Optimization and Control

Our research activities center around the optimal control of complex engineering and economic systems and mathematical optimization. Primary areas of interest include:

• Stochastic control: Markovian decision processes, stochastic dynamic programming.
• Decentralized algorithms for large-scale system optimization: complex network optimization, multi-agent coordinated control.
• Dynamic games: economic regulations of network industries.

Projects:

• Dynamic Coordination of Distributed Planning with Limited Communication:

  This project investigates coordination in distributed engineering system with limited communication, particularly by posing a new class of sequential decision processes, known as coordination processes. Our research will provide new theoretical insights for the design and control of decentralized systems, along with new computational algorithms for distributed planning and decision-making. This project is funded by the NSF.

• Economic Regulation of Network Industries (electricity, gas, telecom):

  We study the long run reliability (or security of supply) of electricity markets under price caps. This (and other forms or market intervention) cast doubts on the market ability to provide new capacity in a socially efficient manner (scale, technology and timing). We propose to develop a dynamic game model of investment. A full characterization of equilibrium investment will shed light on a number of contentious issues in the restructuring debate. Examples include; the possibility of "boom and bust" cycles in equilibrium, a potential technology bias with harmful effects on the environment, and the need to incorporate capacity markets.

  We will also study learning algorithms as potentially powerful computational tools for electricity markets. The complexity of electricity markets calls for the incorporation of some form of bounded rationality in the modeling efforts. However, when players use simple, adaptive (possibly sub-optimal) rules, repeated interaction may induce equilibrium outcomes in the long run. Although, many "agent based" simulation models have been advocated for analyzing electricity markets, they lack solid theoretical support on issues such as convergence and/or the nature of equilibrium. In this proposal we will represent competition in electricity markets under certain congestion management protocols, as games with a special structure, i.e. "potential games'. For this class of games, the class of "fictitious play" learning algorithms has been proven to converge with probability one. Computational tests a large-scale model will serve to validate and assess the practicality of the class of strategic learning models proposed. This project is funded by the NSF.

• Complex Networks Optimization:

  This research project will study optimization algorithms rooted in the ideas of game theory in the context of complex network optimization, and particularly decentralized network optimization. Probably the central issue in managing such decentralized networks has been how to set prices so as to motivate the competing users to evolve to an overall system optimal configuration. The research will investigate the powerful paradigm of economic competition in the framework of artificial dynamic games that are played off-line, resulting in an algorithm that is potentially practical for large-scale systems optimization. The basic paradigm that will be investigated derives from Fictitious Play which is an adaptive procedure wherein each player assumes that other players will play according to the empirical distribution of their previous plays. The Fictitious Play method is a novel paradigm for optimization that draws from several distinct disciplines and application areas, including classical optimization, game theory, transportation science, and queueing network protocols. The robust nature of the algorithm allows for the ill-structured black box models of real systems which seldom exhibit the kind of smoothness properties that classical optimization methods demand. Its applicability in the context of two important real-world systems: a) internet traffic routing protocols and b) dynamic route guidance will be tested. This project is funded by the NSF.