Impulse Control Problem Research Articles

Optimal impulse dividend and capital injection model with proportional and fixed transaction costs

In this paper, a hybrid strategy with optimal proportional reinsurance, dividends, and capital injections is discussed by a diffusion model with impulse process of discrete dividend events and discrete capital injections. Due to the presence of fixed transaction costs, the problem is formulated as a more complicated impulse stochastic control problem. By using methodologies from impulse control theory and the techniques of translation transformation, we obtain the explicit solutions of the value function and the corresponding optimal strategy. Firstly, the original problem is transformed into two types of suboptimal impulse control problems, one of which is “the case without capital injections” and the other one of which is “the case with compulsory capital injections.” Then, by verification theorem and the expressions of value functions of these two suboptimal problems, we verify that the optimal solution of the original problem is either “keeping bankruptcy without injections” or “never bankruptcy with injections.” It depends on the parameters of the model.

An algorithm based on an iterative optimal stopping method for Feller processes with applications to impulse control, perturbation, and possibly zero random discount problems

In this paper we present an iterative optimal stopping method for general optimal stopping problems for Feller processes. We show using an approximating scheme that the value function of an optimal stopping problem for some general operator is the unique viscosity solution to an Hamilton–Jacobi–Bellman equation (see for example Theorems 2.3 and 2.4). We apply our results to study impulse control problems for Feller–Markov processes and derive explicit solutions in the case of one dimensional regular Feller diffusion. We also use our result to study optimal stopping problems for both regime switching and semi-Markov processes and characterize their value functions as the limit of iterative optimal stopping problems (see Corollary 4.2 and Proposition 4.3 ). Finally, we examine optimal stopping problems for random (possibly zero) discount.

Generalized invexity and duality in multiobjective variational problems involving non-singular fractional derivative

AbstractIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo–Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.

The associations between ADHD, pain, inflammation, and quality of life in children and adolescents-a clinical study protocol.

New research shows that the prevalence of neurodevelopmental disorders, such as attention-deficit/hyperactivity disorder (ADHD), is increased in children and adolescents as well as in adults with chronic pain, compared to those without chronic pain. Children and adolescents with ADHD also have an increased incidence of various physical conditions associated with pain, and they more frequently suffer from inflammatory diseases. Moreover, parents of children with ADHD can often suffer from pain conditions. These epidemiological and clinical observations form the scientific basis of our study, which aims to map the relationships between ADHD, altered pain experiences/central sensitization, and inflammation in children and adolescents. We will investigate the presence of central sensitization in children and adolescents with newly diagnosed ADHD and compare it with those who have not been diagnosed with ADHD. Participants (and their biological parents) will complete surveys about their somatic health, pain experience, and quality of life. Biological samples (saliva and stool) will be collected, aiming to utilize proteome and metabolome data to discover disease mechanisms and to predict, prevent and treat them. The results from our investigation should enable an expanded understanding of the pathophysiology behind both ADHD and pain/central sensitization. Presently, there are no established protocols for addressing psychiatric symptoms when examining patients with pain conditions in a somatic care setting, nor is there any knowledge of offering patients with ADHD or other neurodevelopmental disorders adapted treatments for pain conditions. Our results, therefore, can contribute to the development of new treatment strategies for pathological pain conditions in children and adolescents with ADHD. They may also increase awareness about and provide opportunities for the treatment of attention and impulse control problems in children and adolescents with pain syndromes.

Impulsive Control for Nonlinear Systems Under DoS Attacks: A Dynamic Event-Triggered Method

In this brief, the impulsive control problem is addressed for a class of unstable nonlinear systems under denial-of-service (DoS) attacks. A dynamic event-triggered impulsive control (DETIC) method is proposed to achieve asymptotic stability for the resulting closed-loop systems. A new class of impulsive control systems with dynamic event-triggered impulse instants are formulated, and some easily verifiable conditions are provided. The introduction of internal dynamic variable facilitates the regulation of the control frequency. Here, Zeno behaviors can be easily excluded by the proposed method. Finally, two examples, which include a Chua’s circuit and a numerical example, are given to demonstrate the efficiency of the method.

