Lap time optimisation of a racing go-kart

The minimum lap time optimal control problem has been solved for a go-kart model. The symbolic algebra software Maple has been used to derive equations of motion and an indirect method has been adopted to solve the optimal control problem. Simulation has been successfully performed on a full track lap with a multibody model endowed with seven degrees of freedom. Geometrical and mechanical characteristics of a real kart have been measured by a lab test to feed the mathematical model. Telemetry recorded in an entire lap by a professional driver has been compared to simulation results in order to validate the model. After the reliability of the optimal control model was proved, the simulation has been used to study the peculiar dynamics of go-karts and focus to tyre slippage dynamics, which is highly affected by the lack of differential.     

Comparison of direct and indirect methods for minimum lap time optimal control problems

Minimum lap time simulations are especially important in the design, optimisation and setup of race vehicles. Such problems usually come in different flavours, e.g. quasi-steady state models vs. full dynamic models and pre-defined (fixed) trajectory problems vs. free trajectory problems. This work is focused on full dynamic models with free trajectory. Practical solution techniques include direct methods (i.e. solution of an nonlinear programming problem problem, widespread approach) and indirect method (i.e. based on Pontryagin's principle, less common, yet quite efficient in some cases). In this contribution the performance of the direct and indirect methods are compared in a number of vehicle-related problems.     

Air traffic management: Optimization models and algorithms

Current air traffic control systems are mainly conceived to ensure the safety of flights by means of tactical interventions, because of the difficulty of accurately foreseeing the traffic evolution. In fact, in real traffic conditions, planes are often penalized since sometimes safety standards are redundant. Today, this management philosophy is no longer valid because of congestion phenomena which often occur in the most important terminal areas. Therefore, as to future control systems it is necessary to introduce not only more automated procedures to keep adequate safety levels, but also planning functions in order to increase the system capacity and to improve system efficiency. In recent years several studies have been carried out, new control concepts have been introduced and some optimization models and algorithms developed to improve air traffic management. In this paper a survey of our early works in this field is reported and a multilevel model of air traffic management is proposed and discussed. The functions corresponding to the on-line control, that is flow control, strategic control of flights and aircraft sequencing in a terminal area, are examined and the optimization models and solution algorithms are illustrated. Finally, relevant problems coped by recent research are mentioned and new trends are indicated.     

A bilevel flow model for hazmat transportation network design

In this work we consider the following hazmat transportation network design problem. A given set of hazmat shipments has to be shipped over a road transportation network in order to transport a given amount of hazardous materials from specific origin points to specific destination points, and we assume there are regional and local government authorities that want to regulate the hazmat transportations by imposing restrictions on the amount of hazmat traffic over the network links. In particular, the regional authority aims to minimize the total transport risk induced over the entire region in which the transportation network is embedded, while local authorities want the risk over their local jurisdictions to be the lowest possible, forcing the regional authority to assure also risk equity. We provide a linear bilevel programming formulation for this hazmat transportation network design problem that takes into account both total risk minimization and risk equity. We transform the bilevel model into a single-level mixed integer linear program by replacing the second level (follower) problem by its KKT conditions and by linearizing the complementary constraints, and then we solve the MIP problem with a commercial optimization solver. The optimal solution may not be stable, and we provide an approach for testing its stability and for evaluating the range of its solution values when it is not stable. Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution. The proposed bilevel model and heuristic algorithm are experimented on real scenarios of an Italian regional network.