Final Report Summary - SADCO (Sensitivity Analysis for Deterministic Controller Design) Objective: Optimisation-based design of control systems is concerned with determination of control strategies for complex, dynamical systems, to optimise some measures of best performance. It has the potential for applications to a wide range of fields, including aerospace, chemical processing, transportation systems and resource economics. The multi-partner initial training network SADCO aims at: Training young researchers and future scientific leaders in the field of control theory with emphasis on two major themes sensitivity of optimal strategies to changes in the model specifications, and deterministic controller design; Advancing the theory and developing new numerical methods; Conveying fundamental scientific contributions within European industrial sectors. In order to achieve these objectives, SADCO establishes a collaborative research and training network of eleven full partners from both the academic and industrial sectors, and gathers participants with expertise in complementary disciplines in mathematics and engineering. The network also offers a complete range of theoretical, practical and complementary training. SADCO works together with the young researchers to develop and implement effective training plans tailored to each individual requirements. Multi-disciplinary training based on the integrated scientific programme, secondments, regular meetings, active networking, have ensured the success of this project. The development of new 'clean' technologies in power, transportation and other domains is a major opportunity for EU industries. The proposed research programme helps place EU universities in the forefront of Optimal Control, a field of mathematics that supports these technologies. The training programme, based on institutions covering the principal areas of the field, provides a new generation of young mathematicians and engineers with broad skills in Optimal Control, which are not readily acquired at one institution alone.Achievements: The research and training activities of the project really started right from the beginning of the project. In addition to the numerous training and research events organized over the four years of the project (workshops, summer schools, industrial workshops, internal research reviews, doctoral days, final conference), the program included some complementary skills trainings organized at the network level (grant writing, oral communication, job opportunities in the private sector) in order to provide the fellows with a set of skills and tools for their future career.Over the four years of the project, the events organized (sometimes in cooperation with other projects) have attracted an increasing participation and attention from the participating organizations and also from the outside. Indeed, the project topics and activities proved to be of interest not only to the fellows, but also to the control community more generally.The first fellow was recruited as early as January 2011 and the training programme started right away. In total, twenty-eight fellows (20 ESRs and 8 ERs) joined the network. Most ESRs were working towards a PhD. Some defended their thesis in the last months of the project and some will complete their thesis in 2015. The training they received within SADCO and the dense network they developed have equipped them with the relevant skills to get postdoc positions. Some of them were already recruited in Europe and in the US before the end of the project. All the ERs have found new positions in Europe (four with permanent positions).The young researchers played an increasingly leading role within the project, in particular by organizing some events (young researchers workshops, conference sessions) and by proposing and editing a special volume gathering contributions from the SADCO fellows.Several studies have been undertaken by the SADCO members with significant results obtained in the following domains:WP1: Necessary and Sufficient Optimality Conditions and Sensitivity Analysis• First order conditions for control problems with state constraints. • Non-degeneracy of the first order necessary conditions (key concept - ’metric regularity’)• Higher order conditions providing refined information• Numerical methods for solution based on 1st and 2nd order conditions (shooting methods, and supporting analysis)WP2: Hamilton-Jacobi approach• Caracterisation of the value functions of state-constrained control problems (state constraints, unbounded velocity sets, etc.)• Analysis of gradients of value functions and optimal synthesis (links with first order optimality conditions)• Regularity and properties of Minimum Time Problems and Eikonal equations.• Dynamic programming on stratified domains and singular domains (state evolution in networks, etc. )• Computational methods and applications: numerical schemes, high dimensionality, software development, collision avoidance, …WP3: Stabilisation Methods For Nonlinear Systems• Model Predictive Control (stabilizing schemes without endpoint constraints, analysis of transient response, . .)• Computational Lyapunov approaches via Zubov’s equation, etc• Discontinuous feedback controllers : constructions on ’patchy’ domains.• Applications: wind-energy extraction, disease control, irrigation, . .WP4: Perturbed Systems• Analysis of multiscale optimal control problems via singular perturbations• Asymptotic analysis of steady state optimal controllers (’homogenization’, asymptotics of rapidly varying parameters)WP5: Differential Games• Non zero-sum differential games (problems with incomplete information, ’mean field games’)• Differential games with state constraints• Relation of Stochastic Control and Differential Games (Large deviations techniques)• Computation (techniques for handling high-dimensional problems - decomposition, grid-selection, exploit special structure, . .)During the project, a real collaborative momentum has emerged between the network members (fellows and senior researchers) through the organization of common activities and the production of common publications. This sets strong basis for continued cooperation between the participating teams as well as with the new institutions that the fellows will be joining. The tools developed thanks to SADCO can lead to economic and environmental benefits for all of Europe and the research carried out can contribute to innovative solutions in key technological domains. For instance, in aerospace, the sparse, large scale NLP solver WORHP was elected to be the standard solver for ESA activities for future projects. In the automotive industry, Volkswagen intends to use the methods to be developed in the project as a verification tool for their collision avoidance algorithms. Some of the work carried within SADCO has had some influence beyond the scope originally intended, such as health and physical activity (personalized workouts program depending on the physiological state of each individual) or macroeconomics models (nonlinear model predictive control).General information: Information on the project activities, events and publications can be found on the SADCO website: http://itn-sadco.inria.fr/Project website: http://itn-sadco.inria.fr/Publications: https://hal.inria.fr/SADCO
