arXiv subjects

Roy S. Smith

Publications and source records attributed to Roy S. Smith.

75 records · Page 5Linked to original sources

arXiv2016

Mutually Quadratically Invariant Information Structures in Two-Team Stochastic Dynamic Games

We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic invariance in (single team) decentralized control, defines a class of interacting information structures for the two teams under which optimal linear feedback control strate- gies are easy to compute. We show that, for zero-sum two- team dynamic games, structured state feedback Nash (saddle- point) equilibrium strategies can be computed from equivalent structured disturbance feedforward saddle point equilibrium strategies. However, for nonzero-sum games we show via a counterexample that a similar equivalence fails to hold. The results are illustrated with a simple yet rich numerical example that illustrates the importance of the information structure for dynamic games.

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arXiv2016

The Power of Diversity: Data-Driven Robust Predictive Control for Energy Efficient Buildings and Districts

The cooperative energy management of aggregated buildings has recently received a great deal of interest due to substantial potential energy savings. These gains are mainly obtained in two ways: (i) Exploiting the load shifting capabilities of the cooperative buildings; (ii) Utilizing the expensive but energy efficient equipment that is commonly shared by the building community (e.g., heat pumps, batteries and photovoltaics). Several deterministic and stochastic control schemes that strive to realize these savings, have been proposed in the literature. A common difficulty with all these methods is integrating knowledge about the disturbances affecting the system. In this context, the underlying disturbance distributions are often poorly characterized based on historical data. In this paper, we address this issue by exploiting the historical data to construct families of distributions which contain these underlying distributions with high confidence. We then employ tools from data-driven robust optimization to formulate a multistage stochastic optimization problem which can be approximated by a finite-dimensional linear program. The proposed method is suitable for tackling large scale systems since its complexity grows polynomially with respect to the system variables. We demonstrate its efficacy in a numerical study, in which it is shown to outperform, in terms of energy cost savings and constraint violations, established solution techniques from the literature. We conclude this study by showing the significant energy gains that are obtained by cooperatively managing a collection of buildings with heterogeneous characteristics.

math.OC↗

arXiv2015

A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems

We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative matrices and we use this result to derive necessary and sufficient Linear Matrix Inequality (LMI) conditions for robust stability that involve only the system's static gain. We show how this approach can be applied to test the robust stability of the Foschini-Miljanic algorithm for power control in wireless networks in presence of uncertain interference.

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