Adaptive Output Feedback Boundary Control Design For A Class Of First-Order Hyperbolic PDE System

In practice,variety of physical process can be described by the class of hyperbolic PDE system.Over the past two decades,boundary control for hyperbolic PDE systems has become one of the research hotspots in this field.Actually,the parameters of the PDE system are usually uncertain,sometimes it's unpractical or even impossible to measure all the state variables.Therefore,the adaptive output-feedback boundary control for hyperbolic PDE system is challenging.On the one hand,the boundary control for PDEs system is challenging as a result of the system dynamics being infinite dimensional.On the other hand,the adaptive control is tricky for the reason that an adaptive controller should be constructed for the model whose parameters may be highly uncertain as well as spatially varying.This dissertation mainly studies the adaptive output feedback boundary control problem for a class of hyperbolic PDE systems with uncertain spatially varying parameters.The main results are as follows:Firstly,an adaptive state feedback control approach which is based on error variable for hyperbolic PDE systems is constructed.The main idea is to construct a virtual system which is similar to the original system structure.The dynamic compensation for the unknown parameters is given based on the error variable(the error between the virtual system and the original system).It is worth to point out that compared with the approach of using projection operator to address uncertain parameters,the approach we give does not rely on the upper and lower bounds of the parameters.In the end,the adaptive output feedback control law can be given according to the certainty equivalence principle.The effectiveness of the proposed approach can be verified by a numerical simulation.Secondly,this dissertation addresses the problem of output-feedback adaptive control for a class of first-order hyperbolic PDE system with uncertain spatially varying parameter.To estimate the state variable of the PDE system,an adaptive observer which consists of input filter and output filter is given.Then,based on the observer,an outputfeedback adaptive boundary controller is constructed by certainty equivalence principle.It is worth to point out that due to the infinite dimensional property of the spatially varying parameters,the output filter dimension is one-dimensional higher than the hyperbolic PDE system.Moreover,to deal with the system unknowns,a dynamic compensation for the unknown parameters is given by projection operator as well as Lyapunov approach.What's more,the efficiency of the proposed control design is illustrated by numerical simulations.