Minimum time output regulation for general linear heterodirectional hyperbolic systems

ABSTRACT

This paper considers the minimum time output regulation problem for general linear heterodirectional hyperbolic systems with spatially-varying coefficients. For this, a state feedback regulator achieving output regulation in minimum time is determined. In order to obtain an output feedback regulator, finite-time reference and disturbance observers are designed. The latter observer achieves the estimation of the disturbance model and plant states in minimum time. For this, only an additional ODE has to be added to the usual asymptotic-time disturbance observer. The combination of the state feedback regulator with these observers results in an output feedback regulator, for which minimum time output regulation is verified. The output regulation approach is formulated for general signal models, that need not be diagonalisable, and is applied to an unstable $5\times 5$ hyperbolic system. The comparison of the obtained results with an asymptotic-time design confirms the performance increase gained by the solution of the minimum time output regulation problem.

KEYWORDS:

• Distributed-parameter systems
• hyperbolic systems
• backstepping
• boundary control
• output regulation
• observers

Disclosure statement

No potential conflict of interest was reported by the authors.