WP1 - Necessary and sufficient optimality conditions, and sensitivity analysis

• State of the art:

A major breakthrough in trajectory optimization was achieved in the 1950’s by Pontryagin’s research group, who successfully generalized and extended to an optimal control setting, the classical Euler-Lagrange and Weiserstarass conditions of the Calculus of Variations. This early work, and the computational schemes that it inspired, have found application in design of automatic landing systems, trajectory selection for aerospace applications, process control and other areas. The early optimality conditions were subsequently strengthened and extended using methods of convex and nonsmooth analysis. Methods of differential geometry have provided valuable, new insights into the nature of optimal controls and, in particular, have improved our understanding of situations in which optimal controls can be realised by a feedback control law.

• Objectives

Many practical optimal control problems involve constraints on state variables, to avoid regions of the state space where perhaps operation is unsafe or the dynamic models considered are no longer valid. A serious deficiency of the early theory was that it could not take account of such constraints. While optimal control problems with state constraints have been subsequently studied, our understanding of state-constrained optimal controls is in many important respects incomplete, and important questions concerning the structure of optimal state constrained trajectories, higher order conditions, conditions for local optimality and efficient computational methods all require answers. The aim of this WP is to further develop the fundamental theory governing problems of optimal control differential games under state constraints, and also to provide computational schemes for their solution. 

• Fellows projects

• Planned person-months: 234