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.

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.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

On the solvability of implicit differential inclusions

In the paper, the set-valued covering mappings are studied. The statements on solvability, solution estimates, and well-posedness of inclusions with conditionally covering mappings are proved. The results obtained are applied to the investigation of differential inclusions unsolved for the unknown function. The statements on solvability, solution estimates, and well-posedness of these inclusions are derived.

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Aeroelastic stability analysis using linear matrix inequalities

The present work describes an alternative methodology for identification of aeroelastic stability in a range of varying parameters. Analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms. The theory is outlined and simulations are carried out on a benchmark system to illustrate the method. The classical methodology with the analysis of the system's eigenvalues is presented for comparing the results and validating the approach. The aeroelastic model is represented in state space format and the unsteady aerodynamic forces are written in time domain using rational function approximation. The problem is formulated as a polytopic differential inclusion system and the conceptual idea can be used in two different applications. In the first application the method verifies the aeroelastic stability in a range of air density (or its equivalent altitude range). In the second one, the stability is verified for a rage of velocities. These analyses are in contrast to the classical discrete analysis performed at fixed air density/velocity values. It is shown that this method is efficient to identify stability regions in the flight envelope and it offers promise for robust flutter identification.

Espaços vetoriais e topológicos de intervalos generalizados com alguns conceitos de cálculo e otimização intervalar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope. (C) 2014 Elsevier Ltd. All rights reserved.

Inclusões Dinâmicas em Escalas Temporais: Existência de Soluções sob a Hipótese de Semicontinuidade Inferior

In this paper we consider the problem of differential inclusion in time scales whose vector field is a multifunction, that is, a function that maps points to sets. It is provided conditions of existence without requiring compactness of the vector field; it is required that the vector field is closed, convex, and lower semicontinuous. In previous work in literature, it is required that the field is either scalar or compact, convex, and has closed graph.

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

Stability results for impulsive functional differential equations with infinite delay

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

Development and pharmacological evaluation of ropivacaine-2-hydroxypropyl-beta-cyclodextrin inclusion complex

Ropivacaine (RVC) is an enantiomerically pure local anesthetic (LA) largely used in surgical procedures, which presents physico-chemical and therapeutic properties similar to those of bupivacaine (BPV), but associated to less systemic toxicity This study focuses on the development and pharmacological evaluation of a RVC in 2-hydroxypropyl-beta-cyclodextrin (HP-P-CD) inclusion complex. Phase-solubility diagrams allowed the determination of the association constant between RVC and HP-beta-CD (9.46 M-1) and showed an increase on RVC solubility upon complexation. Release kinetics revealed a decrease on RVC release rate and reduced hemolytic effects after complexation. (onset at 3.7 mM and 11.2 mM for RVC and RVCHP-beta-CD, respectively) were observed. Differential scanning calorimetry (DSC), scanning electron microscopy (SEM) and X-ray analysis (X-ray) showed the formation and the morphology of the complex. Nuclear magnetic resonance (NMR) and job-plot experiments afforded data regarding inclusion complex stoichiometry (1:1) and topology. Sciatic nerve blockade studies showed that RVCHP-beta-CD was able to reduce the latency without increasing the duration of motor blockade, but prolonging the duration and intensity of the sensory blockade (p < 0.001) induced by the LA in mice. These results identify the RVCHP-beta-CD complex as an effective novel approach to enhance the pharmacological effects of RVC, presenting it as a promising new anesthetic formulation. (c) 2007 Elsevier B.V All rights reserved.

Non-inclusion complexes between riboflavin and cyclodextrins

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

Computational analysis and physico-chemical characterization of an inclusion compound between praziquantel and methyl-beta-cyclodextrin for use as an alternative in the treatment of schistosomiasis

Schistosomiasis is still an endemic disease in many regions, with 250 million people infected with Schistosoma and about 500,000 deaths per year. Praziquantel (PZQ) is the drug of choice for schistosomiasis treatment, however it is classified as Class II in the Biopharmaceutics Classification System, as its low solubility hinders its performance in biological systems. The use of cyclodextrins is a useful tool to increase the solubility and bioavailability of drugs. The aim of this work was to prepare an inclusion compound of PZQ and methyl-beta-cyclodextrin (MeCD), perform its physico-chemical characterization, and explore its in vitro cytotoxicity. SEM showed a change of the morphological characteristics of PZQ:MeCD crystals, and IR data supported this finding, with changes after interaction with MeCD including effects on the C-H of the aromatic ring, observed at 758 cm(-1). Differential scanning calorimetry measurements revealed that complexation occurred in a 1:1 molar ratio, as evidenced by the lack of a PZQ transition temperature after inclusion into the MeCD cavity. In solution, the PZQ UV spectrum profile in the presence of MeCD was comparable to the PZQ spectrum in a hydrophobic solvent. Phase solubility diagrams showed that there was a 5.5-fold increase in PZQ solubility, and were indicative of a type A(L) isotherm, that was used to determine an association constant (K(a)) of 140.8 M(-1). No cytotoxicity of the PZQ:MeCD inclusion compound was observed in tests using 3T3 cells. The results suggest that the association of PZQ with MeCD could be a good alternative for the treatment of schistosomiasis.

Stability of neutral functional differential equations in terms of measures

In this paper we investigate the relationships between different concepts of stability in measure for the solutions of an autonomous or periodic neutral functional differential equation.