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Finite-Time H Control of Switched Nonlinear Systems under State-Dependent Switching
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作者 Xiaoyue Zhang Yao Wang 《Journal of Applied Mathematics and Physics》 2023年第7期2053-2068,共16页
This paper investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dep... This paper investigates the finite-time H<sub>∞</sub> control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H<sub>∞</sub> control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions. 展开更多
关键词 Finite-Time H Control Switched Nonlinear Systems Multiple Lyapunov-Like Functions state-dependent Switching
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Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay
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作者 Suping Wang Qiaozhen Ma Xukui Shao 《Engineering(科研)》 2023年第10期632-646,共15页
This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability ... This work is devoted to the following suspension bridge with state-dependent delay: . The main goal of this paper is to investigate the long-time behavior of the system. Under suitable hypothesis, the quasi-stability estimates of the system are established, based on which the existence of global attractor with finite fractal dimension is obtained. Furthermore, the existence of exponential attractor is proved. 展开更多
关键词 Suspension Bridge Equation state-dependent Delay Global Attractor Exponential Attractor Quasi-Stability
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EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY 被引量:17
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作者 马和平 刘斌 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期235-258,共24页
In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ... In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results. 展开更多
关键词 CONTROLLABILITY continuous dependence fractional neutral integro-differentialequations state-dependent delay resolvent operator
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Attitude controller for reentry vehicles using state-dependent Riccati equation method 被引量:3
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作者 谢道成 王中伟 张为华 《Journal of Central South University》 SCIE EI CAS 2013年第7期1861-1867,共7页
To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated.... To get better tracking performance of attitude command over the reentry phase of vehicles, the use of state-dependent Riccati equation (SDRE) method for attitude controller design of reentry vehicles was investigated. Guidance commands are generated based on optimal guidance law. SDRE control method employs factorization of the nonlinear dynamics into a state vector and state dependent matrix valued function. State-dependent coefficients are derived based on reentry motion equations in pitch and yaw channels. Unlike constant weighting matrix Q, elements of Q are set as the functions of state error so as to get satisfactory feedback and eliminate state error rapidly, then formulation of SDRE is realized. Riccati equation is solved real-timely with Schur algorithm. State feedback control law u(x) is derived with linear quadratic regulator (LQR) method. Simulation results show that SDRE controller steadily tracks attitude command, and impact point error of reentry vehicle is acceptable. Compared with PID controller, tracking performance of attitude command using SDRE controller is better with smaller control surface deflection. The attitude tracking error with SDRE controller is within 5°, and the control deflection is within 30°. 展开更多
关键词 reentry vehicle attitude controller nonlinear control state-dependent Riccati equation Schur algorithm trackingperformance
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A numerical study of comparison of two one-state-variable,rate-and state-dependent friction evolution laws 被引量:2
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作者 Jeen-Hwa Wang 《Earthquake Science》 CSCD 2009年第2期197-204,共8页
The two one-state-variable, rate- and state-dependent friction laws, i.e., the slip and slowness laws, are com- pared on the basis of dynamical behavior of a one-degree-of-freedom spring-slider model through numerical... The two one-state-variable, rate- and state-dependent friction laws, i.e., the slip and slowness laws, are com- pared on the basis of dynamical behavior of a one-degree-of-freedom spring-slider model through numerical simulations. Results show that two (normalized) model parameters, i.e., A (the normalized characteristic slip distance) and β-α (the difference in two normalized parameters of friction laws), control the solutions. From given values of △, β, and α, for the slowness laws, the solution exists and the unique non-zero fixed point is stable when △〉(β-α), yet not when △ 〈(β-α). For the slip law, the solution exists for large ranges of model parameters and the number and stability of the non-zero fixed points change from one case to another. Results suggest that the slip law is more appropriate for controlling earthquake dynamics than the slowness law. 展开更多
关键词 one-state-variable rate- and state-dependent friction law direct effect evolution effect characteristic slip displacement
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Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach 被引量:1
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作者 Xueyan Zhao Feiqi Deng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第4期654-660,共7页
The relationship between the technique by state- dependent Riccati equations (SDRE) and Hamilton-Jacobi-lsaacs (HJI) equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix ... The relationship between the technique by state- dependent Riccati equations (SDRE) and Hamilton-Jacobi-lsaacs (HJI) equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective. 展开更多
关键词 nonlinear system robust control Hamilton-Jacobi-Isaacs (HJI) equation state-dependent Riccati equation (SDRE) global stabilization optimal control.
