Optimal control of systems governed by differential equations with applications in air traffic management and systems biology

Differential equations are arguably the most widespread formalism to model dynamical systems in sciences and engineering. In this dissertation, we strive to design a practical methodology which can be used for the optimal control of most systems modeled by differential equations. Namely, the method is applicable to ordinary differential equations (ODEs), partial differential equations (PDEs) and stochastic differential equations (SDEs) driven by deterministic control. The algorithm draws from both optimization and control theory. It solves the Pontryagin Maximum Principle conditions in an iterative fashion via a novel approximate Newton method. We also extend the method to the case in which multiple agents are involved in the optimal control problem. For this purpose, we use dual decomposition techniques which allow us to decentralize the control algorithm and to distribute the computational load among each individual agent.; Most of the dissertation is devoted to promoting the applicability of the method to practical problems in air traffic management and systems biology. In air traffic management; we use the technique to optimize a new PDE-based Eulerian model of the airspace; suitable to represent and control air traffic flow at the scale of the US national airspace. We also apply the technique to aircraft coordination problems in the context of formation flight, in which aircraft dynamics are described by ODEs.; In systems biology, we use the method to perform fast parameter identification in the analysis of protein networks, which allows us to gain some insights about the biological processes regulating the system. In particular we perform parameter identification for a PDE model of a spatially distributed network of proteins, playing a key role in the planar cell polarity of Drosophila wings. We also study a general representation of intra-cellular genetic networks, described as a stochastic nonlinear regulatory network, in which our control system approach proves to greatly speed up the discovery of the system.; We finally show applications of the method to SDE driven systems, through benchmark examples in engineering and finance.