Maria Prandini

Simone Garatti, Lucrezia Manieri, Alessandro Falsone et al.

The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to a single appropriateness criterion for the solution based on a dataset, whereas many practical applications - including multi-agent decision problems - require the simultaneous consideration of multiple criteria and the assessment of their robustness based on multiple datasets, one per criterion. This paper develops a general scenario theory for multi-criteria data-driven decision making. A central innovation lies in the collective treatment of the risks associated with violations of individual criteria, which yields substantially more accurate robustness certificates than those derived from a naive application of standard results. In turn, this approach enables a sharper quantification of the robustness level with which all criteria are simultaneously satisfied. The proposed framework applies broadly to multi-criteria data-driven decision problems, providing a principled, scalable, and theoretically grounded methodology for design under uncertainty.

Nikolaus Vertovec, Kostas Margellos, Maria Prandini

We consider a moving target that we seek to learn from samples. Our results extend randomized techniques developed in control and optimization for a constant target to the case where the target is changing. We derive a novel bound on the number of samples that are required to construct a probably approximately correct (PAC) estimate of the target. Furthermore, when the moving target is a convex polytope, we provide a constructive method of generating the PAC estimate using a mixed integer linear program (MILP). The proposed method is demonstrated on an application to autonomous emergency braking.

Basak Sakcak, Luca Bascetta, Gianni Ferretti et al.

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the RRT* algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction {at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be }asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.

Daniele Ioli, Alessandro Falsone, Alessandro Vittorio Papadopoulos et al.

This paper proposes a compositional modeling framework for the optimal energy management of a district network. The focus is on cooling of buildings, which can possibly share resources to the purpose of reducing maintenance costs and using devices at their maximal efficiency. Components of the network are described in terms of energy fluxes and combined via energy balance equations. Disturbances are accounted for as well through their contribution in terms of energy. Different district configurations can be built, and the dimension and complexity of the resulting model will depend on the number and type of components and on the adopted disturbance description. Control inputs are available to efficiently operate and coordinate the district components, thus enabling energy management strategies to minimize the electrical energy costs or track some consumption profile agreed with the main grid operator.

Alessandro Vittorio Papadopoulos, Federico Terraneo, Alberto Leva et al.

We study feedback control for discrete-time linear time-invariant systems in the presence of quantization both in the control action and in the measurement of the controlled variable. While in some application the quantization effects can be neglected, when high-precision control is needed, they have to be explicitly accounted for in control design. In this paper we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables in the case of a simple integrator with unitary delay, a model that is quite common in the computing systems domain, for example in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach.

Aida Brankovic, Alessandro Falsone, Maria Prandini et al.

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion of the original attributes and a model structure selection process is applied to find the relevant terms of the model. The selection method progressively refines a probability distribution defined on the model structure space, by extracting sample models from the current distribution and using the aggregate information obtained from the evaluation of the population of models to reinforce the probability of extracting the most important terms. To reduce the initial search space, distance correlation filtering can be applied as a preprocessing technique. The proposed method is evaluated and compared to other well-known feature selection and classification methods on standard benchmark classification problems. The results show the effectiveness of the proposed method with respect to competitor methods both in terms of classification accuracy and model complexity. The obtained models have a simple structure, easily amenable to interpretation and analysis.