Milad Farsi | Applied Math, University of Waterloo
Optimal Control of Hybrid Dynamical Systems in Applications
In recent years, hybrid dynamical systems have attracted much attention from researchers due to their wide variety of applications in engineering, including power electronics and flight control. Moreover, the optimal control formulation of such problems allows us to regulate the state and the control input of the system to design efficient control systems. In particular, consider the optimal feedback control problem of switched systems over an infinite horizon. In this regard, various approaches are presented in the literature that usually exploit the dynamic programming approach or the minimum principle. However, analytical and computational approaches which apply to general optimal control problems of hybrid systems do not normally result in a control rule in a feedback form. By exploiting the idea of inverse optimal control, we can measure the cost functional in a closed form as far as the running cost depends somehow on a Lyapunov function by which the asymptotic stability of the nonlinear closed-loop system is guaranteed. We show that, by the appropriate choice of optimal value function and running cost, obtaining an optimal control rule in feedback mode is feasible for a class of switched systems with a state-dependent input. Hence, we pose and solve an optimal control problem for this class of switched systems, which is beneficial for addressing the maximum power point tracking problem of solar photo-voltaic (PV) systems. In the next step, by extending the obtained results, we will aim at solving the problem for other classes of switched systems in which the state-dependent input is a nonconvex function of the state to consider the partial shading effect in solar PV systems.