Optimal control problems for path planing of AUV using simplified models

Here we propose a simplified model for the path planning of an Autonomous Underwater Vehicle (AUV) in an horizontal plane when ocean currents are considered. The model includes kinematic equations and a simple dynamic equation. Our problem of interest is a minimum time problem with state constraints where the control appears linearly. This problem is solved numerically using the direct method. We extract various tests from the Maximum Principle that are then used to validate the numerical solution. In contrast to many other literature we apply the Maximum Principle as defined in [9]

On first order state constrained optimal control problems

We show that exact penalization techniques canbe applied to optimal control problems with state constraintsunder a hard to verify hypothesis. Investigating conditionsimplying our hypothetical hypothesis we discuss some recenttheoretical results on regularity of multipliers for optimalcontrol problem involving first order state constraints. We showby an example that known conditions asserting regularity ofthe multipliers do not prevent the appearance of atoms in themultiplier measure. Our accompanying example is treated bothnumerically and analytically. Extension to cover problems withadditional mixed state constraints is also discusse

Perspetiva dos professores do 2º ciclo sobre a importância do jogo no desenvolvimento de alunos com perturbação da hiperatividade e défice de atenção

As crianças com Perturbação da Hiperatividade e Défice de Atenção (PHDA), podem ser um verdadeiro desafio para os pais, professores e para os próprios. Apresentamos a PHDA, nomeadamente as suas causas, diagnóstico e tratamento numa tentativa de perspetivar a importância do jogo no desenvolvimento de crianças com esta perturbação. O objetivo fundamental deste trabalho é tornar-se um instrumento para professores, de forma a tornar possível o processo de ensino e aprendizagem um sucesso para o aluno, tanto do ponto de vista cognitivo como social e emocional, para além de sensibilizar os docentes para uma problemática que vai muito além da irrequietude e agressividade, que vulgarmente apelida estes alunos. Pretendemos demonstrar que os jogos podem ser ferramentas relevantes no desenvolvimento destas crianças, contribuindo para que aprendam a viver em sociedade. O jogo é uma ferramenta cultural muito importante, pois através dele o ser humano desfruta de momentos de diversão e descontração, beneficiando ainda de momentos de aprendizagem criativa. Os jogos permitem ao ser humano conhecer e refletir sobre a sua cultura, dando-lhe a oportunidade de modificar a sua forma de estar no mundo. O uso do jogo faculta a libertação da imaginação e criatividade, culminando em melhorias a nível social, intelectual, emocional, motor e até mesmo académico. A prática pedagógica em crianças com PHDA, com base no jogo, permite o desenvolvimento de capacidades sociais, que são, de facto, um dos seus piores problemas. Cabe ao professor usar o jogo como metodologia motivando os seus alunos, proporcionando-lhes momentos de aprendizagem únicos

Differential Inclusion Approach for Mixed Constrained Problems Revisited

Properties of control systems described by differentialinclusions are well established in the literature. Ofspecial relevance to optimal control problems are propertiesconcerning measurability, convexity, compactness of trajectoriesand Lipschitz continuity of the multifunctions mapping defining thedifferential inclusion of interest. In this work we concentrateon dynamic control systems coupled with mixed state-controlconstraints. We characterize a class of such systems thatcan be described by an appropriate differential inclusion soas exhibit good'' properties of the multifunction.We also illustrate the importance of our findings bytreating some applications scenarios

On application of optimal control to SEIR normalized models: Pros and cons

In this work we normalize a SEIR model that incorporates exponential natural birth and death, as well as disease-caused death. We use optimal control to control by vaccination the spread of a generic infectious disease described by a normalized model with L-1 cost. We discuss the pros and cons of SEIR normalized models when compared with classical models when optimal control with L-1 costs are considered. Our discussion highlights the role of the cost. Additionally, we partially validate our numerical solutions for our optimal control problem with normalized models using the Maximum Principle

A MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL PROBLEMS WITH STATE AND MIXED CONSTRAINTS

Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614-632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints

A Hybrid Direct-Indirect Approach for Solving the Singular Optimal Control Problems of Finite and Infinite Order

This paper presents a hybrid approach to solve singular optimal control problems. It combines the direct Euler method with a modified indirect shooting method. The presented method circumvents the main difficulties and drawbacks of both the direct and indirect methods, when applied to the singular optimal control problems. This method does not require a priori knowledge of the switching structure of the solution and it can be applied to finite or infinite order singular optimal control problems. It provides not only an approximate optimal solution for the problem but, remarkably, it also produces the switching times. We illustrate the features of this new approach treating numerically through two optimal control problems, one of finite order and the other with infinite order

A new version of necessary conditions for optimal control problems with differential algebraic equations

Appealing to recent results for nonsmooth mixed constrained problems we derivenew variants of necessary optimality conditions for optimal control problems involving differentialalgebraic equations. The analysis is quite suitable for index one problems with no need for theintroduction of implicit functions. It is also suitable to some higher index problems

Optimal control of normalized simr models with vaccination and treatment

We study a model based on the so called SIR model to control the spreading of a disease in a varying population via vaccination and treatment. Since we assume that medical treatment is not immediate we add a new compartment, M, to the SIR model. We work with the normalized version of the proposed model. For such model we consider the problem of steering the system to a specified target. We consider both a fixed time optimal control problem with L-1 cost and the minimum time problem to drive the system to the target. In contrast to the literature, we apply different techniques of optimal control to our problems of interest. Using the direct method, we first solve the fixed time problem and then proceed to validate the computed solutions using both necessary conditions and second order sufficient conditions. Noteworthy, we perform a sensitivity analysis of the solutions with respect to some parameters in the model. We also use the Hamiltonian Jacobi approach to study how the minimum time function varies with respect to perturbations of the initial conditions. Additionally, we consider a multi-objective approach to study the trade off between the minimum time and the social costs of the control of diseases. Finally, we propose the application of Model Predictive Control to deal with uncertainties of the model