arXiv subjects

Xingwu Zeng

Publications and source records attributed to Xingwu Zeng.

5 recordsLinked to original sources

arXiv2026

Global exponential turnpike properties for optimal control of the viscous Burgers equation

We establish global exponential turnpike properties for quadratic optimal tracking problems governed by the one-dimensional viscous Burgers equation with localized internal control. For every initial datum, finite-horizon optimal solutions approach the unique optimal periodic regime when the periodic tracking target is sufficiently small; the zero-target case yields a global steady turnpike at the origin, with no smallness assumption on the initial datum. To our knowledge, these are the first global exponential turnpike results for the viscous Burgers equation. The proof combines a local exponential turnpike, obtained through strict convexity and periodic Riccati theory, with a parabolic dissipation argument that provides an absorbing time independent of the horizon.

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arXiv2026

A Periodic Dichotomy in Linear Control Theory

In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic linear quadratic optimal control problems. Specifically, we establish a complete characterization of the optimal extremal under suitable exponential stabilizability and detectability assumptions.

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arXiv2025

Small-time approximate controllability for the nonlinear complex Ginzburg-Landau equation with bilinear control

In this paper, we consider the bilinear approximate controllability for the complex Ginzburg-Landau (CGL) equation with a power-type nonlinearity of any integer degree on a torus of arbitrary space dimension. Under a saturation hypothesis on the control operator, we show the small-time global controllability of the CGL equation. The proof is obtained by developing a multiplicative version of a geometric control approach, introduced by Agrachev and Sarychev in \cite{AS05,AS06}.

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arXiv2024

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.

math.AP↗

arXiv2024

The exponential turnpike property for periodic linear quadratic optimal control problems in infinite dimension

In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a periodic orbit when the time horizon tends to infinity. Similar results are obtained for the optimal control and adjoint state. Our proof is based on the large time behavior of solutions of operator differential Riccati equations with periodic coefficients.

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