In this work we propose a novel adaptive switching strategy for the design of pulse width modulation signals in power converters. Instead of an uncertain averaged model of the power converter, an uncertain switched model is considered, which can better represent the actual power converter dynamics. Uncertainties in the power converters parameters are handled via an adaptive control approach, and all circuit parameters of the switched model are assumed to be unknown (including the load and parasitic effects). After defining the pulse width modulation in terms of a reverse mode-dependent dwell time, an elementary-time-unit Lyapunov function is used to derive a set of linear matrix inequalities (LMIs) based on global uniformly ultimately boundedness of the switched system. The LMIs are solved in an adaptive fashion using an exploitation–exploration mechanism: exploitation is achieved by solving the LMIs based on the estimated switched model, while exploration is achieved by a persistently exciting input voltage source, which guarantees convergence of the estimated parameters to the true system parameters.

This work proposes an online policy iteration procedure for the synthesis of sub-optimal control laws for uncertain Linear Time Invariant (LTI) Asymptotically Null-Controllable with Bounded Inputs (ANCBI) systems. The proposed policy iteration method relies on: a policy evaluation step with a piecewise quadratic Lyapunov function in both the state and the deadzone functions of the input signals; a policy improvement step which guarantees at the same time close to optimality (exploitation) and persistence of excitation (exploration). The proposed approach guarantees convergence of the trajectory to a neighborhood around the origin. Besides, the trajectories can be made arbitrarily close to the optimal one provided that the rate at which the the value function and the control policy are updated is fast enough. The solution to the inequalities required to hold at each policy evaluation step can be efficiently implemented with semidefinite programming (SDP) solvers. A numerical example illustrates the results.