Two-sided boundary control and state estimation of 2 × 2 semilinear hyperbolic systems

Abstract

© 2017 IEEE. We solve the problem of controlling a class of one-dimensional semilinear 2 × 2 hyperbolic systems to the origin in minimum time using actuation at both boundaries of the domain. The control method can also be used to solve a class of tracking problems. For the special case of time-invariant linear systems, the state-feedback control law can be written explicitly as the inner product of kernels with the state. We further design an observer to estimate the distributed state from measurements at both boundaries, also in minimum time. The state-feedback controller and observer are combined to solve the output-feedback control problem. A numerical example is given to demonstrate the..