NCO Tracking for Singular Control Problems using Neighboring Extremals

Robust Predictive Control Based on Neighboring Extremals

The performance of predictive controller is typically poor when the true plant evolution deviates significantly from that predicted by the model. A robust approach that considers model uncertainty explicitly is then needed. However, it is often difficult to find a single input profile that works for the range of uncertainty considered. Thus, multiple input profiles, i.e. one for each realizatio...

Quadratic order conditions for bang-singular extremals

This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case. The results use in an essential way t...

Singular extremals on Lie groups

Quadratures of Pontryagin Extremals for Optimal Control Problems

We obtain a method to compute effective first integrals by combining Noether’s principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls taking values on open sets is obtained. We illustrate our approach on some problems taken from the literature. An alternative proof of the integrability of ...

Autonomous Underwater Vehicles: Singular Extremals and Chattering

In this paper, we consider the time minimal problem for an Autonomous Underwater Vehicle. We investigate, on a simplified model, the existence of singular extremals and discuss their optimality status. Moreover, we prove that singular extremals corresponding to the angular acceleration are of order 2. We produce in this case a semicanonical form of our Hamiltonian system and we can conclude the...