Optimality conditions for infinite horizon control problems with state constraints

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

KT-invexity in optimal control problems

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

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

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.

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.

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.

Free time and mixed constrained optimal control problems

We consider free time optimal control problems with pointwise set control constraints u(t) ∈ U(t). Here we derive necessary conditions of optimality for those problem where the set U(t) is defined by equality and inequality control constraints. The main ingredients of our analysis are a well known time transformation and recent results on necessary conditions for mixed state-control constraints. ©2010 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.

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Development of CAN-based distributed control system for variable rate technology in agricultural machinery

The number of electronic devices connected to agricultural machinery is increasing to support new agricultural practices tasks related to the Precision Agriculture such as spatial variability mapping and Variable Rate Technology (VRT). The Distributed Control System (DCS) is a suitable solution for decentralization of the data acquisition system and the Controller Area Network (CAN) is the major trend among the embedded communications protocols for agricultural machinery and vehicles. The application of soil correctives is a typical problem in Brazil. The efficiency of this correction process is highly dependent of the inputs way at soil and the occurrence of errors affects directly the agricultural yield. To handle this problem, this paper presents the development of a CAN-based distributed control system for a VRT system of soil corrective in agricultural machinery. The VRT system is composed by a tractor-implement that applies a desired rate of inputs according to the georeferenced prescription map of the farm field to support PA (Precision Agriculture). The performance evaluation of the CAN-based VRT system was done by experimental tests and analyzing the CAN messages transmitted in the operation of the entire system. The results of the control error according to the necessity of agricultural application allow conclude that the developed VRT system is suitable for the agricultural productions reaching an acceptable response time and application error. The CAN-Based DCS solution applied in the VRT system reduced the complexity of the control system, easing the installation and maintenance. The use of VRT system allowed applying only the required inputs, increasing the efficiency operation and minimizing the environmental impact.