Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ 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∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Long-Time Behavior of Solution for Autonomous Suspension Bridge Equations with State-Dependent Delay

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.

EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

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.

Attitude controller for reentry vehicles using state-dependent Riccati equation method

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°.

A numerical study of comparison of two one-state-variable,rate-and state-dependent friction evolution laws

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.

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

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.

Discontinuous event-trigger scheme for global stabilization of state-dependent switching neural networks with communication delay

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.

EXISTENCE,UNIQUENESS AND APPROXIMATION OF THE SOLUTION OF AN ODE WITH (INFINITELY MANY) STATE-DEPENDENT IMPULSES VIA FIXED MESH GALERKIN FORMULATION

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.

Suggested New Terms for Describing Chiral States and the State-Dependent Behavior of Chiral Systems

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%).

The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population

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.

Transient postseismic slip and aftershock triggering:A case study of the 2008 M_W7.9 Wenchuan Earthquake,China

In this study,we investigate how a stress variation generated by a fault that experiences transient postseismic slip(TPS)affects the rate of aftershocks.First,we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion,that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law,and that the TPS can be explained by a continuous creep process undergoing reloading.Second,we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS.For the Wenchuan sequence,we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law(MOL),the Dieterich model,and the specific TPS model.The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12,where A and B are the parameters in the rate-and state-dependent friction law respectively.Moreover,the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance,respectively.Because the B/A ratio in the current model is always larger than 1,the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1.Finally,the influence of the background seismicity rate r on parameters is studied;the results show that except for the apparent aftershock duration,other parameters are insensitive to r.

Advances in experiments and numerical simulations on the effects of stress perturbations on fault slip

Laboratory experiments and numerical simulations on rock friction perturbations,an important means for understanding the mechanism and influencing factors of stress-triggered earthquakes,are of great significance for studying earthquake mechanisms and earthquake hazard analysis.We reviews the experiments and numerical simulations on the effects of stress perturbations on fault slip,and the results show that stress perturbations can change fault stress and trigger earthquakes.The Coulomb failure criterion can shed light on some questions about stress-triggering earthquakes but cannot explain the time dependence of earthquake triggering nor be used to investigate the effect of heterogeneous stress perturbations.The amplitude and period are important factors affecting the correlation between stress perturbation and fault instability.The effect of the perturbation period on fault instability is still controversial,and the effect of the high-frequency perturbation on earthquakes may be underestimated.Normal and shear stress perturbation can trigger fault instability,but their effects on fault slip differ.It is necessary to distinguish whether the stress perturbation is dominated by shear or normal stress change when it triggers fault instability.Fault tectonic stress plays a decisive effect on the mode of fault instability and earthquake magnitude.Acoustic emission activity can reflect the changes in fault stress and the progression of fault nucleation,and identify the meta-instability stage and precursor of fault instability,providing a reference for earthquake prediction.

Robust Feedback Set Stabilization of Logic Networks with State-Dependent Uncertain Switching and Control Constraints

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.

一类串联控制系统的优化设计:Backstepping方法

针对一类多输入非线性串联系统提出了基于Backstepping方法的次优控制的设计.首先,将串联控制系统分为几个子系统,然后为每个子系统分别设计辅助子系统及相应的辅助控制变量,进一步利用State_DependentAlgebraicRiccatiEquation(SDARE)技术为每个辅助子系统设计次优控制律.设计出的次优控制律使得原状态变量和辅助控制变量(即:辅助反馈变量)具有一定的渐近特性,因此,不但可在线获得次优控制律的解析解,而且保证了原闭环系统的全局渐近稳定性.最后通过一个两输入的二阶串联系统的数字仿真结果验证了该优化设计方法的有效性.

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an outputdependent switching law by constructing a robust Luenberger observer for each subsystem.

Dynamic optimization of 1,3-propanediol fermentation process:A switched dynamical system approach

This paper considers a dynamic optimization problem(DOP)of 1,3-propanediol fermentation process(1,3-PFP).Our main contributions are as follows.Firstly,the DOP of 1,3-PFP is modeled as an optimal control problem of switched dynamical systems.Unlike the existing switched dynamical system optimal control problem,the state-dependent switching method is applied to design the switching rule.Then,in order to obtain the numerical solution,by introducing a discrete-valued function and using a relaxation technique,this problem is transformed into a nonlinear parameter optimization problem(NPOP).Although the gradient-based algorithm is very efficient for solving NPOPs,the existing algorithm is always trapped in a local minimum for such problems with multiple local minima.Next,in order to overcome this challenge,a gradient-based random search algorithm(GRSA)is proposed based on an improved gradient-based algorithm(IGA)and a novel random search algorithm(NRSA),which cannot usually be trapped in a local minimum.The convergence results are also established,and show that the GRSA is globally convergent.Finally,a DOP of 1,3-PFP is provided to illustrate the effectiveness of the GRSA proposed by this paper.

Linear and nonlinear control of a robotic excavator

Various control systems for a robotic excavator named LUCIE (Lancaster University Computerized and Intelligent Excavator),were investigated. The excavator is being developed to dig trenches autonomously. One stumbling block is the achievement of adequate,accurate,quick and smooth movement under automatic control. Here,both classical and modern approaches are considered,including proportional-integral-derivative (PID) control tuned by conventional Zigler-Nichols rules,linear proportional-integral-plus (PIP) control,and a novel nonlinear PIP controller based on a state-dependent parameter (SDP) model structure,in which the parameters are functionally dependent on other variables in the system. Implementation results for the excavator joint arms control demonstrate that SDP-PIP controller provides the improved performance with fast,smooth and accurate response in comparison with both PID and linearized PIP control.

Nonlinear suboptimal tracking control of spacecraft approaching a tumbling target

We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass（CM）, the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft＇s sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom（DOF） relative motion model for the instrument（feature point） is set up. To make the chaser spacecraft＇s feature point track the target＇s, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation（SDRE）. The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.

Optimal control of a nonlinear state-dependent impulsive system in fed-batch process

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.

Telecloning Quantum States with Trapped Ions

We propose a scheme for telecloning quantum states with trapped ions. The scheme is based on a single ion interacting with a single laser pulse. In the protocol, an ion is firstly measured to determine whether the telecloning succeeds or not, and then another ion is detected to complete the whole procedure. The required experimental techniques are within the scope of what can be obtained in the ion-trap setup.