Impulse Control Problem Research Articles

Management of Carbon Emissions via a Nonzero-Sum Stochastic Differential Game

This study examines an environmental management strategy to effectively cap greenhouse gas (GHG) emissions in an electricity market. To do so, we model a stochastic impulse two-person, nonzero-sum game between a power plant, a representative of electricity production within a country whose primary aim is to maximize profits, and government who is motivated to minimize the social and environmental cost of pollution. We assume that the power plant’s competitive price is equal to the marginal cost whilst the government’s running cost is linear. When the uncontrolled output of GHG emissions evolves as a Geometric Brownian motion, we provide a more dynamic and robust depiction of the interplay between government and the energy sector. We provide solutions to the impulse control problem derived via the quasi-variational inequalities (QVIs). We then present a sufficiency criterion for the existence of a Nash equilibrium for the optimal policy. Ultimately, our use of short-run price competition characterized by strategic supplies for renewable and fossil resources and inclusion of endogenous constraints on production capacity provides a more robust model and an effective framework for the development of policy that allows governments to meet emissions targets whilst guaranteeing energy supply.

Examining the Effect of Disorders upon Impulsive Behavior in Criminal Actions and its Legal Implications in Emergency Department: Systematic Review

Abstract: Background: There are significant concerns regarding the relationship between mental health and criminal culpability since impulse control problems have long been linked to the genesis of criminal behaviour. In trying to clarify the complex legal ramifications that result from this link, this study explores the close link between diseases that inhibit impulse control and their possible role in criminal behaviour in patients coming to the emergency department. Aim: This research aims to explore how impulse control disorders contribute to criminal actions, emphasizing significant correlations and calling for transformative changes in emergency help for psychiatric patients and in the criminal justice system. Methodology: This study utilized Bullion Words for a literature review, identifying 24,400 hits, and narrowing down to 24 papers after rigorous selection. The systematic review explores the interplay between impulse control disorders and criminal actions, emphasizing legal implications. Ethical considerations ensure confidentiality. The study concludes with key findings, relationship insights, legal discussions, and future research suggestions. Result: This systematic review reveals a nuanced understanding of how impulse control disorders contribute to criminal actions. Identifying specific disorders like kleptomania and intermittent explosive disorder emphasizes the complex interplay of genetic, environmental, and psychological factors. The legal implications highlight the need for a paradigm shift in the criminal justice system, advocating tailored interventions and rehabilitation strategies, and offering a novel perspective for future legal frameworks. Conclusion: This systematic review provides a comprehensive overview of the complex interconnection between impulse control disorders and criminal actions. The findings underscore the importance of recognizing these disorders in legal contexts and advocate for a nuanced approach to sentencing and treatment. Future research should focus on refining diagnostic criteria, exploring intervention strategies, and elucidating the long-term impact of impulse control disorders on legal outcomes. Overall, this review contributes to a more informed understanding of the legal implications surrounding impulse control disorders and criminal actions.

Optimal impulse control problems with time delays: An illustrative example

For impulse control systems described by a measure driven differential equation, depending linearly on the measure, it is customary to interpret the state trajectory corresponding to an impulse control, specified by a measure, as the limit of state trajectories associated with some sequence of conventional controls approximating the measure. It is known that, when the measure is vector valued, it is possible that different choices of approximating sequences for the measure give rise to different limiting state trajectories. If the measure is scalar valued, however, there is a unique limiting trajectory. Now consider impulse control systems, in which the right side of the measure driven differential equation depends on both the current and delayed states. In recent work by the authors it has been shown that, for such impulse control systems with time delay, the state trajectory corresponding to a given measure may be non-unique, even when the measure is scalar valued. It was also shown that each limiting state trajectory can be identified with the unique state trajectory associated with some measure together with a family of ‘attached controls’. (The attached controls capture the nature of the measure approximation.) The authors also derived a maximum principle governing minimizers for a general class of impulse optimal control problems with time delay, in which the domain of the optimization problem comprises measures coupled with a family of ‘attached controls’. The purpose of this paper is both to illustrate, by means of an example, this newly discovered non-uniqueness phenomenon and to provide the first application of the new maximum principle, to investigate minimizers for scalar input impulse optimal control problems with time delay, in circumstances when limiting state trajectories associated with a given measure control are not unique. The example is an optimal control problem, for which the underlying control system is a forced harmonic oscillator, with scalar impulse control, in which the control gain is a nonlinear function of the current and delayed states.

