Topics on Optimization Strategies for Constrained Mechanical Systems

In the first part of the work we analyze the problem of optimal control of a vehicle along a preassigned trajectory. The vehicle system is studied and simplified in order to obtain a computationally tractable model, which still presents the main characteristics of the real vehicle. The control algorithm, based on MPC techniques, is then explained and its effectiveness is proved through simulation results. The “minimum lap time problem” is afterward considered, which can be considered as an evolution of the trajectory tracking problem; its analysis is presented and is followed by the developed solution, based on pseudospectral methods. In the second part of the thesis the problem of control of underactuated mechanical systems is discussed. The nonholonomic system classically called “rolling disk” is considered as test case; it is a wheel with punctiform contact surface that can roll on the plane without sliding laterally. Differently from the literature we consider the torque as the unique control input signal. This system is modeled through the Lagrangian formalism and then the control strategy, based on backstepping and receding horizon techniques, is shown and proved to be effective.