Minimum time control of heterodirectional linear coupled hyperbolic PDEs

Minimum time control of heterodirectional linear coupled hyperbolic PDEs

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems. Considered systems feature an arbitrary number of coupled transport PDEs convecting in either direction. Using the backstepping approach, we derive a full-state feedback law and a boundary observer enabling stabilization by output feedback. Unlike previous results, finitetime convergence to zero is ach...

Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs

We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and delay-robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delayrobust...

Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems

Boundary Feedback Control of Coupled Hyperbolic Linear PDEs Systems with Nonlinear Boundary Conditions

We try to stabilize equilibrium solutions of physical models described by a class of coupled first-order linear partial differential equations with nonlinear boundary conditions. These systems are distributed parameter systems in which spatio-temporal chaos occurs. In order to stabilize the equilibrium solutions of the systems, at first, we reduce the PDEs to discrete-time systems using the met...

Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

In this paper, we extend recent results on state and boundary parameter estimation in coupled systems of linear partial differential equations (PDEs) of the hyperbolic type consisting of n rightward and one leftward convecting equations, to the general casewhich involves an arbitrary number of PDEs convecting in both directions. Two adaptive observers are derived based on swapping design, where...