Reliable Real-Time Solution of Parametrized Elliptic Partial Differential Equations: Application to Elasticity

The optimization, control, and characterization of engineering components or systems require fast, repeated, and accurate evaluation of a partial-differential-equation-induced input-output relationship. We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine parameter dependence. The method has three components: (i) rapidly convergent reduced{basis approximations; (ii) a posteriori error estimation; and (iii) off-line/on-line computational procedures. These components -- integrated within a special network architecture -- render partial differential equation solutions truly "useful": essentially real{time as regards operation count; "blackbox" as regards reliability; and directly relevant as regards the (limited) input-output data required.Singapore-MIT Alliance (SMA

Demand shifting using model-assisted control

Increasing energy demand and more strict environmental regulations have led to a turn to renewable energy generation sources, thus enabling the transition from traditional centralized electric grids to smart grids where the existing power grid is enhanced by distributed, small-scale renewables-based energy generation systems. In this new, complex landscape, buildings equipped with dedicated renewables are tasked to properly shape their thermal loads in order to consume as much power as possible from the renewables during peak-demand periods - a behavior enforced by Time-of-Use tariffs communicated from the grid. Under this perspective, in the present work, the ability to explore different operation strategies for the building systems to shape the thermal loads while accounting for the stochastic production profile of the renewables and maintaining comfortable building interiors is ensured by designing Building Energy Management Systems optimized for a specific building and targeted to the microclimate conditions of each area, maximizing the renewables' energetic benefits while preserving indoor comfort requirements. This is achieved utilizing a detailed thermal simulation model of the building, along with weather and occupancy forecasts and a response surface-based stochastic optimization algorithm. The potential of the proposed approach is demonstrated on example building located in Athens, Greece, but the generality of the method allows application in any building and in any test area, regardless of constructional, geographical, and climatic variations

Nonlinear control of large scale complex systems using convex control design tools

Based on recent advances on convex design for Large-Scale Control Systems (LSCSs) and robust and efficient LSCS self-tuning/adaptation, a methodology is proposed in this paper which aims at providing an integrated LSCS-design, applicable to large-scale systems of arbitrary scale, heterogeneity and complexity and capable of: 1) Providing stable, efficient and arbitrarily-close-to-optimal LSCS performance; 2) Being able to incorporate a viarety of constraints, including limited control constraints as well as constraints that are nonlinear functions of the system controls and outputs (sensor measurements); 3) Being intrinsically self-tunable, able to rapidly and efficiently optimize LSCS performance when short-, medium- or long-time variations affect the large-scale system; 4) Achieving the above, while being scalable and modular. The purpose of the present paper is to provide the main features of the proposed control design methodology