Controllability on impulsive systems with delays in both input and impulse and its applications to multi-agent networks

This paper investigates the controllability of impulsive systems with input delay and impulse delay and its applications in multi-agent networks. We adopt the geometric and algebraic analytical tools to establish some easily verified controllability conditions for the considered system model. First, the analytic solution of the considered system is established on every impulsive interval by using ordinary differential equation theory. Then, according to the solution derived, some sufficient complete controllability criteria are developed to reveal the role of the Gramian matrices in different subintervals. By introducing a row matrix of different kinds of Gramian matrices, a complete controllability condition that is proved to be necessary and sufficient is further obtained. By using the relevant geometric matrix theory, the derived algebraic controllability condition is then converted to a geometric one. On other hand, we introduce a multi-agent network with delayed input and impulse and investigate its controllability. By resorting to graph theory and matrix theory, several factors affecting the controllability of the considered multi-agent networks are investigated, such as the topology structure, the inner coupling matrix, and the dynamics of each agent. Finally, two numerical examples are worked out to verify the derived controllability criteria.

The effects of nalmefene on the impulsive and reflective system in alcohol use disorder: A resting-state fMRI study

RATIONALE

Central aspects of alcohol use disorder (AUD) are the irresistible desire for alcohol and impaired control over its intake. According to the triadic neurocognitive model of addiction, this arises from aberrant functioning of different neural and cognitive systems: an impulsive system, a reflective system, and the abnormal dynamics between both systems based on an insular-dependent system.

OBJECTIVES

In this study, we examined the effects of a single dose of nalmefene on resting-state functional connectivity (rsFC) patterns within and between these addiction-related neural systems in AUD.

METHODS

Non-treatment seeking participants with AUD (N = 17; 19-66 years, 6 female) took part in a randomized, placebo-controlled, double-blind, crossover study and received either a single dose of 18 mg nalmefene or a placebo. Using seed-based correlation analyses on resting-state functional magnetic resonance imaging data, we examined the effects of nalmefene on key nodes related to the (1) impulsive system; (2) reflective system; (3) salience network; and (4) default mode network.

RESULTS

Under nalmefene, participants showed reduced rsFC between components of the impulsive system (Nucleus accumbens-putamen/pallidum/insula). Reduced rsFC was found between elements of the reflective system and impulsive system (orbitofrontal cortex-insula/putamen/pallidum), salience network (orbitofrontal cortex-insula/inferior frontal gyrus), and default mode network (lateral prefrontal cortex-precuneus/cuneus). Components of the salience network showed both increased (anterior cingulate cortex) and decreased (insular cortex) rsFC to elements of the reflective system.

CONCLUSION

A single dose of nalmefene impacts rsFC and alters the interaction between key nodes of addiction-related neural systems in non-treatment seeking participants with AUD. Nalmefene may normalize rsFC patterns by weakening the impulsive system while strengthening the reflective system.

TRIAL REGISTRATION

clinicaltrials.gov: NCT02372318.