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Discontinuous event-trigger scheme for global stabilization of state-dependent switching neural networks with communication delay
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作者 Yingjie Fan Zhen Wang +1 位作者 Jianwei Xia Hao Shen 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第3期119-128,共10页
This paper is concerned with the global stabilization of state-dependent switching neural networks(SDSNNs)viadiscontinuous event-triggered control with network-induced communication delay.Aiming at decreasing triggeri... This paper is concerned with the global stabilization of state-dependent switching neural networks(SDSNNs)viadiscontinuous event-triggered control with network-induced communication delay.Aiming at decreasing triggering times,a discontinuous event-trigger scheme is utilized to determine whether the sampling information is required to be sent outor not.Meanwhile,under the effect of communication delay,the trigger condition and SDSNNs are transformed into twotractable models by designing a fictitious delay function.Then,using the Lyapunov–Krasovskii stability theory,someinequality estimation techniques,and extended reciprocally convex combination method,two sufficient criteria are established for ensuring the global stabilization of the resulting closed-loop SDSNNs,respectively.A unified framework isderived that has the ability to handle the simultaneous existence of the communication delay,the properties of discontinuousevent-trigger scheme,as well as feedback controller design.Additionally,the developed results demonstrate a quantitativerelationship among the event trigger parameter,communication delay,and triggering times.Finally,two numerical examples are presented to illustrate the usefulness of the developed stabilization scheme. 展开更多
关键词 global stabilization state-dependent switching neural networks discontinuous event-trigger scheme communication delay
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EXISTENCE,UNIQUENESS AND APPROXIMATION OF THE SOLUTION OF AN ODE WITH (INFINITELY MANY) STATE-DEPENDENT IMPULSES VIA FIXED MESH GALERKIN FORMULATION
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作者 Francois Dubeau(d’informatique Universite,de Sherbooke) 《Analysis in Theory and Applications》 1999年第2期55-73,共19页
A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses on the right-hand side. This appr... A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (in finitely many) state-dependent in pulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution.The convergence of the approximation is proved and its asymptatic order obtained. 展开更多
关键词 ODE MESH EXISTENCE UNIQUENESS AND APPROXIMATION OF THE SOLUTION OF AN ODE WITH INFINITELY MANY state-dependent IMPULSES VIA FIXED MESH GALERKIN FORMULATION VIA
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Suggested New Terms for Describing Chiral States and the State-Dependent Behavior of Chiral Systems
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作者 Karel D. Klika 《International Journal of Organic Chemistry》 2012年第3期224-232,共9页
Deficiencies in the terminology used to describe chiral systems exist for behaviors under various processes and thus a more general, robust terminology is considered. For example, the descriptions for characterizing m... Deficiencies in the terminology used to describe chiral systems exist for behaviors under various processes and thus a more general, robust terminology is considered. For example, the descriptions for characterizing melting point, solubility, and recrystallization behaviors were adopted well before it was realized that perturbation of the enantiomeric com-position (ec) due to self-disproportionation could be effected by processes other than recrystallization such as sublimation, chromatography over achiral substrates, and even distillation. Thus, an endeavor has been made to address the question of universally describing behaviors under processes that effect, or are dependent on, the ec. The main terms that have been defined with respect to behavior are homomate (analogous to a conglomerate), heteromate, bimate (analogous to a racemic compound), and unimate (analogous to a solid solution) and they apply to melting point, solubility, recrystallization, sublimation, distillation, and chromatographic processes. Additionally, suggestions for improving the terminology for describing the states of chiral systems are also considered and the defined terms are: holemate (hol, ec = 100%), scalemate (scl, 50% ec eqm, ec = 50%). 展开更多
关键词 STEREOCHEMISTRY Terminology CHIRALITY state-dependent BEHAVIOR CONGLOMERATE RACEMATE
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The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population
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作者 Fuwei Zhang Linfei Nie 《Journal of Applied Mathematics and Physics》 2016年第10期1889-1898,共10页
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptib... Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population. 展开更多
关键词 SIRS Epidemic Model Varying Total Population state-dependent Pulse Control Periodic Solution Orbital Stability
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Robust Feedback Set Stabilization of Logic Networks with State-Dependent Uncertain Switching and Control Constraints
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作者 DAI Chaoqun GUO Yuqian GUI Weihua 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第2期629-646,共18页
This study investigates the robust feedback set stabilization of switched logic control networks(SLCNs)with state-dependent uncertain switching and control constraints.First,based on the properties of the semi-tensor ... This study investigates the robust feedback set stabilization of switched logic control networks(SLCNs)with state-dependent uncertain switching and control constraints.First,based on the properties of the semi-tensor product of matrices and the vector representation of logic,an SLCN with state-dependent uncertain switching and control constraints is expressed in algebraic form.Second,an input transformation and a switching model are constructed to transfer the original SLCN into one with a free control input and arbitrary switching.The equivalence between the set stabilizability of the original SLCN and that of the resulting SLCN is established.Based on such equivalence,the authors propose a necessary and sufficient condition for robust feedback set stabilizability.Finally,an example is presented to demonstrate the application of the results obtained. 展开更多