The solution to an impulse control problem motivated by optimal harvesting

We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a non-explosive positive linear diffusion. The control that can be applied to this system takes the form of one-sided impulsive action. The objective of the control problem is to maximise a discounted performance criterion that rewards the effect of control action but involves a fixed cost at each time of a control intervention. We derive the complete solution to this problem under general assumptions. It turns out that the solution can take four qualitatively different forms, several of which have not been observed in the literature. In two of the four cases, there exist only ε-optimal control strategies. We also show that the boundary classification of 0 may play a critical role in the solution of the problem. Furthermore, we develop a way for establishing the strong solution to a stochastic impulse control problem's optimally controlled SDE.

A Deep Learning–Derived Transdiagnostic Signature Indexing Hypoarousal and Impulse Control: Implications for Treatment Prediction in Psychiatric Disorders

BackgroundPsychiatric disorders are traditionally classified within diagnostic categories, but this approach has limitations. The Research Domain Criteria (RDoC) constitute a research classification system for psychiatric disorders based on dimensions within domains that cut across these psychiatric diagnoses. The overall aim of RDoC is to better understand mental illness in terms of dysfunction in fundamental neurobiological and behavioral systems, leading to better diagnosis, prevention, and treatment. MethodsA unique electroencephalographic feature, referred to as spindling excessive beta, has been studied in relation to impulse control and sleep as part of the arousal/regulatory system RDoC domain. Here, we studied electroencephalographic frontal beta activity as a potential transdiagnostic biomarker capable of diagnosing and predicting impulse control and sleep problems. ResultsWe showed in the first dataset (n = 3279) that the probability of having spindling excessive beta, classified by a deep learning algorithm, was associated with poor sleep maintenance and low daytime impulse control. Furthermore, in 2 additional, independent datasets (iSPOT-A [International Study to Predict Optimized Treatment in ADHD], n = 336; iSPOT-D [International Study to Predict Optimized Treatment in Depression], n = 1008), we revealed that conventional frontocentral beta power and/or spindling excessive beta probability, referred to as Brainmarker-III, is associated with a diagnosis of attention-deficit/hyperactivity disorder, with remission to methylphenidate in children with attention-deficit/hyperactivity disorder in a sex-specific manner, and with remission to antidepressant medication in adults with major depressive disorder in a drug-specific manner. ConclusionOur results demonstrate the value of the RDoC approach in psychiatry research for the discovery of biomarkers with diagnostic and treatment prediction capacities.

Optimal drift rate control and two-sided impulse control for a Brownian system with the long-run average criterion

Abstract In this paper, we consider a joint drift rate control and two-sided impulse control problem in which the system manager adjusts the drift rate as well as the instantaneous relocation for a Brownian motion, with the objective of minimizing the total average state-related cost and control cost. The system state can be negative. Assuming that instantaneous upward and downward relocations take a different cost structure, which consists of both a setup cost and a variable cost, we prove that the optimal control policy takes an $\left\{ {\!\left( {{s^{\ast}},{q^{\ast}},{Q^{\ast}},{S^{\ast}}} \right),\!\left\{ {{\mu ^{\ast}}(x)\,:\,x \in [ {{s^{\ast}},{S^{\ast}}}]} \right\}} \right\}$ form. Specifically, the optimal impulse control policy is characterized by a quadruple $\left( {{s^{\ast}},{q^{\ast}},{Q^{\ast}},{S^{\ast}}} \right)$ , under which the system state will be immediately relocated upwardly to ${q^{\ast}}$ once it drops to ${s^{\ast}}$ and be immediately relocated downwardly to ${Q^{\ast}}$ once it rises to ${S^{\ast}}$ ; the optimal drift rate control policy will depend solely on the current system state, which is characterized by a function ${\mu ^{\ast}}\!\left( \cdot \right)$ for the system state staying in $[ {{s^{\ast}},{S^{\ast}}}]$ . By analyzing an associated free boundary problem consisting of an ordinary differential equation and several free boundary conditions, we obtain these optimal policy parameters and show the optimality of the proposed policy using a lower-bound approach. Finally, we investigate the effect of the system parameters on the optimal policy parameters as well as the optimal system’s long-run average cost numerically.

