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Data-Driven Direct Adaptive Risk-Sensitive Control of Stochastic Systems

Journal of Systems Science & Complexity 2024年第4期37卷 1446-1469页

作者： QIAO Nan LI Tao School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice School of Mathematical SciencesEast China Normal UniversityShanghai 200241China

The authors propose a data-driven direct adaptive control law based on the adaptive dynamic programming(ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive *** authors use online data of the system to iteratively solve the generalized algebraic Riccati equation(GARE) and to learn the optimal control law *** the case with measurable system noises,the authors show that the adaptive control law approximates the optimal control law as time goes *** the case with unmeasurable system noises,the authors use the least-square solution calculated only from the measurable data instead of the real solution of the regression equation to iteratively solve the *** authors also study the influences of the intensity of the system noises,the intensity of the exploration noises,the initial iterative matrix,and the sampling period on the convergence of the ADP ***,the authors present two numerical simulation examples to demonstrate the effectiveness of the proposed algorithms.

关键词： Adaptive dynamic programming direct adaptive control generalized algebraic Riccati equation risk-sensitive control

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THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

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Acta Mathematica Scientia 2024年第1期44卷 37-77页

作者：孙印正屈爱芳袁海荣 Department of Mathematics Shanghai Normal UniversityShanghai200234China School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal UniversityShanghai200241China

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial *** over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the ***,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its *** an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic *** particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic *** indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

关键词： compressible Euler equations Riemann problem Radon measure solution delta shock discontinuous flux wave interactions

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Group Rent-or-Buy: the Benefits of Having Grouped Consumers

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Journal of the Operations Research Society of China 2025年 1-18页

作者： Meng, Li-Yuan Wang, Chang-Jun Ye, Qing-Jie State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Key Laboratory of Ministry of Education Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal University Shanghai200241 China

We introduce and investigate the group rent-or-buy problem, a generalization of the classical ski rental problem. In contrast to the classical version, where a single consumer decides when to switch from renting to buying based on an uncertain usage period, the group must jointly decide how to minimize their total rent and buy cost over the period. While grouping does not reduce the optimal total cost in the offline setting, we explore its impact on making best possible online decisions. We design both optimal randomized and deterministic algorithms for the group version and show that grouping does not improve the optimal randomized algorithm, with its competitive ratio remaining ee-1. However, grouping benefits the deterministic case, where the optimal competitive ratio is strictly smaller than 2, which is the best competitive ratio achievable in the classical problem. Additionally, as the group size increases, the optimal competitive ratio of the deterministic algorithm decreases, approaching ee-1 in the limit. © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

关键词： Operations research

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Distance two Heegaard splittings,JSJ decompositions and ranks of 3-manifolds

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Science China mathematics 2025年第6期68卷 1431-1442页

作者： Wenjie Diao Yanqing Zou School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal UniversityShanghai 200241China

For any pair of integers g and n with g≥3 and 1≤n≤g,we build a 3-manifold with a distance-2,genus-g Heegaard splitting so that(1)it contains n pairwise disjoint and nonisotopic essential tori;(2)after it is cut open along these tori,one resulting piece is hyperbolic while the others are small Seifert fibered spaces;(3)it provides a substantial result to the rank versus genus *** generalize a result in Qiu and Zou(2019).

关键词： Heegaard distance Heegaard genus rank hyperbolic 3-manifold curve complex JSJ decomposition

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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 358-378页

作者： Jin-yan ZHU Yong CHEN School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

The Gerdjikov-Ivanov(GI)hierarchy is derived via recursion operator,in this article,we mainly investigate the third-order flow GI *** the framework of the Riemann-Hilbert method,the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing *** advantage of this result,some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed,and the simple elastic interaction of two soliton are *** with soliton solution of the classical second-order flow,we find that the higher-order dispersion term affects the propagation velocity,propagation direction and amplitude of the ***,by means of a certain limit technique,the high-order soliton solution matrix for the third-order flow GI equation is derived.

关键词： Gerdjikov-Ivanov hierarchy third-order flow GI equation Riemann-Hilbert method high-order soliton

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Demand response management of smart grid based on Stackelberg-evolutionary joint game

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Science China(Information Sciences) 2023年第8期66卷 169-186页

作者： Jun LI Tao LI Daoyi DONG School of Mathematics-Physics and Finance Anhui Polytechnic University Key Laboratory of Pure Mathematics and Mathematical Practice School of Mathematical SciencesEast China Normal University School of Engineering and Information Technology University of New South Wales

We investigated the real-time pricing demand response management system of multiple microgrids and multiple power users. Accordingly, we have proposed a Stackelberg-evolutionary joint game framework to examine the real-time pricing scheme of multiple microgrids and multiple power users so as to establish equilibrium strategies. Both a non-cooperative game among multiple microgrids and a multipopulation evolutionary game among multiple power users were considered. Furthermore, we constructed a Stackelberg game between microgrids and power users to reflect their sequential interaction, wherein the microgrids are leaders, and the power users are followers. We also proved the existence and uniqueness of the Stackelberg equilibrium. Furthermore, we proposed an iterative algorithm to compute the equilibrium strategy and demonstrate the convergence and effectiveness through numerical simulations, which demonstrated that the algorithm could achieve a balance between power supply and demand balance.

