Model reference adaptive control of \(n+1\) coupled linear hyperbolic PDEs. (English) Zbl 1377.93085
Summary: We solve a Model Reference Adaptive Control (MRAC) problem for a class of systems consisting of \(n+1\) coupled linear hyperbolic partial differential equations. The goal is achieved from a single boundary sensing anti-collocated with the actuation, with the only knowledge of the system being the system’s transport delays and the sign of the product of the actuation and measurement scaling constants. Boundedness in \(L_2\) is shown for all signals in the closed loop system. Moreover, the adaptive output feedback stabilization problem is a subproblem of the MRAC problem, and it is shown that if the reference signal is set identically zero, the system’s \(L_2\)-norms are bounded and square integrable. The theory is demonstrated in simulations.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35Q93 | PDEs in connection with control and optimization |
| 93C05 | Linear systems in control theory |
| 35L40 | First-order hyperbolic systems |
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