Laboratory Notes

Optimization Methods for Analysis and Design

Pablo A. Parrilo
Laboratory for Information and Decision Systems

The conventional techniques for design of control and communications systems have been mostly based on human creativity, intuition, and incremental improvements. In recent years, however, there has been a strong trend towards the use of formal and automated tools. In particular, in many areas of control and communications, as well as electrical and mechanical design, the ideas and methods of mathematical optimization theory have revolutionized the state of the art.

Indeed, to be able to carry analysis, design, resource allocation, and optimization tasks on large scale or high-performance engineered systems, the use of formal techniques based on well-defined system descriptions is unavoidable. For many current and future man-made systems, the sheer size, complexity, performance and robustness requirements are formidable, and simply cannot be easily guaranteed or estimated, requiring instead intensive computational and simulation-based methods.

Prof. Parrilo’s research addresses the development of efficient methods for the analysis and design of engineering systems, often requiring the integration and extension of techniques from different domains. These efforts include the development of a theoretical framework that unifies algebraic tools and convex optimization, and applications to dynamical systems and game theory.

A challenging project currently under investigation is the specification, design and verification of distributed dynamical systems (e.g., teams of autonomous vehicles collaborating towards some higher-level task in an uncertain environment), and the complications that communication constraints impose on their performance. These complex problems often require a combination of ideas from continuous optimization, optimal control, information theory, dynamic games, model checking, and distributed systems.

Besides their intended direct application, an important side effect of the development of fundamental computational methodologies is their practical relevance in a variety of scientific and technological contexts. In collaboration with domain experts, some of the techniques developed by Prof. Parrilo have been successfully applied in areas as diverse as quantum information theory and biochemical system modeling.

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