Necessary conditions for joining optimal singular and nonsingular subarcs

Necessary conditions for optimality of junctions between singular and nonsingular subarcs for singular optimal control problem

Conjugate gradient optimization programs for shuttle reentry

Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45211/1/10957_2004_Article_BF00933131.pd

Repetitive process control of additive manufacturing with application to laser metal deposition

Additive Manufacturing (AM) is a set of manufacturing processes which has promise in the production of complex, functional structures that cannot be fabricated with conventional manufacturing and the repair of high-value parts. However, a significant challenge to the adoption of additive manufacturing processes to these applications is proper process control. In order to enable closed-loop process control compact models suitable for control design and for describing the layer-by-layer material addition process are needed. This dissertation proposes a two-dimensional modeling and control framework, with an application to a specific metal-based AM process, whereby the deposition of the current layer is affected by both in-layer and layer-to-layer dynamics, both of which are driven by the state of the previous layer. The proposed modeling framework can be used to create two-dimensional dynamic models for the analysis of layer-to-layer stability and as a foundation for the design of layer-to-layer controllers for AM processes. In order to analyze the stability of this class of systems, linear repetitive process results are extended enabling the treatment of the process model as a two-dimensional analog of a discrete time system. For process control, the closed-loop repetitive process is again treated as a two-dimensional analog of a discrete time system for which controllers are designed. The proposed methodologies are applied to a metal-based AM process, Laser Metal Deposition (LMD), which is known to exhibit layer-to-layer unstable behavior and is also of significant interest to high-value manufacturing industries --Abstract, page iii

Existence results and applications for some non-linear optimal control problems

Tese de doutoramento, Matemática (Análise Matemática), 2010, Universidade de Lisboa, Faculdade de CiênciasOs resultados clássicos de existência, para problemas de controlo óptimo, governados por sistemas de equações diferenciais ordinárias, baseam-se em condições de convexidade que resultam frequentemente muito difíceis de verificar. Apresentamos uma abordagem geral para este problema, com base em várias relaxações do mesmo, na qual a convexidade surge de um modo inesperada. Isolamos uma condição suficiente, para a existência de soluções óptimas, que pode ser verificada em vários contextos. Podemos chegar a um resultado de existência para problemas vectoriais, com uma estrutura particular, proveniente de problemas de controlo e manobra deve veículos subaquáticos. Numa abordagem diferente, recuperamos técnicas clássicas baseadas na reformulação variacional, que nos permitem obter resultados de existência através da aplicação de teoremas para problemas variacionais, sem condições de convexidade. Em particular, provamos a existência de solução, no caso escalar, para problemas de controlo óptimo autónomos.Utilizamos o nosso resultado de existência, demonstrado para problemas de controlo óptimo com variáveis vectoriais, para provar a existência de solução para um problema de manobra de veículos subaquáticos. Para terminar, apresentamos algumas ideias para trabalho futuro. Propomos a implementação de um método numérico, baseado em direcções de descida mais rápida, para aproximar soluções de problemas de controlo óptimo vindos das aplicações. Mostramos resultados preliminares desta implementação, para alguns exemplos académicos.Classical existence results for optimal control problems governed by systems of ordinary differential equations are based on typical convexity assumptions, which are quite often, very difficult to check. We present a general approach to prove existence of solutions for optimal control problems, based on several relaxations of the problem, where the convexity arises inan unexpected way. We isolate one sufficient condition for the existence of optimal solutions, which can be validated in various contexts. We end up with a main existence result for vector problems with a particular structure, motivated by underwater-vehicles-maneuvering problems. Alternatively, we recover the classical approach based on a purely variational reformulation, which can lead to existence results by using one existence theorems for variational problems without convexity assumptions. In particular we prove the existence of solution for autonomous scalar optimal control problems. Finally, we apply our existence result for vector state and control variables, to prove the local existence of solution for an optimal control problem describing the control of an underwater vehicle. Additionally to the main work described above, we introduce some ideas for future work. We propose to implement a numerical method, based on steepest descent directions, to approximate the solutions of realistic optimal control problems. Some preliminary results for academic examples are shown.Fundação para a Ciência e Tecnologia (SFRH-BD-22107-2005), Programa Operacional Ciência e Inovaçao 201