Finite-Horizon Parameterizing Manifolds, and Applications to Suboptimal Control of Nonlinear Parabolic PDEs

Special Session 36: Nonlinear Elliptic and Parabolic PDEs with Applications

with n > 2. Here the nonlinear term f is assumed to be a smooth function of u that is positive for u > 0 and is equal to 0 for u ≤ 0. Then any radial solution u = u(r), r = |x|, of the equation is shown to be classi ed into one of several types according to its behavior as r → 0 and r → ∞. Under the assumption that f is supercritical for small u > 0 and is subcritical for large u > 0, we clarif...

Persistence of Invariant Manifolds for Nonlinear PDEs

We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under C perturbation. In particular, we extend well known finite-dimensional results to the setting of an infinite-dimensional Hilbert manifold with a semi-group that leaves a submanifold invariant. We...

Infinite dimensional backstepping for nonlinear parabolic PDEs

Special Session 4: Nonlinear PDEs and Control Theory with Applications

In the large context of nonlinear evolution equations we will focus on systems of PDEs which exhibit a hyperbolic or parabolic-hyperbolic structure. The topics of this special session will revolve around qualitative and quantitative properties of solutions to these equations, such as existence and uniqueness, regularity of solutions, and long time asymptotic behavior. Associated control theoret...

Suboptimal Control of Constrained Nonlinear Systems via Receding Horizon State Dependent Riccati Equations (I)

Feedback stabilization of systems subject to constraints has been a long-standing problem in control theory. In contrast with the case of LTI plants where several techniques for optimizing performance have recently appeared, very few results are available for the case of nonlinear systems. In this paper we propose a new controller design method, based on the combination of Receding Horizon and ...