Event-Triggered Impulsive Control for Stochastic Networked Control Systems Under Cyber Attacks

The event-triggered impulsive control (ETIC) problem is studied for stochastic networked control systems (NCSs) under random cyber attacks. The random cyber-attacks model is proposed to integrate denial-of-service (DoS) attacks and deception attacks into a unified framework by means of two independent Bernoulli random sequences. In ETIC systems, the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. In order to exclude the Zeno behavior, an easy and effective method is provided to choose the waiting time of continuous ETM and the sampling period of periodic ETM. According to the proposed ETMs, sufficient conditions of the mean-square exponential stability are derived for stochastic NCSs. An example of Chua’s circuits is given to explain our ETIC schemes.

Stabilization Analysis and Impulsive Controller Design for Positive Interval Type-2 Polynomial Fuzzy Systems

This article investigates the polynomial fuzzy impulsive control problem for positive nonlinear systems subject to parameter uncertainties. The positive nonlinear systems are represented as positive interval type-2 (IT2) polynomial fuzzy-model-based systems, while the parameter uncertainties are captured by the IT2 membership functions (MFs). Considering that the controller being designed needs to be implementable and practical, in addition to ensuring the positivity and stability of the system, there are still some potential requirements for the controller, such as lower implementation cost and control cost. To reduce the implementation cost, the IT2 polynomial fuzzy impulsive controller is designed under the imperfect premise matching concept that the premise MFs and the number of rules of fuzzy controller are different from those of fuzzy model. To reduce the control cost, the impulsive controller that can tolerate larger impulse control interval (ICI) is designed by the following two novel methods. The first one is the proposed impulse-time-dependent discretized polynomial copositive Lyapunov function whose Lyapunov variable is designed as the interpolation polynomial function of time. The second one is the advanced IT2 membership-function-dependent (IT2MFD) analysis method which is improved by a novel footprint of uncertainty partitioning method proposed by this paper, so that this advanced IT2MFD method can alleviate the negative impact of parameter uncertainties on the ICI. Finally, a simulation example using lipoprotein metabolism and potassium ion transfer model as the nonlinear system to be controlled is used to verify the effectiveness of the proposed impulsive control methods.

On an Approximation of Average Cost per Unit Time Impulse Control of Markov Processes

In this paper we consider impulse control of continuous time Markov processes with average cost per unit time functional. This problem is approximated using impulse control problems stopped at the first exit time from an increasing sequence of open sets. We find a solution to the Bellman equation corresponding to the original problem and show that stopped impulse control problems approximate optimal value of the cost functional.

Sequential Systems of Reflected Backward Stochastic Differential Equations with Application to Impulse Control

We consider a system of finite horizon, sequentially interconnected, obliquely reflected backward stochastic differential equations (RBSDEs) with stochastic Lipschitz coefficients. We show existence of solutions to our system of RBSDEs by applying a Picard iteration approach. Uniqueness then follows by relating the limit to an auxiliary impulse control problem. Moreover, we show that the solution to our system of RBSDEs is connected to weak solutions of a stochastic differential game where one player implements an impulse control while the opponent plays a continuous control that enters the drift term. As all our arguments are probabilistic and hence hold in a non-markovian framework, we are able to consider the setting where the underlying uncertainty in the game stems from an impulsively and continuously controlled path-dependent stochastic differential equation driven by Brownian motion.

Treating Patients with Aripiprazol: A Safe Gamble?

