ROBUST-CONTROL OF HYPERBOLIC PDE SYSTEMS

This work concerns systems of quasi-linear first-order hyperbolic part ial differential equations (PDEs) with uncertain variables and unmodel ed dynamics. For systems with uncertain variables, the problem of comp lete elimination of the effect of uncertainty on the output via distri buted feedback (uncertainty decoupling) is initially considered; a nec essary and sufficient condition for its solvability as well as explici t controller synthesis formulas are derived. Then, the problem of synt hesizing a distributed robust controller that achieves asymptotic outp ut tracking with arbitrary degree of attenuation of the effect of unce rtain variables on the output of the closed-loop system is addressed a nd solved. Robustness with respect to unmodeled dynamics is studied wi thin a singular perturbation framework. It is established that control lers which are synthesized on the basis of a reduced-order slow model, and achieve uncertainty decoupling or uncertainty attenuation, contin ue to enforce these objectives in the presence of unmodeled dynamics, provided that they are stable and sufficiently fast. The developed con troller synthesis results are successfully implemented through simulat ions on a fixed-bed reactor, modeled by two quasi-linear first-order h yperbolic PDEs, where the reactant wave propagates through the bed wit h significantly larger speed than the heat wave, and the heat of react ion is unknown and time varying. (C) 1997 Elsevier Science Ltd.