Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

摘要

This paper presents a backstepping solution for the output feedback controlof general linear heterodirectional hyperbolic PDE-ODE systems withspatially-varying coefficients. Thereby, the coupling in the PDE is in-domainand at the uncontrolled boundary, whereby the ODE is coupled with the latterboundary. For the state feedback design a two-step backstepping approach isdeveloped, that yields the conventional kernel equations and additionaldecoupling equations of simple form. The latter can be traced back to simpleVolterra integral equations of the second kind, which are directly solvablewith a successive approximation. In order to implement the state feedbackcontroller, the design of observers for the ODE-PDE systems in question isconsidered, whereby anticollocated measurements are assumed. Simple conditionsfor the existence of the resulting observer-based compensator are formulated,that can be evaluated in terms of the plant transfer behaviour. The resultingsystematic compensator design is illustrated for a 4x4 heterodirectionalhyperbolic system coupled with a third order ODE modelling a dynamic boundarycondition.