Caballero–Engel meet Lasry–Lions: A uniqueness result

In a Mean Field Game (MFG) each decision maker cares about the cross sectional distribution of the state and the dynamics of the distribution is generated by the agents’ optimal decisions. We prove the uniqueness of the equilibrium in a class of MFG where the decision maker controls the state at optimally chosen times. This setup accommodates several problems featuring non-convex adjustment costs, and complements the well known drift-control case studied by Lasry–Lions. Examples of such problems are described by Caballero and Engel in several papers, which introduce the concept of the generalized hazard function of adjustment. We extend the analysis to a general “impulse control problem” by introducing the concept of the “Impulse Hamiltonian”. Under the monotonicity assumption (a form of strategic substitutability), we establish the uniqueness of equilibrium. In this context, the Impulse Hamiltonian and its derivative play a similar role to the classical Hamiltonian that arises in the drift-control case.

Event-triggered impulsive tracking control for uncertain strict-feedback nonlinear systems via the neural-network-based backstepping technique

This paper studies the problem of event-triggered impulsive tracking control (ETITC) for uncertain strict-feedback nonlinear systems (USFNSs). In contrast to existing impulsive control schemes, this paper incorporates the neural-network (NN)-based backstepping technique into impulsive control design, such that stronger nonlinearities and uncertainties are allowed to be included in the concerned systems. The proposed state-feedback ETITC scheme guarantees that all the signals of the closed-loop system are bounded and the tracking error ultimately converges to an adjustable bounded region, while also avoiding the Zeno behavior. In addition, by constructing a NN-based observer, this paper further develops an output-feedback ETITC scheme to extend its investigation to the scenario where full states are not available for impulsive control design. Finally, an illustrative example involving a chemical reactor system is presented to demonstrate the effectiveness of our control schemes.

Existence and uniqueness for the evolutionary impulse control problem using an asynchronous algorithms

Impulse control problems pose significant challenges in decision making under uncertainty, particularly in scenarios where actions must be taken at irregular intervals or in response to abrupt changes in the environment. Ensuring both the existence and uniqueness of optimal control policies in such settings is paramount for practical implementation and theoretical understanding. In this study, we investigate the existence and uniqueness of solutions for impulse control problems utilizing asynchronous algorithms. This study presents a novel demonstration concerning the uniqueness and existence of Partially Quasi-Variational Inequalities (PQVIs). Our approach unfolds through a four-step methodology, leveraging distinctive features of a discrete iterative technique. This methodology integrates semi-implicit techniques with respect to the variable t and employs spatial approximation via finite element methods. We establish a pivotal connection between a fixed-point mapping and the discrete EQVIs system, utilizing it to formulate a discrete algorithm featuring a semi-implicit time scheme. Furthermore, we introduce a monotone iterative scheme inspired by Bensoussan’s algorithm and rigorously confirm several of its properties through mathematical proofs. This work contributes to advancing the understanding and application of iterative techniques in solving PQVIs, offering insights into their uniqueness and existence.

Neurofeedback and meditation technology in outpatient offender treatment: a feasibility and usability pilot study.