IntroductionAripiprazole (ARI) is an atypical antipsychotic drug with D2 partial agonist properties, usually prescribed to treat mood disorders (major depression or bipolar disorder) and schizophrenic disorder (schizophrenia or schizoaffective disorder). Dopamine receptor agonists, as is ARI, have been implicated in some cases of impulse-control problems, such as gambling disorder (GD), increased spending, hypersexuality and compulsive eating.ObjectivesCurrently, it is hypothesized that aripiprazole may cause impulse-control problems because it can produce a hyperdopaminergic state in the mesolimbic pathway (reward system) through its predominant action on dopamine D3 receptors. We intend to do a non-systematic review of the scientific information regarding this subject.MethodsThe authors revised the published literature about this topic, selecting relevant articles, systematic reviews and case reports, with the topic words: “aripiprazol”, “gambling disorder” and “dopamine receptor” in scientific data base.ResultsOverall, a few cases of ARI-induced pathological gambling as well as ARI-induced hypersexuality have been reported. In one study it was verified that comorbid psychiatric and substance use disorders were common among those who have experienced GD or worsened GD after beginning ARI treatment. In another study, it was verified that the group of patients who reported this alleged side-effect were mostly young (mean age, 33.6 years), mostly men (88.2%) and most lived alone.ConclusionsAttributing to dopamine agonists the only factor that can explain the onset of GD is simplistic and dangerous. Many other potential risk factors, including individual vulnerability factors (temperament, genetics) as well as environmental factors, must be considered.DisclosureNo significant relationships.

Stabilization of Positive Systems With Time Delay via the Takagi-Sugeno Fuzzy Impulsive Control.

In this study, the Takagi-Sugeno (T-S) fuzzy impulsive control problem is investigated for a class of nonlinear positive systems with time delay. The time delay under consideration is both in the continuous-time dynamics and at the impulsive instants, which can model practical systems more accurately. An impulse-time-dependent copositive Lyapunov function (IDCLF) is constructed, and the Razumikhin technique is adopted to develop conditions that ensure the globally exponential stability of T-S fuzzy positive systems with delayed impulses. The size constraint between the impulse delay and the bound of impulsive intervals is removed. A T-S fuzzy impulsive controller is designed in terms of the solutions to certain vector inequalities that are readily solvable. Numerical examples and a practical example of lipoprotein metabolism and potassium ion transfer model are given to demonstrate the effectiveness, advantages, and practicality of the proposed results.

Moment-constrained optimal dividends: precommitment and consistent planning

AbstractA moment constraint that limits the number of dividends in an optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz’s consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame-perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.

Saturated impulsive control of nonlinear systems with applications

The problem of saturated impulsive control of nonlinear systems is studied, where the saturation structure of impulse action is fully considered. Based on impulsive control theory and average dwell time (ADT) method, sufficient conditions for local exponential stabilization (LES) are derived. An optimization problem on designing controller is presented in order to maximize the domain of attraction. To get a less conservative estimate of the domain of attraction, a linear matrix inequality (LMI) based algorithm is proposed to solve such kind of optimization problems. The applications of the developed results are illustrated through examples from a Chua’s circuit and a problem of pulse transmission of a simple ball motion model.

Spiking Adaptive Dynamic Programming Based on Poisson Process for Discrete-Time Nonlinear Systems.

In this article, a new iterative spiking adaptive dynamic programming (SADP) method based on the Poisson process is developed to solve optimal impulsive control problems. For a fixed time interval, combining the Poisson process and the maximum likelihood estimation (MLE), the three-tuple of state, spiking interval, and probability of Poisson distribution can be computed, and then, the iterative value functions and iterative control laws can be obtained. A property analysis method is developed to show that the value functions converge to optimal performance index function as the iterative index increases from zero to infinity. Finally, two simulation examples are given to verify the effectiveness of the developed algorithm.

Robust Space Trajectory Design Using Belief Optimal Control

This paper presents a novel approach to the robust solution of optimal impulsive control problems under aleatory and epistemic uncertainty. The novel approach uses belief Markov decision processes to reformulate the control problem in terms of uncertainty distributions, called beliefs, rather than the realizations of the system states. This formulation leads to the definition of a belief optimal control problem where the cost function and constraints are functions of the uncertainty distributions. The control formulation encompasses orbit determination arcs as well. The belief optimization is solved with a shooting-like transcription and a nonlinear programming solver to optimize the resulting discretized problem. Both aleatory and epistemic uncertainties are propagated with a nonintrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimization of a flyby trajectory of the Europa Clipper mission in a scenario characterized by knowledge, execution, and observation uncertainty.

