Suboptimal Stochastic Control with Compensators of Reduced Size for Discrete-Time Non-Stationary Systems

The design of stochastic optimal compensators for time-varying multivariable systems leads to a tandem combination of a Kalman filter and a state regulator having both time-varying gains and whose implementation normally requires storage of n² + nm + nr functions of time, where n, m and r are the dimensions of the system model, of the control and of the measurement, respectively. A methodology is here proposed to reduce the bulk storage requirements of the overall compensator. A sequence of operations, including a canonical transformation, a 1-order reduction by continued-fraction expansion of instantaneous transfer function, a transformation to Schur form, a smoothing of time evolutions, and a parameter optimization with respect to the initial cost function, is executed on the initially optimal compensator. A greatly reduced suboptimal compensator is obtained. This method is applied to the autopilot design of a space launcher during its initial atmospheric flight. A reduction ratio exceeding 100 to 1 is obtained for the storage requirements in the on-board computer with only minor degradation in the regulation and disturbance rejection performance of the autopilot.