LQG-Based Real-Time Scheduling and Control Codesign

Having multiple control tasks concurrently running on a single computing platform increases the processor utilization but degrades the control performance due to delay and jitter. In scheduling and control codesign, the objective is to optimize the combined performance of all the controllers, subject to a schedulability constraint. The codesign procedure consists of selecting task parameters, e.g., periods and priorities, as well as designing the controllers so that the scheduling-induced delay and jitter are taken into account.

In the thesis, four linear-quadratic-Gaussian (LQG) codesign methods are proposed: stochastic, periodic, harmonic, and robust LQG codesign. In stochastic LQG codesign, the delay distributions are calculated at design-time. Then LQG controllers are designed assuming these delay distributions. The obtained task periods generally give rise to infinite hyperperiods. This can be avoided by perturbing the periods slightly in order to obtain a finite hyperperiod, yielding a periodic delay pattern for the control loops. The periodicity is then accounted for by using periodic LQG control design, resulting in a periodic sequence of feedback gains for each controller. In harmonic LQG codesign, again the task periods are perturbed, but this time to make the periods harmonic. The scheduling-induced delays will be constant and standard LQG design can be applied. Finally, a robust LQG codesign method is presented. The design is based on convex optimization and guarantees system robustness in the presence of delay and jitter. A new rule of thumb for initial sampling period assignment is proposed. We propose a jitter-aware priority and period assignment codesign method to optimize the overall system performance.

A large evaluation of the proposed four codesign methods is performed using the Jitterbug toolbox. All of the four methods lead to improved control performance compared to earlier work. The harmonic scheduling and control codesign shows the largest overall improvements.