Hybrid Optimal Control of Large-Scale Linear Systems

This paper presents a hybrid technique for optimal discrete-time control of a large-scale linear system. For effective design of a large-scale linear system with multiple flexible modes, the original model is block-decoupled into a multi-time scale structure using the fast and stable matrix sign algorithm. To enhance the robust stability and performance of the linear system, an optimal regional-pole placement technique is applied to design a continuous-time optimal state-feedback control law with regional-pole constraints for individual block-decoupled subsystems. For digital control of the continuous-time system, the designed continuous-time state-feedback control law needs to be converted into an equivalent discrete-time state-feedback control law, using the recently developed digital redesign technique. Since the states of the linear system are, in general, inaccessible, a digital observer needs to be constructed for practical digital implementation of the digitally redesigned discrete-time state-feedback control law. The effectiveness of the proposed technique is demonstrated through the design of the optimal digital controller for the X-ray Timing Explorer (XTE) spacecraft system. The designed results are demonstrated by the digital simulator of the XTE spacecraft system.