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Guanhua Liu

Publications and source records attributed to Guanhua Liu.

9 recordsLinked to original sources
arXiv2026

Koopman-Based Robust Model Predictive Control for Nonlinear Systems with Stochastic Intermittent Measurements

Intermittent state measurements pose fundamental challenges to model predictive control of constrained nonlinear systems because prediction uncertainty grows during feedback outages and measurement-triggered resets disrupt nominal state propagation, potentially compromising closed-loop stability and recursive feasibility. This paper develops a Koopman-based stochastic MPC framework with probabilistically truncated soft constraints. Specifically, a Lipschitz-constrained deep Koopman model provides a linear latent predictor, enabling computationally efficient online optimization. The intermittent measurement process is modeled as a two-mode discrete-time Markov chain, yielding a unified Markov jump error model for open-loop propagation and measurement-triggered resets. Under numerically verifiable sufficient conditions, the prediction error is shown to be mean-square ultimately bounded, and an explicit uniform second-moment bound is obtained. A distribution-free probabilistic error radius is then constructed for a prescribed confidence level and used to truncate dropout-dependent constraint tightening. An exact-penalty soft-constraint mechanism accommodates reset-induced jumps and prolonged dropouts. Under the stated terminal compatibility and bounded-disturbance conditions, recursive feasibility and mean-square ultimate boundedness of the closed-loop regulation error are established. Numerical simulations on a visual-servoing tracking task corroborate these theoretical results and demonstrate effective tracking under stochastic measurement unavailability.

cs.RO↗
arXiv2026

Inhomogeneous Scaling Function and Heat Kernel Estimates on Fractals Satisfying Some Resistance Conditions

In this paper, we focus on strongly local regular Dirichlet forms, especially those satisfying Morrey-type inequalities. We prove the equivalence between resistance estimates and heat kernel estimates in this case. Self-similar forms on fractals serve as a major application, where we construct a spatially inhomogeneous scaling function and characterize all the doubling self-similar measures. Further, on some special examples, the resistance conditions are reduced to some geometric conditions, on which a complete theory on self-similar Dirichlet spaces is established therein. In particular, we construct a concrete example on rotated triangle fractals, where the optimal heat kernel estimate is not related at all to the lower scaling exponent.

math.AP↗
arXiv2025

The parabolic Harnack inequality on non-local Dirichlet spaces in the view of pure analysis

This paper provides the general theory on parabolic Harnack inequalities (PHI, for short) for regular Dirichlet forms without killing part. We prove PHI by pure analytic methods, using both Nash and Moser approaches, and yield some important properties contained in PHI. Combining our recent result on weak Harnack inequalities, we greatly enlarge the list of equivalent characterizations of PHI.

math.AP↗
arXiv2025

Weak parabolic Harnack inequality and Hölder regularity for non-local Dirichlet forms

In this paper we give equivalent conditions for the weak parabolic Harnack inequality for general regular Dirichlet forms without killing part, in terms of local heat kernel estimates or growth lemmas. With a tail estimate on the jump measure, we obtain from these conditions the Hölder continuity of caloric and harmonic functions. Our results generalize the theory of Chen, Kumagai and Wang, in the sense that the upper jumping smoothness condition is canceled. We also derive the complete forms of Harnack inequalities from the globally non-negative versions, and obtain continuity of caloric functions with worse tails.

math.AP↗
arXiv2024

A Novel Shortest Path Query Algorithm Based on Optimized Adaptive Topology Structure

Urban rail transit is a fundamental component of public transportation, however, commonly station-based path search algorithms often overlook the impact of transfer times on search results, leading to decreased accuracy. To solve this problem, this paper proposes a novel shortest path query algorithm based on adaptive topology optimization called the Adaptive Topology Extension Road Network Structure (ATEN). This algorithm categorizes transfer stations into different types and treats travel time and transfer time equivalently as weights for edges in the topological graph. The proposed algorithm introduces virtual stations to differentiate between pedestrian paths and train paths, eliminating the need for additional operations on transfer stations. The algorithm controls the extent of expansion in the urban rail transit topology, overcoming query errors caused by mishandling of transfer stations in the existing algorithm. Finally, a series of simulation experiments were conducted on Beijing's urban rail transit network to validate both correctness and efficiency of the proposed adaptive topology optimization algorithm. The results demonstrate significant advantages compared to existing similar algorithms.

cs.CE↗
arXiv2023

Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition

In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest $\varepsilon$-chain between two points $x,y$ is comparable with a function of $d(x,y)$ and $\varepsilon$. For a diffusion, the best estimate is already given by Grigor'yan and Telcs, and we make it explicit in our particular case. For jump processes, especially those where the scale of the process is different with that of the jump kernel, we improve the results by Bae, Kang, Kim and Lee. Uniformity of the coefficients (or parameters) in the known estimates and metric transforms play the key role in our proof. We also show by examples how the weak chain condition is valid in practice.

math.PR↗
arXiv2021

On the comparison between jump processes and subordinated diffusions

Given a symmetric diffusion process and a jump process on the same underlying space, is there a subordinator such that the jump process and the subordinated diffusion processes are comparable? We address this question when the diffusion satisfies a sub-Gaussian heat kernel estimate and the jump process satisfies a polynomial-type jump kernel bounds. Under these assumptions, we obtain necessary and sufficient conditions on the jump kernel estimate for such a subordinator to exist. As an application of our results and the recent stability results of Chen, Kumagai, and Wang, we obtain parabolic Harnack inequality for a large family of jump processes. In particular, we show that any jump process with polynomial-type jump kernel bounds on such a space satisfies the parabolic Harnack inequality.

math.PR↗
arXiv2020

Parabolic Harnack inequality implies the existence of jump kernel

We prove that the parabolic Harnack inequality implies the existence of jump kernel for symmetric pure jump process. This allows us to remove a technical assumption on the jumping measure in the recent characterization of the parabolic Harnack inequality for pure jump processes by Chen, Kumagai and Wang. The key ingredients of our proof are the Lévy system formula and a near-diagonal heat kernel lower bound.

math.PR↗