关键词 Input transformation robust control invariant subset robust feedback set stabilizability semi-tensor product state-dependent constraints switched logic control network
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Optimal control of a nonlinear state-dependent impulsive system in fed-batch process 被引量:1
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作者 Chongyang Liu Guoqing Shi +1 位作者 Gang Liu Dianzhong Hu 《International Journal of Biomathematics》 SCIE 2023年第8期297-324,共28页
Optimal control technique is crucial to improve the yield of microbial fermentation production.In this paper,we propose a nonlinear control system with state-dependent impulses,where the impulsive volume of feeding gl... Optimal control technique is crucial to improve the yield of microbial fermentation production.In this paper,we propose a nonlinear control system with state-dependent impulses,where the impulsive volume of feeding glycerol and the critical concentration of glycerol for occurring impulse are the control variables,to formulate 1,3-propanediol(1,3-PD)fed-batch production process.We also discuss a quantity of important properties for this control system.Then,we analyze the sensitivity of system state with respect to the kinetic parameters.We further propose a constrained optimal control model governed by the control system with state-dependent impulses.The existence of the optimal impulsive controls is established.For solving this problem,we utilize an exact penalty method to transform the problem into an optimization problem with only box constraints.Moreover,an improved differential evolution method is developed to seek the optimal impulsive strategy.Finally,numerical simulation results demonstrate that,by using the optimal impulsive strategies,final 1,3-PD concentration is considerably increased under the nominal parameter values and disturbances of kinetic parameters have significant effects on the optimal final 1,3-PD yield. 展开更多
关键词 state-dependent impulsive system sensitivity analysis optimal control differential evolution fed-batch culture
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On the stability of diffusion processes with state-dependent switching 被引量:5
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作者 XI Fubao & ZHAO Liqin Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China 《Science China Mathematics》 SCIE 2006年第9期1258-1274,共17页
In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity... In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes. 展开更多
关键词 FELLER continuity coupling strong FELLER continuity EXPONENTIAL ergodicity state-dependent switching.
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Jump-diffusions with state-dependent switching:existence and uniqueness,Feller property,linearization,and uniform ergodicity 被引量:3
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作者 XI FuBao YIN Gang 《Science China Mathematics》 SCIE 2011年第12期2651-2667,共17页
This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be a-finite. The exis... This work focuses on a class of jump-diffusions with state-dependent switching. First, compared with the existing results in the literature, in our model, the characteristic measure is allowed to be a-finite. The existence and uniqueness of the underlying process are obtained by representing the switching component as a stochastic integral with respect to a Poisson random measure and by using a successive approximation method. Then, the Feller property is proved by means of introducing auxiliary processes and by making use of Radon-Nikodym derivatives. Furthermore, the irreducibility and all compact sets being petite are demonstrated. Based on these results, the uniform ergodicity is established under a general Lyapunov condition. Finally, easily verifiable conditions for uniform ergodicity are established when the jump-diffusions are linearizable with respect to the variable x (the state variable corresponding to the jump-diffusion component) in a neighborhood of the infinity, and some examples are presented to illustrate the results. 展开更多
关键词 JUMP-DIFFUSION sigma-finite characteristic measure state-dependent switching Feller property uniform ergodicity LINEARIZATION
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Optimal Reinsurance and Investment Strategies for Insurers with Regime-Switching and State-Dependent Utility Function 被引量:3
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作者 GU Ailing LI Zhongfei 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2016年第6期1658-1682,共25页
This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer,where price processes of the risky assets and wealth process of the insurer are bo... This paper considers a proportional reinsurance-investment problem and an excess-of-loss reinsurance-investment problem for an insurer,where price processes of the risky assets and wealth process of the insurer are both described by Markovian regime switching.The target of the insurer is assumed to maximize the expected exponential utility from her terminal wealth with a state-dependent utility function.By employing the dynamic programming approach,the optimal value functions and the optimal reinsurance-investment strategies are derived.In addition,the impact of some parameters on the optimal strategies and the optimal value functions is analyzed,and lots of interesting results are discovered,such as the conclusion that excess-of-loss reinsurance is better than proportional reinsurance is not held in the regime-switching jump-diffusion model. 展开更多
关键词 Excess-of-loss reinsurance optimal investment strategy proportional reinsurance REGIME-SWITCHING state-dependent utility function.
