Distributed non-cooperative robust economic predictive control for dynamically coupled linear systems.

In this thesis, a tube-based Distributed Economic Predictive Control (DEPC) scheme is presented for a group of dynamically coupled linear subsystems. These subsystems are components of a large scale system and control inputs are computed based on optimizing a local economic objective. Each subsystem is interacting with its neighbors by sending its future reference trajectory, at each sampling time. It solves a local optimization problem in parallel, based on the received future reference trajectories of the other subsystems. To ensure recursive feasibility and a performance bound, each subsystem is constrained to not deviate too much from its communicated reference trajectory. This difference between the plan trajectory and the communicated one is interpreted as a disturbance on the local level. Then, to ensure the satisfaction of both state and input constraints, they are tightened by considering explicitly the effect of these local disturbances. The proposed approach averages over all possible disturbances, handles tightened state and input constraints, while satisfies the compatibility constraints to guarantee that the actual trajectory lies within a certain bound in the neighborhood of the reference one. Each subsystem is optimizing a local arbitrary economic objective function in parallel while considering a local terminal constraint to guarantee recursive feasibility. In this framework, economic performance guarantees for a tube-based distributed predictive control (DPC) scheme are developed rigorously. It is presented that the closed-loop nominal subsystem has a robust average performance bound locally which is no worse than that of a local robust steady state. Since a robust algorithm is applying on the states of the real (with disturbances) subsystems, this bound can be interpreted as an average performance result for the real closed-loop system. To this end, we present our outcomes on local and global performance, illustrated by a numerical example.

New assessments of global sea level rise from tide gauges

Estimates of global sea-level change rates based on observations from Tide Gauges (TGs) show a long-term global mean sea-level rise (GMSLR) of 1÷2 mm/yr for the 20th century. The considerable scatter in these estimates is mainly attributable to the uneven distribution of the TG sites and to several physical phenomena that cause local sea level to deviate from the global mean, or to affect the TG record through land subsidence or uplift. The main cause of vertical ground motion on a regional space scale is the response of the Earth to past ice loads, called Glacial Isostatic Adjustment (GIA), which is often modelled and corrected for. In this work, a simple average approach was used to revisit two past estimates based on small sets of long, high-quality TG records in view of the longer record available, employing a newer GIA model (ICE-6G) from Peltier et al. [2015]. The value of GMSLR obtained from both sets is (1.5±0.4) mm/yr. In addition, a much larger set of TGs was used to estimate the contemporary (post 1993) GMSLR using satellite estimates from Cazenave et al. [2018] as a benchmark, in an attempt to understand how a simple average approach could perform for larger sets. The resulting estimate of (3.4÷3.5)±0.2 mm/yr (depending on the GIA correction applied) is comparable to the satellite result of (3.1±0.3) mm/yr.