Observability of fractional order differential impulsive multi control problem with fractional integral nonlocal initial condition

In this paper ,the obsevability of fractional differential impulsive multi control abstract problem with fractional integral nonlocal initial condition have been studied as abstract Cauchy problem for using Banach fixed point which defined on space of presented problem which is piecewise continuous space and proprieties of the initial observable condition for their problem.

Hybrid optimal impulse control

This paper is concerned with an optimal impulse control problem under a hybrid diffusion (or, regime switching) model, where the state of the system consists of a number of diffusions coupled by a continuous-time finite-state Markov chain. The objective is to minimize the expected discounted cost from exerting the impulse control in the infinite horizon. Based on the dynamic programming principle (DPP), the value function of the hybrid optimal impulse control problem is shown to be the unique viscosity solution to the associated Hamilton–Jacobi–Bellman (HJB) equation, which is in the form of a coupled system of variational inequalities. Moreover, a verification theorem as the sufficient condition for optimality of a solution is also established. The optimal impulse control, indicates when and how it is optimal to intervene, is described by the obstacle part of the HJB equation. Finally, the general theoretical results are applied to an optimal cash management problem. The value function in closed-form and an explicit optimal policy are obtained, which exhibit clearly the effect of regime switching on the agent’s decision.

Optimal impulse control of West Nile virus

<abstract><p>We construct a West Nile virus epidemic model that includes the interaction between the bird hosts and mosquito vectors, mosquito life stages (eggs, larvae, adults), and the dynamics of both larvicide and adulticide. We derive the basic reproduction number for the epidemic as the spectral radius of the next generation matrix. We formulate two impulsive optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with the benefit of (1) vector control: reducing the number of mosquitoes or (2) disease control: reducing the disease burden. We reformulate these impulsive optimal control problems as nonlinear optimization problems and derive associated necessary conditions for the optimal controls. Numerical simulations are used to address three questions: How does the control and its impact on the system vary with the objective type? Is it beneficial to optimize the treatment timing? How does the control and its impact on the population vary with the type of pesticide used?</p></abstract>

Jacobi stability analysis and impulsive control of a 5D self-exciting homopolar disc dynamo

<p style='text-indent:20px;'>In this paper, we make a thorough inquiry about the Jacobi stability of 5D self-exciting homopolar disc dynamo system on the basis of differential geometric methods namely Kosambi-Cartan-Chern theory. The Jacobi stability of the equilibria under specific parameter values are discussed through the characteristic value of the matrix of second KCC invariants. Periodic orbit is proved to be Jacobi unstable. Then we make use of the deviation vector to analyze the trajectories behaviors in the neighborhood of the equilibria. Instability exponent is applicable for predicting the onset of chaos quantitatively. In addition, we also consider impulsive control problem and suppress hidden attractor effectively in the 5D self-exciting homopolar disc dynamo.</p>

Mathematical modeling and analysis of biological control strategy of aphid population

<abstract><p>To study the biological control strategy of aphids, in this paper we propose host-parasitoid-predator models for the interactions among aphids, parasitic wasps and aphidophagous Coccinellids incorporating impulsive releases of Coccinellids, and then study the long-term control and limited time optimal control of aphids by adjusting release amount and release timing of Coccinellids. For the long-term control, the existence and stability of the aphid-eradication periodic solution are investigated and threshold conditions about the release amount and release period to ensure the ultimate extinction of the aphid population are obtained. For the limited-time control, three different optimal impulsive control problems are studied. A time rescaling technique and an optimization algorithm based on gradient are applied, and the optimal release amounts and timings of natural enemies are gained. Our simulations indicate that in the limited-time control, the optimal selection of release timing should be given higher priority compared with the release amount.</p></abstract>