arXiv subjects

Na Xiang

Publications and source records attributed to Na Xiang.

5 recordsLinked to original sources

arXiv2026

Stochastic Linear-Quadratic Optimal Control Problems with Markovian Regime Switching and $H_\infty$ Constraint under Partial Information

This paper is concerned with a stochastic linear-quadratic optimal control problem of Markovian regime switching system with model uncertainty and partial information, where the information available to the control is based on a sub-$\sigma$-algebra of the filtration generated by the underlying Brownian motion and the Markov chain. Based on $H_\infty$ control theory, we turn to deal with a soft-constrained zero-sum linear-quadratic stochastic differential game with Markov chain and partial information. By virtue of the filtering technique, the Riccati equation approach, the method of orthogonal decomposition, and the completion-of-squares method, we obtain the closed-loop saddle point of the zero-sum game via the optimal feedback control-strategy pair. Subsequently, we prove that the corresponding outcome of the closed-loop saddle point satisfies the $H_\infty$ performance criterion. Finally, the obtained theoretical results are applied to a stock market investment problem to further illustrate the practical significance and effectiveness.

math.OC↗

arXiv2025

Robust Incentive Stackelberg Mean Field Stochastic Linear-Quadratic Differential Game with Model Uncertainty

This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the state average and control averages enter into the leader's dynamics and cost functional. Based on the zero-sum game approach, mean field approximation and duality theory, firstly the representation of the leader's limiting cost functional and the closed-loop representation of decentralized open-loop saddle points are given, via decoupling methods. Then by convex analysis and the variational method, the decentralized strategies of the followers' auxiliary limiting problems and the corresponding consistency condition system are derived. Finally, applying decoupling technique, the leader's approximate incentive strategy set is obtained, under which the asymptotical robust incentive optimality of the decentralized mean field strategy is verified. A numerical example is given to illustrate the theoretical results.

math.OC↗

arXiv2024

Three-Level Multi-Leader-Follower Incentive Stackelberg Differential Game with $H_\infty$ Constraint

This paper is concerned with a three-level multi-leader-follower incentive Stackelberg game with $H_\infty$ constraint. Based on $H_2/H_\infty$ control theory, we firstly obtain the worst-case disturbance and the team-optimal strategy by dealing with a nonzero-sum stochastic differential game. The main objective is to establish an incentive Stackelberg strategy set of the three-level hierarchy in which the whole system achieves the top leader's team-optimal solution and attenuates the external disturbance under $H_\infty$ constraint. On the other hand, followers on the bottom two levels in turn attain their state feedback Nash equilibrium, ensuring incentive Stackelberg strategies while considering the worst-case disturbance. By convex analysis theory, maximum principle and decoupling technique, the three-level incentive Stackelberg strategy set is obtained. Finally, a numerical example is given to illustrate the existence of the proposed strategy set.

math.OC↗

arXiv2024

Stochastic Linear-Quadratic Stackelberg Differential Game with Asymmetric Informational Uncertainties: Robust Optimization Approach

This paper is concerned with a two-person zero-sum indefinite stochastic linear-quadratic Stackelberg differential game with asymmetric informational uncertainties, where both the leader and follower face different and unknown disturbances. We take a robust optimization approach and soft-constraint analysis, a min-max stochastic linear-quadratic optimal control problem is solved by the follower firstly. Then, the leader deal with a max-min stochastic linear-quadratic optimal control problem of forward-backward stochastic differential equations in an augmented space. State feedback representation of the robust Stackelberg equilibrium is given in a more explicit form by decoupling technique, via some Riccati equations.

math.OC↗

arXiv2017

High-Speed Demodulation of weak FBGs Based on Microwave Photonics and Chromatic Dispersion

A high speed quasi-distributed demodulation method based on the microwave photonics and the chromatic dispersion effect is designed and implemented for weak fiber Bragg gratings (FBGs). Due to the effect of dispersion compensation fiber (DCF), FBG wavelength shift leads to the change of the difference frequency signal at the mixer. With the way of crossing microwave sweep cycle, all wavelengths of cascade FBGs can be high speed obtained by measuring the frequencies change. Moreover, through the introduction of Chirp-Z and Hanning window algorithm, the analysis of difference frequency signal is achieved very well. By adopting the single-peak filter as a reference, the length disturbance of DCF caused by temperature can be also eliminated. Therefore, the accuracy of this novel method is greatly improved, and high speed demodulation of FBGs can easily realize. The feasibility and performance are experimentally demonstrated using 105 FBGs with 0.1% reflectivity, 1 m spatial interval. Results show that each grating can be distinguished well, and the demodulation rate is as high as 40 kHz, the accuracy is about 8 pm.

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