State constraints in optimal impulsive controls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of an impulsive force on vortices in a rotating Bose-Einstein condensate

The effects of a sudden increase and decrease of the interatomic interaction and harmonic-oscillator trapping potential on vortices in a quasi two-dimensional rotating Bose-Einstein condensate are investigated using the mean-field Gross-Pitaevskii equation. We also study the decay of vortices when the rotation of the condensate is suddenly stopped. Upon a free expansion of a rotating BEC with vortices the radius of the vortex core increases more rapidly than the radius of the condensate. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

Closed loop stability of measure-driven impulsive control systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Astrocytes and human cognition: Modeling information integration and modulation of neuronal activity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Necessary conditions for optimal impulsive control problems

A Maximum Principle is derived for a class of optimal control problems arising in midcourse guidance, in which certain controls are represented by measures and, the state trajectories are functions of bounded variation. The optimality conditions improves on previous optimality conditions by allowing nonsmooth data, measurable time dependence, and a possibly time varying constraint set for the conventional controls.

Necessary conditions of optimality for vector-valued impulsive control problems

A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary standard optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided. © 2000 Elsevier Science B.V. All rights reserved.

Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

The chaotic oscillation in an attractive Bose-Einstein condensate (BEC) under an impulsive force was discussed using mean-field Gross-Pitaevskii (GP) equation. It was found that sustained chaotic oscillation resulted in a BEC under the action of an impulsive force generated by suddenly changing the interatomic scattering length or the harmonic oscillator trapping potential. The analysis suggested that the final state interatomic attraction played an important role in the generation of the chaotic dynamics.

Lyapounov stability for impulsive dynamical systems

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.

Invariance for Impulsive Control Systems

In this article, we provide invariance conditions for control systems whose dynamics are given by measure driven differential inclusions. The solution concept plays a critical role in the extension of the conventional conditions for the impulsive control context. A couple of examples illustrating the specific features of impulsive control systems are included.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

Impulsive compulsivity in obsessive-compulsive disorder: A phenotypic marker of patients with poor clinical outcome

Although traditionally obsessive-compulsive disorder (OCD) and impulse control disorders (ICD) have represented opposing ends of a continuum, recent research has demonstrated a frequent co-occurrence of impulsive and compulsive behaviours, which may contribute to a worse clinical picture of some psychiatric disorders. We hypothesize that individuals with 'impulsive' OCD as characterized by poor insight, low resistance, and reduced control towards their compulsions will have a deteriorative course, greater severity of hoarding and/or symmetry/ordering symptoms, and comorbid ICD and/or substance use disorders (SUD). The sample consisted of 869 individuals with a minimum score of 16 on the Yale-Brown Obsessive Compulsive Scale (Y-BOCS). Of these, 65 had poor insight, low resistance, and reduced control towards compulsions ('poor IRC') and 444 had preserved insight, greater resistance and better control over compulsions ('good IRC'). These two groups were compared on a number of clinical and demographic variables. Individuals with poor IRC were significantly more likely to have a deteriorative course (p < 0.001), longer duration of obsessions (p = 0.017), greater severity of symmetry/ordering (p < 0.001), contamination/cleaning (p < 0.001) and hoarding (p = 0.002) symptoms, and comorbid intermittent explosive disorder (p = 0.026), trichotillomania (p = 0.014) and compulsive buying (p = 0.040). Regression analysis revealed that duration of obsessions (p = 0.037) and hoarding severity (p = 0.005) were significant predictors of poor IRC. In the absence of specific measures for impulsivity in OCD, the study highlights the utility of simple measures such as insight, resistance and control over compulsions as a phenotypic marker of a subgroup of OCD with impulsive features demonstrating poor clinical outcome. © 2012 Elsevier Ltd.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Optimal impulsive control in a powered Swing-By

This paper studies the problem of applying an impulsive control in a spacecraft that is performing a Swing-By maneuver. The objective is to study the changes in velocity, energy and angular momentum for this maneuver as a function of the three usual parameters of the standard Swing-By plus the three parameters (the magnitude of the impulse, the point of its application and the angle between the impulse and the velocity of the spacecraft) that specify the impulse applied. The dynamics used is the restricted three body problem under the regularization of Lemaitre, made to increase the accuracy of the numerical integration near the primaries. The present research develops an algorithm to calculate the variation of energy and angular momentum in a maneuver where the application of the impulsive control occurs before or after the passage of the spacecraft by the periapsis, but within the sphere of influence of the secondary body and in a non-tangential direction. Using this approach, it is possible to find the best position and direction to apply the impulse to maximize the energy change of the total maneuver. The results showed that the application of the impulse at the periapsis and in the direction of motion of the spacecraft is usually not the optimal solution.