D. Corona, J. Buisson, and B. De Schutter, "A Hamiltonian approach for the optimal control of the switching signal for a DC-DC converter," Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp. 7654-7659, July 2008.
The optimal control problem of a switching DC-DC converter is considered in this paper. An LQ (Linear Quadratic) type performance index of the error between the current state variables and the target working point is defined. The feedback control on the decision variable of the duty cycle frequency is then formulated as a minimization of an appropriate Hamiltonian function of which suboptimal solutions are proposed. These are based on a detailed study of the average model of the system, obtained from the desired steady state solution. This paper focuses on a particular converter (the Buck-Boost converter), but the results are easily extensible to all single switch-cell converters.