New Optimal Control Algorithms for Battery-Supercapacitor HESS Based on Wirtinger-Based Integral Inequality

This paper focuses on the design of new optimal control algorithms for battery-supercapacitor hybrid energy storage system (HESS) with input saturation and time delay. Different from the existing research results, a new state feedback system to track the output DC bus voltage and battery current is developed via the state-space averaged model method. By fully considering the state delay information, a proper Lyapunov–Krasovskii functional (LKF) is constructed. In order to reduce the inherent conservation, Wirtinger-based integral inequality is firstly employed to establish novel stability criteria of battery-supercapacitor HESS. Meanwhile, for the sake of shortening the transition time and realizing the smooth transition of some key variables during the load switch, new optimal control algorithms with actuator saturation can be achieved in terms of linear matrix inequalities (LMIs). Finally, numerical results are presented to verify the effectiveness and superiority of the analysis results.