Optimal switching Lyapunov-based control of a boost DC-DC converter

A new methodology for designing robust and efficient state-feedback control laws for a switched-mode boost DC-DC power converter has been recently proposed. This approach has adopted the so-called stabilizing or Lyapunov-based control paradigm which is well-known in the area of energy-based control of DC-DC converters, whereby the control law takes a state-feedback form parameterized by a positive scalar gamma. Extension to state-dependent switching state-feedback control laws has been proposed, where the switching surfaces are parameterized by a number of positive scalars gamma(i). In this paper this methodology is revisited by considering the problem of designing optimal switching state-feedback control laws, i.e. finding the optimal control parameters gamma(i) corresponding to the optimal position of the switching surfaces. This permits minimization of the number of switchings required for achieving an optimal performance and hence reduced complexity of the control law. Systematic derivation of gradient information to apply gradient-descent algorithms is provided. The proposed technique is numerically evaluated using the exact switched model of the converter.