Optimal tracking control of Markov jump bilinear system based on Krotov's method and its application

The control and optimization of the Markov jump bilinear system (MJBLS) are challenging due to the bilinear dynamics in different modes and the mode-switching controlled by a Markov chain. To address this, an optimal tracking control method for discrete-time MJBLS based on Krotov's method is proposed and applied to the optimal tracking control of blast furnace molten iron quality. First, the state equation of the MJBLS and the reference trajectory are combined to construct an augmented system, transforming the optimal tracking control problem into an optimal quadratic regulation problem. Concurrently, an improving function suitable for MJBLS is designed to update the admissible process iteratively. Then, the established performance index is iteratively optimized, and the result obtained in the final iteration, which meets the convergence condition, is employed as the optimal controller. Finally, the effectiveness of the proposed method is verified through numerical simulation, and its application to blast furnace molten iron quality control achieves satisfactory tracking control results.