Direct Adaptive Control for Infinite-dimensional Symmetric Hyperbolic Systems

Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we show that there exists a stabilizing direct model reference adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. The plant is described by a closed densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states.Symmetric Hyperbolic Systems of partial differential equations describe many physical phenomena such as wave behavior, electromagnetic fields, and quantum fields. To illustrate the utility of the adaptive control law, we apply the results to control of symmetric hyperbolic systems with coercive boundary conditions.