Luca Schenato

We consider the problem of controlling a smart lighting system of multiple luminaires with collocated occupancy and light sensors. The objective is to attain illumination levels higher than specified values (possibly changing over time) at the workplace by adapting dimming levels using sensor information, while minimizing energy consumption. We propose to estimate the daylight illuminance levels at the workplace based on the daylight illuminance measurements at the ceiling. More specifically, this daylight estimator is based on a model built from data collected by light sensors placed at workplace reference points and at the luminaires in a training phase. Three estimation methods are considered: Regularized least squares, locally weighted regularized least squares, and cluster-based regularized least squares. This model is then used in the operational phase by the lighting controller to compute dimming levels by solving a linear programming problem, in which power consumption is minimized under the constraint that the estimated illuminance is higher than a specified target value. The performance of the proposed approach with the three estimation methods is evaluated using an open-office lighting model with different daylight conditions. We show that the proposed approach offers reduced under-illumination and energy consumption in comparison to existing alternative approaches.

In this paper, we study the problem of real-time optimal distributed partitioning for perimeter patrolling in the context of multicamera networks for surveillance, where each camera has limited mobility range and speed, and the communication is unreliable. The objective is to coordinate the cameras in order to minimize the time elapsed between two different visits of each point of the perimeter. We address this problem by casting it into a convex problem in which the perimeter is partitioned into nonoverlapping segments, each patrolled by a camera that sweeps back and forth at the maximum speed. We then propose an asynchronous distributed algorithm that guarantees that these segments cover the whole patrolling perimeter at any time and asymptotically converge to the optimal centralized solution under reliable communication. We finally modify the proposed algorithm in order to attain the same convergence and covering properties even in the more challenging scenario, where communication is lossy and there is no channel feedback, i.e., the transmitting camera is not aware whether a packet has been received or not by its neighbors.

The problem of daylight estimation in a smart lighting system is considered. The smart lighting system consists of multiple luminaires with collocated occupancy and light sensors. Using sensor information, the objective is to attain illumination levels higher than specified values at the workspaces. We consider a training phase wherein light sensors are used at the workspaces in addition. Data from the light sensors at the ceiling and workspaces is used to estimate the mapping across the sensors. In the operational phase, the estimated mapping is used at the lighting controller to obtain an estimate of the illuminance value at the workspaces. Under the constraint that the estimated illuminance is higher than a specified target value, the controller optimizes the dimming levels of the luminaires to minimize power consumption. We evaluate the performance of the proposed approach in an open-office lighting model by considering different daylight conditions.

We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where a network of agents, each endowed with local private multidimensional convex cost and subject to communication constraints, wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proven, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.

In this paper we analyze the performances of some popular algorithms used to solve distributed optimization problems involving quadratic cost functions in a multi agent system. Namely, we study the performances of standard consensus, accelerated consensus and ADMM.  We analyze the scalar quadratic function case, under different scenarios and with structured graphs. We find that accelerated consensus is the algorithm with the best performance in all the cases analyzed. On the other hand, ADMM has performance comparable to the accelerated consensus when the graph is scarcely connected, while for dense graphs its performance deteriorates and becomes worse than the one of standard consensus. The results therefore suggest that the choice of the algorithm to solve the problem we analyze strongly depends on the graph, and that accelerated consensus should always be preferred.