Minimum time control of 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...

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...

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...

LQ-optimal control for a class of time-varying coupled PDEs-ODEs system

This contribution addresses the development of a Linear Quadratic Regulator (LQR) for a set of time-varying hyperbolic PDEs coupled with a set of time-varying ODEs through the boundary. The approach is based on an infinitedimensional Hilbert state-space realization of the system and operator Riccati equation (ORE). In order to solve the optimal control problem, the ORE is converted to a set of ...