A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez ( 2000 Fliess, M and Marquez, R . 2000. Continuous-time Linear Predictive Control and Flatness: A Module-theoretic Setting with Examples. International Journal of Control, 73: 606–623. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b Hagenmeyer, V and Delaleau, E . 2003b. Exact Feedforward Linearization Based on Differential Flatness. International Journal of Control, 76: 537–556. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.

With the increasing number of applications for both surface and underwater autonomous vehicles, a great amount of control methods and guidance principles has been developed over the years. This work proposes a review of the most common of these methods. It is mainly focused on model-based nonlinear control methods and guidance principles. Notably, this work details examples and variations of model-based linearizing controllers, applications of line of sight guidance, sliding mode controllers and several other less common control methods for both fully-actuated and underactuated vehicles. Additionally, this work proposes an alternative definition of underactuation with respect to the task allowing for a better understanding of the consequences of underactuation on control. Comparison of fully-actuated and underactuated cases shows how control laws can be used to solve the problems of underactuation and what mechanisms can be used to compensate for the lack of actuation on a degree of freedom. The reviewed methods are compared and discussed with respect to their capabilities, limitations and suitability for typical tasks.

This work presents a novel method for 3-D path-following and path-tracking of Autonomous Underwater Vehicles (AUVs) using the concept of a Virtual Reference Point (VRP) and a kinematic guidance principle. The origins of the along-, cross- and vertical-track errors are proven globally exponentially stable (GES) using Lyapunov stability analysis. The kinematic guidance law exploits the design flexibility of a user-defined VRP in conjunction with a feedback linearizing controller. In addition, a novel concept called the Handy Matrix is introduced and applied to shape the kinematic equations such that the AUV’s non-actuated degrees of freedom (DOFs) can be controlled in a 3-D path-following scenario. The case study considers the Remus 100, a torpedo-shaped underactuated AUV, performing a 3-D path-following maneuver. The computer simulations show that the kinematic guidance law shows excellent tracking performance and stability even in the presence of ocean currents and white measurement noise.

We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of Kähler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations.