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On the control of hybrid nonlinear systems

Sur la commande des systèmes non linéaires à dynamique hybride

Abstract : This dissertation concerns the development of reduced complexity controllers for
hybrid switched systems. A diverse number of applications from automotive industry, fluid dyna-
mics and power systems are treated. Some general open loop optimal and predictive control schemes
are proposed. The main motivation behind each method is the reduction of the combinatorics. In
this thesis, two main contributions can be distinguished. The first one concerns the optimal control
of switched nonlinear systems where an algorithm based on strong variations is proposed and some
convergence results proven. The complexity of the scheme is linear in the number of locations, this
in conjunction with its simplicity makes it attractive for large scale systems. An example from
the automotive industry is treated to further illustrate the tractability of the scheme. The second
contribution concerns the development of a hierarchical approach for switched nonlinear systems.
At the lower level, feedback controllers are associated to each location and at the higher level a
predictive approach with a reduced order parametrization is in force. Based on this methodology,
two schemes are developed and successfully tested in respectively fluid stabilisation by actuator
switching and voltage stabilization in power systems.