On the control of hybrid nonlinear systems
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.