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This article focuses on the mean-field linear-quadratic Pareto (MF-LQP) optimal strategy design for stochastic systems in infinite horizon, which is with the $H_{\infty }$ constraint when the system is disturbed by external interferences. The stochastic bounded real lemma (SBRL) with any initial state in infinite horizon is first investigated based on the stabilizing solution of the generalized algebraic Riccati equation (GARE). Then, by discussing the convexity of the cost functional, the stochastic indefinite MF-LQP control problem is defined and solved based on the MF-LQ theory and Pareto theory. When the worst case disturbance is considered in the collaborative multiplayer system, we show that the Pareto optimal strategy design with $H_{\infty }$ constraint [or robust Pareto optimal strategy, (RPOS)] can be given via solving two coupled GAREs. When the worst case disturbance and the Pareto efficient strategy work, all Pareto solutions are obtained by a generalized Lyapunov equation. Finally, a practical example shows that the obtained results are effective.

In this paper, we derive conditions for the existence of Pareto efficient strategy and Pareto solution under H ∞ constraint for the linear quadratic (LQ) finite horizon cooperative differential game of stochastic systems with state-, control- and disturbance-multiplicative noise. Firstly, we present a stochastic bounded real lemma (SBRL) with any initial condition for the considered stochastic system. Next, a necessary and sufficient condition for Pareto optimal strategy under the H ∞ constraint is researched by two cross-coupled generalized differential Riccati equations (GDREs), which is the key contribution of this paper. Another contribution is that the Pareto solution for every controller is given under the Pareto efficient strategy and worst-case external disturbance. Finally, a practical example is given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this study, the Pareto optimal strategy problem was investigated for multi-player mean-field stochastic systems governed by Itô differential equations using the reinforcement learning (RL) method. A partially model-free solution for Pareto-optimal control was derived. First, by applying the convexity of cost functions, the Pareto optimal control problem was solved using a weighted-sum optimal control problem. Subsequently, using on-policy RL, we present a novel policy iteration (PI) algorithm based on the ℌ-representation technique. In particular, by alternating between the policy evaluation and policy update steps, the Pareto optimal control policy is obtained when no further improvement occurs in system performance, which eliminates directly solving complicated cross-coupled generalized algebraic Riccati equations (GAREs). Practical numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

•The paper establishes an economic analytical model to investigate the effects of price discrimination based on the heterogeneity of passenger travel purposes on air-HSR competition.•The effects of HSR price discrimination may not necessarily decrease total consumer surplus and increase HSR profit and total social welfare but rather depend on the competitive comparative advantages of transport operators, passenger heterogeneity, and the level of government regulation.•HSR uniform pricing may be necessary to sustain social welfare in highly competitive markets with more homogeneous passengers.•HSR price discrimination may raise antitrust issues and fairness concerns for lower-income groups.•The findings have important policy implications for evaluating HSR flexible pricing and the design of effective regulations.

The Pareto-based guaranteed cost control (GCC) of discrete-time uncertain stochastic systems in the infinite horizon is studied. Firstly, the convexity of the weighted sum objective function is proved. Based on this convexity, we demonstrate the relationship between Pareto optimality and minimization of the weighted sum objective function. This relationship confirms that the Pareto-based GCC strategy can be obtained by optimizing the weighted sum objective function. Secondly, to address the Pareto-based GCC issue for discrete-time uncertain stochastic systems, we derive the generalized algebraic Riccati inequality (GARI) specific to these systems. Thirdly, the necessary condition for a Pareto-based guaranteed cost controller is derived using the Karush-Kuhn–Tucker (KKT) condition. Lastly, we introduce a method based on linear matrix inequality (LMI) to determine the Pareto-based GCC strategy. This method reduces computational complexity and establishes the sufficient conditions for a Pareto-based guaranteed cost controller. To validate our findings, we provide a example implemented in MATLAB, confirming the accuracy of the proposed approach.