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Exponential Nonlinear Observer Based on the Differential State-dependent Riccati Equation 被引量:4
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作者 Hossein Beikzadeh Hamid D.Taghirad 《International Journal of Automation and computing》 EI 2012年第4期358-368,共11页
This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly e... This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics. We prove that under specific conditions, the proposed observer is at least locally exponentially stable. Moreover, a new definition of a detectable state-dependent factorization is introduced, and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate. 展开更多
关键词 DETECTABILITY direct method of Lyapunov exponential stability nonlinear observer region of attraction state-dependent Riccati equation (SDRE) technique
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On the State-dependent Switched Energy Functions of DFIG-based Wind Power Generation Systems 被引量:4
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作者 Yang Liu Zehui Lin +2 位作者 Kaishun Xiahou Mengshi Li Q.H.Wu 《CSEE Journal of Power and Energy Systems》 SCIE CSCD 2020年第2期318-328,共11页
This paper proposes a novel state-dependent switched energy function(SdSEF)for general nonlinear autonomous systems,and constructs an SdSEF for doubly-fed induction generator(DFIG)-based wind power generation systems(... This paper proposes a novel state-dependent switched energy function(SdSEF)for general nonlinear autonomous systems,and constructs an SdSEF for doubly-fed induction generator(DFIG)-based wind power generation systems(WPGSs).Different from the conventional energy function,SdSEF is a piece-wise continuous function,and it satisfies the conditions of conventional energy functions on each of its continuous segments.SdSEF is designed to bridge the gap between the well-developed energy function theory and the description of system energy of complex nonlinear systems,such as power electronics converter systems.The stability criterion of nonlinear autonomous systems is investigated with SdSEF,and mathematical proof is presented.The SdSEF of a typical DFIGbased WPGS is simulated in the whole processes of a grid fault and fault recovery.Simulation results verify the negativeness of the derivative of each continuous segment of the SdSEF. 展开更多
关键词 Doubly-fed induction generator state-dependent switched energy function wind power generation system
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Stochastic approximation with state-dependent noise 被引量:2
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作者 陈翰馥 《Science China(Technological Sciences)》 SCIE EI CAS 2000年第5期531-541,共11页
The purpose of stochastic approximation (SA) is to find the roots of f(·) or the maximiz-er (minimizer) of L(·) when the unknown function f(·) or L(·) can be observed but with noise. SA is an impor... The purpose of stochastic approximation (SA) is to find the roots of f(·) or the maximiz-er (minimizer) of L(·) when the unknown function f(·) or L(·) can be observed but with noise. SA is an important tool in dealing with many problems arising from systems and control, whose solutions often rely on convergence of the SA algorithm applied. Here the pathwise convergence of SA algorithms is considered, when the observation noise may depend on state by which we mean those x at which f( x) or L( x) are observed. The conditions imposed on the observation noise are the weakest in comparison with the existing ones. When the algorithm is to find the roots of f(·), the superiority of the condition given in the paper over those used in literature consists in the fact that the present condition is directly verifiable, needless to see the behaviour of the algorithm. When the algorithm is to find the maximizer (minimizer) of L(·), the present conditioin allows the observation noise to depend on the state. The conditions imposed on f(·) and L(·) are truly general: f(·) is required to be measurable and locally bounded if the roots of f(·) are sought, and the gradient of L(·) is required to be locally Lipschitz continuous if the maximizer (minimizer) of L(·) is searched. 展开更多
关键词 STOCHASTIC APPROXIMATION CONVERGENCE state-dependent noise.
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Feller property and exponential ergodicity of diffusion processes with state-dependent switching 被引量:2
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作者 XI FuBao Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China 《Science China Mathematics》 SCIE 2008年第3期329-342,共14页
In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary pr... In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. 展开更多
关键词 Feller continuity Radon-Nikodym derivative strong Feller continuity exponential ergodicity state-dependent switching 60J60 34D25
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GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED CONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS 被引量:2
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作者 Bin ZHOU Guangren DUAN He KONG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第3期477-490,共14页
By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connection... By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach. 展开更多
关键词 Bounded feedback global stabilization nonlinear control state-dependent saturation functions SP-stable polynomials.
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