ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY

Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.

Predictive functional control of integrating process based on impulse response

The predictive model is built according to the characteristics of the impulse response of integrating process. In order to eliminate the permanent offset between the setpoint and the process output in the presence of the load disturbance, a novel error compensation method is proposed. Then predictive functional control of integrating process is designed. The method given generates a simple control structure, which can significandy reduce online computation. Furthermore, the tuning of the controller is fairly straightforward. Simulation results indicate that the designed control system is relatively robust to the parameters variation of the process.

Robust Impulse Dissipative Control of Singular Systems with Uncertainties

把方法基于线性矩阵不平等( LMI )，这份报纸讨论推动为有在对的描述下面的无常的单个系统的一个班的消散的问题州空间，并且获得柔韧的推动为有由解决线性矩阵不平等的许可的无常的单个系统的消散的州的反馈控制器和产量反馈控制器。最后，我们由一个数字例子证明我们的结果的可行性。

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

PERIODIC OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR PARABOLIC EQUATIONS WITH IMPULSE CONTROL

This paper is concerned with periodic optimal control problems governed by semi- linear parabolic differential equations with impulse control. Pontryagin＇s maximum principle is derived. The proofs rely on a unique continuation estimate at one time for a linear parabolic equation.

Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control

A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.

Impulse Controller Design of a Harmonic Drive System with Friction

A friction model was established for impulse control design in a precision control system. First, the physical characteristics of the impulse in momentum, such as motion and energy, were analyzed and formulated. Then, experimental response to a new pulse with two harmonic expansions was studied. The first harmonic is the main pulse to drive the arm, and the second harmonic has two functions： its first half helps the main pulse eliminate the dead zone, and its second half, a negative pulse, stops the arm motion quickly. Finally, an impulse feedback controller was developed. Comparison between simulation and experiments shows the effectiveness of the proposed controller.

Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model

The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.

Concomitant Othello syndrome and impulse control disorders in a patient with Parkinson’s disease:A case report

BACKGROUND Othello syndrome(OS)is characterized by delusional beliefs concerning the infidelity of a spouse or sexual partner,which may lead to extreme behaviors.Impulse control disorders refer to behaviors involving repetitive,excessive,and compulsive activities driven by an intense desire.Both OS and impulse control disorders in Parkinson’s disease(PD)may be side effects of dopamine agonists.At present,there are only a few case reports and studies related to PD with concomitant OS and impulse control disorders.CASE SUMMARY We describe a 70-year-old male patient with PD,OS,and impulse control disorders,who presented with a six-month history of the delusional belief that his wife was having an affair with someone.He began to show an obvious increase in libido presenting as frequent masturbation.He had been diagnosed with PD ten years earlier and had no past psychiatric history.In his fourth year of PD,he engaged in binge eating,which lasted approximately one year.Both OS and hypersexuality were alleviated substantially after a reduction of his pramipexole dosage and a prescription of quetiapine.CONCLUSION Given its potential for severe consequences,OS should be identified early,especially in patients undergoing treatment with dopamine agonists.

Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay

For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.

Lack of Association between Impulse Control Disorders and REM Sleep Behavior Disorder in Patients with Parkinson’s Disease

Purpose: Rapid eye movement sleep behavior disorder (RBD) and impulse control disorders (ICDs) are common in subjects with Parkinson’s disease. The association between these two conditions has been contradictory. The aim of this study is to analyze the association between these two non-motor symptoms. Methods: Consecutive subjects with Parkinson’s disease attending the Movement Disorders Outpatient Clinic were included. The presence of ICDs was assessed using the Questionnaire for Impulse Control Disorders Rating Scale. RBD was diagnosed by an overnight, single night polysomnography. Results: Fifty-five consecutive subjects with Parkinson’s disease were included. The prevalence of ICDs and related behaviors was 23.6% (ICD in 14.5% and related behaviors in 9.1%). RBD was diagnosed in 47.2% of the patients. No differences were found in the frequency of ICDs and related behaviors when comparing subjects with and without RBD (23% versus 24.1%, p = 0.926, respectively). Conclusion: No association between the presence of RBD and the frequency of ICDs in subjects with Parkinson’s disease was found.

Impulsive control of permanent magnet synchronous motors with parameters uncertainties

The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.

Impulsive control of stochastic system under the sense of stochastic asymptotical stability

This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.

Impulsive control of chaotic systems and its applications in synchronization

In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.

An improved impulsive control approach to nonlinear systems with time-varying delays

A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations （FDEs）, some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Threshold Dynamics of a Vector-Borne Epidemic Model for Huanglongbing with Impulsive Control

In this paper, the basic reproduction number is calculated for Huanglongbing (HLB) model with impulses which is a vector-borne epidemic model with impulses. For controlling HLB, farmers’ experience is replanting of healthy plants and removing infected plants. To reflect the real world, we construct an impulsive control model which considers replanting of healthy plants and removing infected plants at one fixed time. By analyzing the model, we conclude that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number Ro 1, and we prove that the HLB is permanence if the basic reproduction number Ro > 1.

Impulsive controller design for nonlinear networked control systems with time delay and packet dropouts

The globally exponential stability of nonlinear impul- sive networked control systems （NINCS） with time delay and packet dropouts is investigated. By applying Lyapunov function theory, sufficient conditions on the global exponential stability are derived by introducing a comparison system and estimating the corresponding Cauchy matrix. An impulsive controller is explicitly designed to achieve exponential stability and ensure state con- verge with a given decay rate for the system. The Lorenz oscillator system is presented as a numerical example to illustrate the theo- retical results and effectiveness of the proposed controller design procedure.