Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

An analysis of microband orientation in hot deformed aluminium alloy AA5052 using forward and reverse torsion

The effects of strain path reversal on the macroscopic orientation of microbands in AA5052 have been studied using high resolution electron backscatter diffraction. Deformation was carried using two equal steps of forward/forward or forward/reverse torsion at a temperature of 300°C and strain rate of 1s-1 to a total equivalent tensile strain of 0.5. In both cases microbands were found in the majority of grains examined with many having more than one set. The microbands appear to cluster at specific angles to the macroscopic deformation. For the forward/forward condition microbands clustered around -20° and +45° to the maximum principle stress direction and at ± 30-35° to the principal strain direction. For the forward/reverse condition significantly more spread in microband angle was observed though peaks were visible at ±35° with respect to principal stress direction and at -40° and +30° with respect to the principal strain direction of the reverse torsion. This suggests the microbands formed in the forward deformation have or are dissolving and any new microbands formed are related to the deformation conditions of the final strain path.

Performance analysis of two advanced controllers for polystyrene polymerization in batch reactor

The performance of two advanced model based non-linear controllers is analyzed for the optimal setpoint tracking of free radical polymerization of styrene in batch reactors. Artificial neural network-based model predictive controller (NN-MPC) and generic model controller (GMC) are both applied for controlling the system. The recently developed hybrid model [1] as well as available literature models are utilized in the control study. The optimal minimum temperature profiles are determined based on Hamiltonian maximum principle. Different types of disturbances are artificially generated to examine the stability and robustness of the controllers. The experimental studies reveal that the performance of NN-MPC is superior over that of GMC.

Performance analysis of three advanced controllers for polymerization batch reactor: an experimental investigation

The performances of three advanced non-linear controllers are analyzed for the optimal set point tracking of styrene free radical polymerization (FRP) in batch reactors. The three controllers are the artificial neural network-based MPC (NN-MPC), the artificial fuzzy logic controller (FLC) as well as the generic model controller (GMC). A recently developed hybrid model (Hosen et al., 2011a. Asia-Pac. J. Chem. Eng. 6(2), 274) is utilized in the control study to design and tune the proposed controllers. The optimal minimum temperature profiles are determined using the Hamiltonian maximum principle. Different types of disturbances are introduced and applied to examine the stability of controller performance. The experimental studies revealed that the performance of the NN-MPC is superior to that of FLC and GMC. © 2013 The Institution of Chemical Engineers.

Optimal attitude corrections for cylindrical spacecraft

A first order analytical model for optimal small amplitude attitude maneuvers of spacecraft with cylindrical symmetry in an elliptical orbits is presented. The optimization problem is formulated as a Mayer problem with the control torques provided by a power limited propulsion system. The state is defined by Seffet-Andoyer's variables and the control by the components of the propulsive torques. The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints. For small amplitude attitude maneuvers, the optimal Hamiltonian function is linearized around a reference attitude. A complete first order analytical solution is obtained by simple quadrature and is expressed through a linear algebraic system involving the initial values of the adjoint variables. A numerical solution is obtained by taking the Euler angles formulation of the problem, solving the two-point boundary problem through the shooting method, and, then, determining the Serret-Andoyer variables through Serret-Andoyer transformation. Numerical results show that the first order solution provides a good approximation to the optimal control law and also that is possible to establish an optimal control law for the artificial satellite's attitude. (C) 2003 COSPAR. Published by Elsevier B.V. Ltd. All rights reserved.

State constraints in optimal impulsive controls

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimality conditions for infinite horizon control problems with state constraints

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

Optimal pest control problem in population dynamics

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

A class of multiobjective control problems

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

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.

Lattice constellations and codes from quadratic number fields

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional (2-D) grid. In particular, codes over Gaussian integers and Eisenstein-Jacobi integers are extensively studied. Decoding algorithms are proposed for these codes when up to two coordinates of a transmitted code vector are affected by errors of arbitrary Mannheim weight. Moreover, we show that the proposed codes are maximum-distance separable (MDS), with respect to the Hamming distance. The practical interest in such Mannheim-metric codes is their use in coded modulation schemes based on quadrature amplitude modulation (QAM)-type constellations, for which neither the Hamming nor the Lee metric is appropriate.

Optimal control problems with nonsmooth mixed constraints

In this paper we present a weak maximum principle for optimal control problems involving mixed constraints and pointwise set control constraints. Notably such result holds for problems with possibly nonsmooth mixed constraints. Although the setback of such result resides on a convexity assumption on the extended velocity set, we show that if the number of mixed constraints is one, such convexity assumption may be removed when an interiority assumption holds. © 2008 IEEE.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

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.

Análise não-diferenciável e condições necessárias de otimalidade para problema de controle ótimo com restrições mistas

Pós-graduação em Matemática - IBILCE