关键词： smart grid real-time pricing demand response management Stackelberg game multi-population evolutionary game

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Steady Compressible Euler Equations of Concentration Layers for Hypersonic-limit Flows Passing Three-dimensional Bodies and Generalized Newton-Busemann Pressure Law

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Chinese Annals of mathematics,Series B 2023年第4期44卷 561-576页

作者： Aifang QU Hairong YUAN Department of Mathematics Shanghai Normal UniversityShanghai 200234China School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal UniversityShanghai 200241China

For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space,the shock-front coincides with the upwind surface of the body,hence there is an infinite-thin layer of concentrated mass,in which all particles hitting the body move along its upwind *** proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations,which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces,the authors derive the compressible Euler equations for flows in concentration layers,which is a stationary pressureless compressible Euler system with source terms and independent variables on curved *** a by-product,they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows,which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics.

关键词： Compressible Euler equations Hypersonic fow Concentration layer Ramp Cone Radon measure solution Newton-Busemann law

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Almost Periodic Type Group Actions on Compact Quantum Metric Spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 568-594页

作者： Bo Tao LONG Wei WU College of Mathematics MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air VehiclesNanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200241P.R.China

A compact quantum metric space is a complete order unit space A endowed with a Lipnorm *** give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.

关键词： Lip-norm compact quantum metric space Lipschitz isomorphism almost periodicity Arzela-Ascoli theorem metric set

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THE GLOBAL LIPSCHITZ SOLUTION FOR A PEELING MODEL

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Acta Mathematica Scientia 2023年第5期43卷 2263-2278页

作者：黎前锋张永前 School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice East China Normal UniversityShanghai 200241China School of Mathematical Sciences Fudan UniversityShanghai 200433China

This paper focusses on a peeling phenomenon governed by a nonlinear wave equation with a free *** the hypotheses that the total variation of the intial data and the boundary data are small,the global existence of a weak solution to the nonlinear problem(1.1)-(1.3)is proven by a modified Glimm *** regularity of the peeling front is established,and the asymptotic behaviour of the obtained solution and the peeling front at infinity is also studied.

关键词： peeling model nonlinear wave solution free boundary Glimm scheme

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THE SASA-SATSUMA EQUATION ON A NON-ZERO BACKGROUND: THE INVERSE SCATTERING TRANSFORM AND MULTI-SOLITON SOLUTIONS

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Acta Mathematica Scientia 2023年第3期43卷 1045-1080页

作者：温丽丽范恩贵陈勇 School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical Practiceand Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghai200241China School of Mathematical Sciences and Key Laboratory for Nonlinear Science Fudan UniversityShanghai200433China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

We concentrate on the inverse scattering transformation for the Sasa-Satsuma equation with 3×3 matrix spectrum problem and a nonzero boundary condition. To circumvent the multi-value of eigenvalues, we introduce a suitable two-sheet Riemann surface to map the original spectral parameter k into a single-valued parameter z. The analyticity of the Jost eigenfunctions and scattering coefficients of the Lax pair for the Sasa-Satsuma equation are analyzed in detail. According to the analyticity of the eigenfunctions and the scattering coefficients, the z-complex plane is divided into four analytic regions of D_(j) : j = 1, 2, 3, 4. Since the second column of Jost eigenfunctions is analytic in D_(j), but in the upper-half or lowerhalf plane, we introduce certain auxiliary eigenfunctions which are necessary for deriving the analytic eigenfunctions in Dj. We find that the eigenfunctions, the scattering coefficients and the auxiliary eigenfunctions all possess three kinds of symmetries;these characterize the distribution of the discrete spectrum. The asymptotic behaviors of eigenfunctions, auxiliary eigenfunctions and scattering coefficients are also systematically derived. Then a matrix Riemann-Hilbert problem with four kinds of jump conditions associated with the problem of nonzero asymptotic boundary conditions is established, from this N-soliton solutions are obtained via the corresponding reconstruction formulae. The reflectionless soliton solutions are explicitly given. As an application of the N-soliton formula, we present three kinds of single-soliton solutions according to the distribution of discrete spectrum.

关键词： Sasa-Satsuma equation nonzero boundary condition auxiliary eigenfunctions Riemann-Hilbert problem soliton solution

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