Infinite-Dimensional Predictive Control for Hyperbolic Systems
Résumé
This paper presents a predictive control scheme, based on the receding horizon optimalcontrol (RHOC) approach with zero terminal constraint, to guarantee the closed-loop stabilityof linear 2 × 2 hyperbolic systems with boundary control. The extension of this control schemeto networks of such hyperbolic systems is also considered. The boundary control problem is firstreformulated in the abstract form for which the optimal control with terminal constraint was wellstudied. These results are then used in the RHOC scheme to give a complete proof of stability of theclosed-loop system. For the implementation, the calculus of variations is used to derive the adjointstate which is then discretized and solved together with the state to obtain the optimal control.The analysis is applied to open-channel hydraulic systems in cases of single pool and multipoolsin cascade. Finally, simulations are carried out to illustrate the effectiveness of the here-proposedapproach.