Power and bit scheduling of Markov jump systems with convergence rate as an optimization index

Existing power and bit scheduling algorithms mostly focus on open-loop system performance, i.e., improving estimation accuracy. This paper focuses on the scheduling methods for the closed-loop Markov jump systems in the unreliable transmission environments to improve the system stability and save energy. First, a control unit including feedback controller and predictive controller is proposed which improves the system performance while reducing the complexity of predictive controller design. Second, we design a novel optimization indicator based on time-varying convergence rate and sensor energy consumption. Third, by analyzing the relationship between Lyapunov function and the system state, an explicit expression of the time-varying convergence rate is gained. Next, a constant $\chi$ is introduced to obtain the effective power set, in which the convergence rate is always less than 1, thereby ensuring the system stability. Based on this, the optimal power and bit scheduling algorithm is obtained, which improves the system convergence speed while reducing energy consumption. Last, a two-tanks system is used to verify the effectiveness and superiority of the main algorithms.