Although Cognitive Behavioral Therapy (CBT) is the most often used intervention in forensic treatment, its effectivity is not consistently supported. Interventions incorporating knowledge from neuroscience could provide for more successful intervention methods. The current pilot study set out to assess the feasibility and usability of the study protocol of a 4-week neuromeditation training in adult forensic outpatients with impulse control problems. The neuromeditation training, which prompts awareness and control over brain states of restlessness with EEG neurofeedback, was offered in addition to treatment as usual (predominantly CBT). Eight patients completed the neuromeditation training under guidance of their therapists. Despite some emerging obstacles, overall, the training was rated sufficiently usable and feasible by patients and their therapists. The provided suggestions for improvement can be used to implement the intervention in treatment and set up future trials to study the effectiveness of neuromeditation in offender treatment.

The Spanish Short Dark Tetrad (SD4): Association With Personality and Psychological Problems.

The Short Dark Tetrad (SD4) is a recently developed instrument for assessing the "dark" personality traits of psychopathy, narcissism, Machiavellianism, and sadism. We aimed to examine the SD4's psychometric properties, adapting it into Spanish and exploring its structure, gender invariance, reliability, concurrent validity, and nomological network. A sample of 668 adults (Mage = 26.36, SD = 10.64, 69.2% females) completed the SD4 and other self-report questionnaires. The results demonstrated sound indices of reliability and concurrent validity, an adequate four-factor structure, and support for gender invariance. Furthermore, most of the findings about the nomological network were in line with prior hypotheses: All four SD4 scales were associated with low levels of agreeableness and antagonism; psychopathy was also related to low conscientiousness, disinhibition and impulse-control problems; narcissism was positively associated with extraversion and negatively associated with internalizing symptoms; Machiavellianism was uncorrelated with impulsivity-related problems, which made it distinct from the psychopathy profile; finally, sadism showed a similar pattern of associations to psychopathy, albeit less strongly linked to impulsivity problems and externalizing behavior. Overall, the SD4 presents sound psychometric properties, although the overlap between psychopathy and sadism warrants some caution.

Impulsivity profile analysis and it’s potential role in the differential diagnostics of adult Attention Deficit Hyperactivity Disorder and Borderline Personality Disorder

IntroductionImpulsivity is a complex construct, having at least three factors: 1) impulsivity as a personality trait, 2) ismpulsive action – waiting and stopping impulsivity and 3) choice impulsivity. Impulsive symptoms are present in Attention Deficit Hyperactivity Disorder (ADHD) and Borderline Personality Disorder (BPD) as well, eventhough impulsvity profile significantly differs.ObjectivesOur aim is to describe the impulsivity profile in adult ADHD (aADHD) and BPD in comparison with the control group, and describe a characteristic pattern, which associates with these disorders.Methods aADHD (n=100) and BPD Patients (n=63) were included, based on DSM-5 diagnostic criteria. Healthy control subjects (n=100) were screened using the Derogatis Symptom Checklist (SCL-90). Comorbid psychiatric disorders were assessed by structured clinical interviews and those who have both aADHD and BPD were excluded from the study. Participants were further investigated with online questionnaires: e.g. Barratt Impulsiveness Scale (BIS-11) Difficulties in Emotion Regulation Scale (DERS) and neuropsychological tests, like CANTAB Rapid Visual Processing, Stop Signal Task, and the Rogers’ decision-making test.Results Based ont the BIS-11 results, significantly higher attentional impulsivity was present in adult ADHD compared to BPD (p<.001) and healthy controls (p<.001). Emotional regulation difficulties, measured by DERS were significantly higher in BPD (p<.001) than aADHD, but the impulse control problems were more pronounced in the aADHD group, compared to BPD (p<.001). Using CANTAB neuropsychological test battery, strategy formulation difficulties (p=0.16) and stopping impulsivity (p<.001) were only present in aADHD compared to HC. BPD patients did not differ significantly from the control group in strategy formulation and in Stop Signal Reaction Time, a measure of stopping impulsivity. The significantly higher level of total false alarms, reflecting on waiting impulsivity were present both in aADHD and BPD.ConclusionsAccording to our results these two disorders have different impulsivity profile characteristics, which can be useful in differentiating these two disorders, and in buiding treatment plans. Stopping impulsivity, measured by SST was found in aADHD, but not in BPD. In BPD impulsive behavior is more likely attached to emotional dysregulation, a trait rooted in childhood traumatization.This study was supported by the National Research, Development and Innovation Office grant K 129195 and K 135437.Disclosure of InterestNone Declared

