Discrete-Time Optimal Control of Double Integrators and its Application in Maglev Train

As an alternative to bang-bang control, a time optimal control (TOC) algorithm for discrete-time systems was first reported by Han((1)). This algorithm not only acts as a noise-tolerant tracking differentiator (TD) to avoid setpoint jumps in control processes, but also has wide applications in the design of controllers and observers. However, determination of the real-time state position on the phase plane involves complex boundary transformations, which renders this algorithm impractical for some engineering applications. This paper proposes a methodology for discrete-time optimal control (DTOC) of double integrators with disturbances. The closed-form solution with lower computational burden can be easily extended to general second-order systems. Further, in consideration of the inevitable disturbances in the systems, a rigorous and full-convergence proof is presented for the proposed algorithm. The results show finite-time and fast convergence as well as provide the ultimate stable attraction regions for the system states. Examples and experiments are also presented to demonstrate the effectiveness of the proposed algorithm for solving a signal processing problem in a maglev train.