Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs

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...

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...

Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems

Adaptive output-feedback stabilization of non-local hyperbolic PDEs

We address the problem of adaptive output-feedback stabilization of general first-order hyperbolic partial integro-differential equations (PIDE). Such systems are also referred to as PDEs with non-local (in space) terms. We apply control at one boundary, take measurements on the other boundary, and allow the system’s functional coefficients to be unknown. To deal with the absence of both full-s...

Robust Stabilization by Linear Output Delay Feedback

The main result establishes that if a controller C (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant P , then global stabilization of P can also be achieved by an output feedback controller C[h] where the output derivatives in C are replaced by an Euler approximation with sufficiently small delay h > 0. This is proved within the conceptu...