Event-Triggered Impulsive Control for Input-to-State Stabilization of Nonlinear Time-Delay Systems.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

Optimal Impulse Control for Systems Deriven by Stochastic Delayed Differential Equations

In this paper we study the problem of optimal impulse control for stochastic systems with delay in the case when the value function of the impulse problem depends only on the initial data of the given process through its initial value (value at zero) and some weighted averages. A verification theorem for such impulse control problem is given. As an example the optimal stream of dividends with transaction costs is solved.

Deep impulse control: application to interest rate intervention

We propose a deep learning framework for impulse control problems involving multivariate stochastic processes, which can be controllable or uncontrollable. We use this framework to estimate central bank interventions on the (controllable) interest rate to stabilize the (uncontrollable) inflation rate, where the two rates are correlated and cointegrated. This method is useful for small banks or insurance companies with high exposure to Treasury securities to predict and stress-test their potential losses from central bank interventions. We also study the mathematical properties of the proposed framework.

Impulse Control of Conditional McKean–Vlasov Jump Diffusions

In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.

Impulsive optimal control problems with time delays in the drift term

Impulsive optimal control problems with time delays in the drift term

Error estimates of semidiscrete finite element approximation for minimal time impulse control problems

Error estimates of semidiscrete finite element approximation for minimal time impulse control problems

О корректности математической модели вызванной активности первичной зрительной коры

We propose a mathematical model that formalizes the macro- and meso-level dynamics of electrical potentials in the primary visual cortex of subjects, which corresponds to the presentation of visual stimuli to them. The mathematical framework is based on a twolayer neural field model, represented by a system of integro-differential equations, where the deep layer of the neural field models electrical activity that does not depend directly on the spatial orientation of the visual stimuli, whereas the activity of the superficial layer is sensitive to spatially oriented stimuli. The experimental design of presenting a series of visual stimuli is formalised in the present study in terms of an impulse control problem for the aforementioned two-layer neural field model. We propose a special metric space for construction of a unique solution to the control problem under standard assumptions for mathematical neurobiology regarding the functions involved in the modeling equations. We formulate sufficient conditions for continuous dependence of the solutions on the impulse control.

Approximate Solution of Optimal Pulse Control Problem Associated with the Heat Conduction Process

Abstract We consider the approximate solution of the control problem with minimum energy for an object described by the heat equation, with the process described by the linear equation of parabolic type and the system controlled by impulsive external influences. Our optimal control problem deals with finding a control parameter belonging to the class of admissible controls that provides the desired temperature distribution in a finite time with minimal energy consumption (energy consumption is described by the quadratic functional). Previous works dedicated to optimal impulse control problems have mostly used the Pontryagin’s maximum principle. However, from a practical point of view, this approach does not lead to satisfactory results. This is due to the fact that the corresponding boundary value problems in this case have no solution in a traditional class of absolutely continuous trajectories. In this work, we propose a method based on the moment relations. We seek for the approximate solution of the corresponding boundary value problem in the form of finite Fourier sum and state our optimal control problem in a finite-dimensional phase space. As a result, we obtain an optimal impulse control problem in a finite-dimensional function space. Taking into account the given condition for a finite time, we reduce the obtained problem to the L-problem of moments. Thus, the problem of finding a control parameter is reduced to the solution of the system of Fredholm integral equations of the first kind, with the norm of the sought solution not exceeding a given number. By Levi’s theorem, every element of Hilbert space can be represented by the sum of the elements of two orthogonal subspaces. This assertion makes it possible to find control parameters in analytical form. We also establish the convergence of the chosen approximation.