This paper is concerned with the open-loop linear–quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, the follower first solves a mean-field stochastic LQ optimal control problem. Then, the leader turns to solve an optimization problem for a linear mean-field forward–backward stochastic differential equation. By introducing new state and costate variables, we present a sufficient condition for the existence and uniqueness of the Stackelberg strategy in terms of the solvability of some Riccati equations and a convexity condition. Furthermore, it is shown that the open-loop Stackelberg equilibrium admits a feedback representation involving the new state and its mean. Finally, two examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to study the stability of discrete stochastic time-delayed systems with multiplicative noise, where the coefficients are assumed to be time-varying with a general time-varying rate or a small time-varying rate. Firstly, by the Kronecker algebra theory and H -representation technique, the exponential stability of the stochastic system with common time-varying coefficients is investigated by the spectral approach. It is shown that the time-varying stochastic systems with state delays is exponentially stable in mean square sense if and only if its corresponding generalized spectral radius is less than one. Secondly, under definite conditions, by applying the so-called “frozen” technique, it is shown that the stability of a “frozen” system implies that of the corresponding slowly time-varying system. [ABSTRACT FROM AUTHOR]

Revenue management is widely practiced in the airline industry yet rarely applied to high-speed rail (HSR). In the history of the rail and HSR industry, passenger ticket assignment across all stations has often been employed to regulate the supply of seats and demand from rail passengers and thus increase profitability. This study proposes a systematic revenue management approach for HSR passenger ticket assignment with dynamic adjustments. A major advantage of the proposed approach is the integration of dynamic ticket assignment and rigorous short-term demand forecasting; this method can effectively avoid the situation in which passenger tickets are not sufficient at some stations while certain seats remain empty on the train. This novel methodology has three main components. First, it develops a short-term passenger flow forecasting method for dynamic travel demand. Second, it builds a passenger ticket assignment model to allocate passenger tickets during presale periods. Third, it incorporates a dynamic ticket adjustment mechanism to adjust previous passenger ticket assignments. For demonstration purposes, the proposed approach is applied to the HSR system in China. Results show that revenue increases by 13.48% when the existing ticket assignment method is improved by this enhanced revenue management method.

This article considers event-triggered security consensus of continuous-time multi-agent systems (MASs) subject to complex cooperative attacks. First, false data injection attacks (FDIAs) and denial-of-service (DoS) attacks are modeled under a unified framework through the Bernoulli process, which provides a comprehensive understanding of the challenges posed by these attacks in MASs. Second, an improved event-triggered mechanism (ETM) based on aperiodic sampling is constructed, which avoids the Zeno phenomenon and has the potential to improve the efficiency and resilience of MASs. In addition, it can be combined with detection signals to address the challenge of determining trigger times under DoS attacks, which is an important contribution. Third, to overcome the impact of complex cooperative attacks, this article analyses the security consensus of MASs in three steps by combining the characteristics of trigger time and attack time. Based on this, security consensus is guaranteed. Finally, a practical example is used to demonstrate the feasibility of the proposed ETM. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability analysis and synthesis of positive Markov jump systems (PMJSs) in p th moment sense, including stability, strong stability, observability, and detectability. First, by the ℋ -representation technique, the extended system method is constructed. With the help of the extended system method, stability analysis of PMJSs in p th moment sense are transformed into those of the extended systems. Furthermore, the necessary and sufficient conditions for stability, observability, and detectability in p th moment sense are obtained. Moreover, the definitions of p th moment strong stability (PMSS) and p th moment stability threshold (PMST) are given for the first time, and the sufficient/necessary conditions for these are derived, respectively. In addition, the problems of stabilization and strong stabilization in p th moment sense are considered. Finally, several examples are presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the p th moment finite-time stochastic stability (p -MFTS stability) and asynchronous H ∞ control for highly nonlinear hybrid stochastic systems (HNHSSs) are investigated. Firstly, the definition of p -MSFT stability for HNHSSs is proposed, and the stability criteria are given by the mode-dependent average dwell time (MDADT) method. Secondly, the asynchronous H ∞ controller is designed to ensure that HNHSSs are p th moment finite-time stochastically stabilizable (p -MFTS stabilizable) and satisfy H ∞ performance. When designing the asynchronous H ∞ controller, deterministic asynchrony and stochastic asynchrony are considered simultaneously. Moreover, since the coefficients of HNHSSs have highly nonlinear structures without satisfying the linear growth condition (LGC), the Lyapunov function U and the operator L U are bounded by polynomials of degree higher than p , which means that weaker conditions of p -MFTS stability are proposed. Finally, examples are presented to illustrate the availability of the results. [ABSTRACT FROM AUTHOR]