Showing papers by "Maria Prandini published in 2000"

A probabilistic approach to aircraft conflict detection

Abstract: Conflict detection and resolution schemes operating at the mid-range and short-range level of the air traffic management process are discussed. Probabilistic models for predicting the aircraft position in the near-term and mid-term future are developed. Based on the mid-term prediction model, the maximum instantaneous probability of conflict is proposed as a criticality measure for two aircraft encounters. Randomized algorithms are introduced to efficiently estimate this measure of criticality and provide quantitative bounds on the level of approximation introduced. For short-term detection, approximate closed-form analytical expressions for the probability of conflict are obtained, using the short-term prediction model. Based on these expressions, an algorithm for decentralized conflict detection and resolution that generalizes potential fields methods for path planning to a probabilistic dynamic environment is proposed. The algorithms are validated using Monte Carlo simulations.

Probabilistic pursuit-evasion games: a one-step Nash approach

Abstract: This paper addresses the control of a team of autonomous agents pursuing a smart evader in a non-accurately mapped terrain. By describing the problem as a partial information Markov game, we are able to integrate map-learning and pursuit. We propose receding horizon control policies, in which the pursuers and the evader try to respectively maximize and minimize the probability of capture at the next time instant. Since this probability is conditioned to distinct observations for each team, the resulting game is nonzero-sum. When the evader has access to the pursuers' information, we show that a Nash solution to the one-step nonzero-sum game always exists. Moreover, we propose a method to compute the Nash equilibrium policies by solving an equivalent zero-sum matrix game. A simulation example shows the feasibility of the proposed approach.

Optimal maneuver for multiple aircraft conflict resolution: a braid point of view

Abstract: We study conflict resolution for multiple aircraft encounter situations on a plane. First, the homotopy types of resolution maneuvers for n aircraft encounters are classified according to their images in the joint space-time coordinates, which are shown to bear a one-to-one correspondence with the well-known pure braid group PB/sub n/. Energy is then proposed as the cost function for choosing among all conflict-free maneuvers the optimal one. For two aircraft encounters, analytic expressions of the optimal resolution maneuvers are obtained, and for the multiple aircraft case, a convex optimization technique is used to find the optimal two-legged resolution maneuver within each type. The introduced solution, however, becomes computationally intractable as the number of aircraft increases. The use of the probabilistic resolution algorithm in Hu (1999) as "random type chooser" is then suggested as a randomized solution to the combinatorial optimization problem. Finally, simulation results are presented for some typical encounters.

Adaptive LQG Control of Input-Output Systems---A Cost-biased Approach

Abstract: In this paper, we consider linear systems in input-output form and introduce a new adaptive linear quadratic Gaussian (LQG) control scheme which is shown to be self-optimizing. The identification algorithm incorporates a cost-biasing term, which favors the parameters with smaller LQG optimal cost and a second term that aims at moderating the time-variability of the estimate. The corresponding closed-loop scheme is proven to be stable and to achieve an asymptotic LQG cost equal to the one obtained under complete knowledge of the true system (self-optimization). The results of this paper extend in a nontrivial way previous results established along the cost-biased approach in other settings.

A self-optimizing adaptive LQG control scheme for input-output systems

Abstract: We consider the optimal control problem of an unknown linear system in input-output form based on the linear quadratic Gaussian (LQG) control design method. A self-tuning LQG control scheme is proposed which is shown to be stable and self-optimizing. Optimality is achieved by using an identification algorithm which incorporates a cost-biasing term favoring the parameters with smaller LQG optimal cost and a second term aiming at moderating the time-variability of the estimate.

Identification of a model for the stress-strain behavior of the periodontal ligament

Abstract: The periodontal ligament (PDL) is a complex connective tissue layer that surrounds the tooth root and connects it to the alveolar bone. Its main components are the ground substance which is mainly fluid and thin fibres arranged in bundles. These two components are responsible for the transmission of the forces acting on the tooth to its supporting structure. In [3, 4, 5], a triaxial model for the PDL constitutive law relating stresses to strains is derived by considering the contributions of the ground substance matrix and the fibres. The obtained nonlinear, large deformation, anisotropic, elastic law is called fibre-composite law. The interested reader is referred to [5] for a review of other models presented in the literature.