 非线性微分包含扰 函数 设计技术 有效性
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ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS
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作者 李国成 薛小平 宋士吉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第2期168-177,共10页
The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extr... The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed. 展开更多
关键词 evolution inclusion semi-linear differential inclusion periodic solution continuous selector compact operator fixed point
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EXISTENCE OF SOLUTIONS FORP ARABOLIC TYPE EVOLUTION DIFFERENTIAL INCLUSIONS AND THE PROPERTY OF THE SOLUTION SET
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作者 王志华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期328-331,共4页
In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-so... In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved. 展开更多
关键词 evolution operator set-valued map differential inclusion mild-solution fixed-point theorem
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ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS
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作者 刘贵方 刘益良 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1426-1434,共9页
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions an... We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems. 展开更多
关键词 anti-periodic solutions nonmonotone perturbations differential inclusions hemivariational inequalities
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GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY
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作者 Jum-Ran KANG 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期729-738,共10页
In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functio... In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases. 展开更多
关键词 General decay differential inclusion boundary value problem memory term relaxation function
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Mild Solutions for Nonlocal Impulsive Fractional Semilinear Differential Inclusions with Delay in Banach Spaces
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作者 Ahmed Gamal Ibrahim Nawal Abdulwahab Al Sarori 《Applied Mathematics》 2013年第7期40-56,共17页
In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We conside... In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We consider the case when the values of the orient field are convex as well as nonconvex. Our obtained results improve and generalize many results proved in recent papers. 展开更多
关键词 FRACTIONAL differential inclusionS IMPULSIVE SEMILINEAR Functional differential inclusionS The Infinitesimal Generator of a Semigroup NONLOCAL Conditions Mild Solutions
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Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space
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作者 T.Sathiyaraj P.Balasubramaniam 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2016年第4期400-410,共11页
In this paper,sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion(f Bm) via fixed point theorems,namely the Bohnenblust-Karli... In this paper,sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion(f Bm) via fixed point theorems,namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case.The controllability Grammian matrix is defined by using Mittag-Leffler matrix function.Finally,a numerical example is presented to illustrate the efficiency of the obtained theoretical results. 展开更多
关键词 CONTROLLABILITY fractional Brownian motion fractional order derivatives Mittag-Leffler function stochastic differential inclusions
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EXISTENCE OF SOLUTIONS TO DIFFERENTIALINCLUSIONS IN BANACH SPACES
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作者 宋福民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第11期0-0,0-0+0-0+0-0+0-0+0,共11页
In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations be... In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained. 展开更多
关键词 Banach space differential inclusion set-valued mappings existence theorem
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Sufficient Conditions of Optimality for Convex Differential Inclusions of Elliptic Type and Duality
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作者 Elimhan N. Mahmudov 《Advances in Pure Mathematics》 2012年第2期114-118,共5页
This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of conjugacy correspondence the dual problems are constructed. Using the new concepts of locally adjoi... This paper deals with the Dirichlet problem for convex differential (PC) inclusions of elliptic type. On the basis of conjugacy correspondence the dual problems are constructed. Using the new concepts of locally adjoint mappings in the form of Euler-Lagrange type inclusion is established extremal relations for primary and dual problems. Then duality problems are formulated for convex problems and duality theorems are proved. The results obtained are generalized to the multidimensional case with a second order elliptic operator. 展开更多
关键词 differential inclusion DIRICHLET Locally ADJOINT SUFFICIENT Conditions DUALITY
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Solvability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces
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作者 任仙玲 刘辉昭 《Transactions of Tianjin University》 EI CAS 2008年第1期55-60,共6页
Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in Banach spaces has been... Impulsive neutral differential inclusions play an important role in characterizing many social, physical and engineering problems, and the existence of solutions for the initial value problem in Banach spaces has been extensively studied. However, in most cases, the nonlinear term on the right-hand side of differential inclusions has to satisfy the compact or continuous assumptions. The object of this paper is to study the existence of solutions to the initial value problems of the first and second order impulsive neutral functional differential inclusions in Banach spaces under some weaker conditions, where the nonlinear term on the right-hand side does not necessarily satisfy the compact and continuous assumptions. Based on a fixed point theorem for discontinuous multivalued increasing operators, the results are obtained by means of the partial ordering method and measure of noncompactness. 展开更多
关键词 IMPULSIVE differential inclusions multivalued map fixed point Banach spaces
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Periodic Solutions for Functional Differential Inclusion with Nonconvex Right Hand Sides
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作者 吕显瑞 史少云 李晓光 《Northeastern Mathematical Journal》 CSCD 2003年第4期396-406,共11页
In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform ... In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems. 展开更多
关键词 functional differential inclusion periodic solution PERMANENCE equilibrium state
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Existence of Periodic Solutions for Differential Inclusions
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作者 翟延慧 史少云 《Northeastern Mathematical Journal》 CSCD 2000年第1期82-90,共9页
This paper deals with the periodic solution theory to differential inclusions related to periodic optimal control problems. The results of Halanay and Yoshizawa are presented for multivalued systems.
关键词 differential inclusion periodic solution EXISTENCE
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A Kind of Nonconvex-valued Functional Differential Inclusions Problems
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作者 刘晓华 王志华 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第2期90-94, ,共5页
In this paper,we consider nonconvex-valued functional differential inclusions with nonlinear semigroups in Banach spaces,the existence of the integral solutions is proved.
关键词 differential inclusion m-aeeretive operator Schauder's fixed point theorem integral solution
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具有最大项的模糊微分包含的平均法
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作者 王培光 王淳妹 鲍俊艳 《纯粹数学与应用数学》 2024年第1期44-57,共14页
通过引入模糊映射的定义,性质以及半离差概念,应用不等式技巧和Filippov定理,讨论了具有最大项的模糊微分包含解的平均问题,分别给出了右端模糊函数平均极限存在和不存在两种情况下,模糊微分包含和模糊平均包含的解之间的近似关系.
关键词 微分包含 模糊 最大项 平均法
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