Showing papers by "Maria Prandini published in 2012"

A randomized approach to Stochastic Model Predictive Control

Abstract: In this paper, we propose a novel randomized approach to Stochastic Model Predictive Control (SMPC) for a linear system affected by a disturbance with unbounded support. As it is common in this setup, we focus on the case where the input/state of the system are subject to probabilistic constraints, i.e., the constraints have to be satisfied for all the disturbance realizations but for a set having probability smaller than a given threshold. This leads to solving at each time t a finite-horizon chance-constrained optimization problem, which is known to be computationally intractable except for few special cases. The key distinguishing feature of our approach is that the solution to this finite-horizon chance-constrained problem is computed by first extracting at random a finite number of disturbance realizations, and then replacing the probabilistic constraints with hard constraints associated with the extracted disturbance realizations only. Despite the apparent naivety of the approach, we show that, if the control policy is suitably parameterized and the number of disturbance realizations is appropriately chosen, then, the obtained solution is guaranteed to satisfy the original probabilistic constraints. Interestingly, the approach does not require any restrictive assumption on the disturbance distribution and has a wide realm of applicability.

Air traffic complexity in future Air Traffic Management systems

Abstract: In this paper the authors study the issue of characterizing the complexity of air traffic to support Air Traffic Management (ATM) operations. The authors discuss, in particular, the features of a complexity metric that are relevant for application to future ATM systems where part of the responsibility for separation assurance and trajectory management operations is distributed on board of the aircraft. The authors then describe a probabilistic complexity metric that meets all those features and is amenable for supporting on board conflict detection and resolution and trajectory management operations. A numerical example illustrates its possible use in a fully automated self-separation context.

A self-recovery approach to the probabilistic invariance problem for stochastic hybrid systems

Abstract: In this paper, we consider the problem of designing a feedback policy for a discrete time stochastic hybrid system that should be kept operating within some compact set A. To this purpose, we introduce an infinite-horizon discounted average reward function, where a negative reward is associated to the transitions driving the system outside A and a positive reward to those leading it back to A. The idea is that the stationary policy maximizing this reward function will keep the system within A as long as possible, and, if the system happens to exit A, it will bring it back to A as soon as possible, compatibly with the system dynamics. This self-recovery approach is particularly useful in those cases where it is not possible to maintain the system within A indefinitely. The performance of the resulting strategy is assessed on a benchmark example.

Design in the presence of uncertainty: the scenario approach

Abstract: In this chapter, we describe the \scenario approach" methodology to solve design problems in the presence of uncertainty. We focus on problems that can be reformulated as nite-dimensional optimization problems, where a linear cost has