Study On Distributed Parameter Systems With Uncertainty Problems

Many physical phenomena of nature can be described by the partial differential equation(PDE),but there are a lot of uncertainties in these systems,for example,time delay,disturbance and so on.How to effectively control distributed parameter systems with uncertainties become a hot spot.In this article,we study the system with a single uncertainty,we study the Timoshenko beam system with time-delay and wave equation system with disturbances respectively.First of all,we study the system with time delay.We investigate the exponential stability of Timoshenko beam system with interior damping and boundary delays.We use dampings to design internal controller to control boundary disturbances.The main work is as follows: First,we prove the well-posedness of the system applying the semigroup theory of bounded linear operators;Second,we give the exponential stability analysis of the system by constructing an appropriate Lyapunov function;Third,different from the earlier results,we study the solvability of the inequalities detailedly;Finally,we use the damping coefficients and delay coefficients together the parameters of the system to give a description of the stability region.Then we study the system with disturbances.We use nonlinear sliding mode controller to anti-damping and we concern with the stabilization of a wave equation with locally distributed disturbance.Firstly,we design a feedback controller basing on the output to reduce the effects of the internal disturbances.Secondly,we investigate the well-posedness of the nonlinear closed loop system by the theories of nonlinear maximal monotone operators.At last,we show asymptotic stabilization of the nonlinear controlled system by the Lyapunov method.