Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Duality between invariant spaces for max-plus linear discrete event systems

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers. These are useful in situations in which some of the system coefficients may vary within certain intervals. The results are illustrated by an application to a manufacturing system.Comment: 22 pages, 3 figures (6 eps files

Formal methods for resilient control

Many systems operate in uncertain, possibly adversarial environments, and their successful operation is contingent upon satisfying specific requirements, optimal performance, and ability to recover from unexpected situations. Examples are prevalent in many engineering disciplines such as transportation, robotics, energy, and biological systems. This thesis studies designing correct, resilient, and optimal controllers for discrete-time complex systems from elaborate, possibly vague, specifications. The first part of the contributions of this thesis is a framework for optimal control of non-deterministic hybrid systems from specifications described by signal temporal logic (STL), which can express a broad spectrum of interesting properties. The method is optimization-based and has several advantages over the existing techniques. When satisfying the specification is impossible, the degree of violation - characterized by STL quantitative semantics - is minimized. The computational limitations are discussed. The focus of second part is on specific types of systems and specifications for which controllers are synthesized efficiently. A class of monotone systems is introduced for which formal synthesis is scalable and almost complete. It is shown that hybrid macroscopic traffic models fall into this class. Novel techniques in modular verification and synthesis are employed for distributed optimal control, and their usefulness is shown for large-scale traffic management. Apart from monotone systems, a method is introduced for robust constrained control of networked linear systems with communication constraints. Case studies on longitudinal control of vehicular platoons are presented. The third part is about learning-based control with formal guarantees. Two approaches are studied. First, a formal perspective on adaptive control is provided in which the model is represented by a parametric transition system, and the specification is captured by an automaton. A correct-by-construction framework is developed such that the controller infers the actual parameters and plans accordingly for all possible future transitions and inferences. The second approach is based on hybrid model identification using input-output data. By assuming some limited knowledge of the range of system behaviors, theoretical performance guarantees are provided on implementing the controller designed for the identified model on the original unknown system