Advanced control algorithm applied to the Guidance Navigation & Control of complex dynamic systems

In this Thesis a new Optimal control-based algorithm is presented, FLOP is part of a new class of algorithms the group of Mechatronic and Vehicle Dynamic Lab of Sapienza is developing under the name of Variational Feedback Controllers (VFC). The proposed method starts from classical optimal variational principles, usually part of the Pontryagin’s or Bellman’s methods, but it provides the user with the possibility to implement a feedback control, even in the presence of nonlinearities. In fact, even though Pontryagin approach provide the best solution for the considered system, it has an engineering weakness, since the identified solution is a feedforward control law. The control program form of the solution presents an engineering weakness, that is they use only one single information on the system state: the initial condition. This approach would be natural if the system’s model is not affected by any error, the state of the system is perfectly known, and all the environment forces are known in advance. Under these conditions, the system response for any future time depends only on the initial information provided by the initial condition. However, engineering practice and real world meet a different scenario. Models of the controlled process have some degree of approximation, because the real dynamics is only roughly represented by the estimated differential equations, and the environment external disturbance is generally unknown. In this context, use of measurements by sensors is of great value and feedback control strategies use the valuable support of measurements. Variation Feedback Control is aimed at using the power of variational functional calculus to state a well posed optimality principle, but using the information coming from sensors, integrating in this way the available information contained into initial conditions, the only one used in the context of control programs, providing a more reliable controlled system. This chance is obtained by changing the optimality principle used in the classical approach. FLOP approach, respect to classical nonlinear controls, such as Sliding Mode, Lyapunov and feedback linearization controls, presents a great advantage because of the chance of a more flexible specification of the objective function. In this work the FLOP algorithm is applied to define new techniques for Guidance Navigation and Control (GN&C) of complex dynamic systems. Autonomy requires as a main task to be able to self-perceive and define the best way to reach the desired part of the state space, in which the considered system moves by applying different strategies and modification of the applied algorithms to perform the task, whatever the considered dynamic system. Model based control techniques such as LQR, SDRE and MPC have the advantage of being aware of the system dynamics, but in general they present some drawbacks, in fact LQR and SDRE algorithms require linear dynamics or a linearized form of the real dynamics, as well as limitations in terms of penalty function, while MPC, in their nonlinear formulation namely NMPC, can deal with nonlinear dynamics and strong constraints, moreover they can introduce strong constraints for the system state as well as for the control actuation, the major drawback of these techniques is that the online optimization process requires a huge computational effort especially when the dynamics of the system is very complicated, or the system presents an high number of degrees of freedom, moreover time for convergence is strictly connected to the convexification of the considered cost function that has to be minimized, especially in presence of constraints in terms of the state and or of the control. The present technique is applied in complex engineering applications, the autonomous car, an autonomous marine craft for rescue purposes, rocket landing problem, and finally to the control of a micro-magnetic robot, actuated by a Magnetic Resonance Imaging (MRI) for non-invasive surgery. will be discussed, this research projects are part of the activities developed by the group of Mechatronic and Vehicle Dynamic Lab of Sapienza.