Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs

Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs

We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of, quasilinear, first-order hyperbolic PDEs. Since for such PDE–ODE cascades the speed of propagation depends on the PDE state itself (which implies that the prediction horizon cannot be a priori known analytically), the key design challenge is the determination of the pre...

Compensating actuator and sensor dynamics governed by diffusion PDEs

For (possibly unstable) ODE systems with actuator delay, predictor-based infinite-dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization.We extend this concept to another class of PDE-ODE cascades, where the infinite-dimensional part of the plant is of diffusive, rather than convective type. We derive predictor-like feedback laws and observers, with...

An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs

We present a numerical method for solving tracking-type optimal control problems subject to scalar nonlinear hyperbolic balance laws in one and two space dimensions. Our approach is based on the formal optimality system and requires numerical solutions of the hyperbolic balance law forward in time and its nonconservative adjoint equation backward in time. To this end, we develop a hybrid method...

Resonance for Quasilinear Hyperbolic Equation

git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...

Numerical Analysis of Hyperbolic PDEs