Learning-based control for discrete-time constrained nonzero-sum games

A generalized policy-iteration-based solution to a class of discrete-time multi-player nonzero-sum games concerning the control constraints was proposed.Based on initial admissible control policies,the iterative value function of each player converges to the optimum approximately,which is structured by the iterative control policies satisfying the Nash equilibrium.Afterwards,the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player.Meanwhile,neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints.Finally,two numerical simulations of the discrete-time two-player non-zero-sum games for linear and non-linear systems are shown to illustrate the effectiveness of the proposed scheme.

Dark and multi-dark solitons in the three-component nonlinear Schrodinger equations on the general nonzero background

We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrodinger systems, and require more in-depth studies in the future.

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact(VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope(SAEE) is adopted to seek the stationary probability density functions(PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo(MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.

Self-consistent diverted tokamak equilibria with nonzero edge current

The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria （Bingren Shi, Plasma Phys. Control Fusion 50 （2008） 085006, 51 （2009） 105008, Nucl. Fusion 51 （2011） 023004）, is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch Schliiter（PS） cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.

Nonzero Solutions of Generalized Variational Inequalities

The existence of nonzero solutions for a class of generalized variational inequalities is studied by ?xed point index approach for multivalued mappings in ?nite dimensional spaces and re?exive Banach spaces. Some new existence theorems of nonzero solutions for this class of generalized variational inequalities are established.

Application of the Two Nonzero Component Lemma in Resource Allocation

In this paper we will generalize the author's two nonzero component lemma to general self-reducing functions and utilize it to find closed from answers for some resource allocation problems.

The Case of Nonzero Initial Conditions in the Evolution of the Charge Density Distribution Function for a Spherically Symmetric System

We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.

Behavior Prediction of Untrusted Relays Based on Nonzero-Sum Game

To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor into account. A nonzero-sum game is established to capture the interaction among URs and detection strategies. Secrecy capacity is investigated as game payoff to indicate the untrusted behaviors of the relays. The maximum probabilities of the behaviors of relay and the optimal system detection strategy can be obtained by using the proposed algorithm.

Proving and Extending Greub-Reinboldt Inequality Using the Two Nonzero Component Lemma

We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.

判定广义严格对角占优矩阵的新条件

仅利用矩阵自身的元素,得到了广义严格对角占优矩阵的几个新的判定条件,扩大了判别范围.给出了数值算例.

非奇异H-矩阵的新细分迭代判定

利用广义α-对角占优矩阵、不可约α-对角占优矩阵和具有非零元素链α-对角占优矩阵的概念和性质,通过对矩阵非对角占优行的指标集进行细分,构造递进迭代系数,得到一组实用的非奇异H-矩阵判定的细分迭代新准则,通过数值例子说明新准则的有效性。

Tunneling magnetoresistance of the double spin-filter junctions at nonzero bias

A recent theoretical estimation indicated that the NM/FI/FI/NM double spin-filter junction (DSFJ, here the NM and FI represent the nonmagnetic electrode and the ferromagnetic insulator (semiconductor) spacer, respectively) could have very high tunneling magnetoresistance (TMR) at zero bias. To meet the requirement in research and application of the magnetoresistance devices, we have calculated the dependences of tunneling magnetoresistance of DSFJ on the bias (voltage), the thicknesses of ferromagnetic insulators (semiconductors) and the average barrier height. Our results show that except its very high value, the TMR of DSFJ does not decrease monotonously and rapidly with rising bias, but increase slowly at first and decrease then after having reached a maximum value. This feature is in distinct contrast to the ordinary magnetic tunnel junction FM/NI/FM (FM and NI denote the ferromagnetic electrode and the nonmagnetic insulator (semiconductor) spacer, respectively), and is of benefit to the use of DSFJ as a magnetoresistance device.

非零方阵的一类加法分解

基于矩阵的相关性质,证明了数域上任意非零方阵均可分解为一个幂零阵与一个可逆阵之和,推进了已知相关结论.作为所得结果的应用,给出线性空间上线性变换的加法分解.

Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrodinger equation with zero/nonzero boundary conditions

The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.

Nonzero-sum games for continuous-time Markov chains with unbounded transition and average payoff rates

This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.

Outage performance of multihop free-space optical communication system over exponentiated Weibull fading channels with nonzero boresight pointing errors

The outage performance of the multihop free-space optical(FSO) communication system with decode-and-forward(DF) protocol is studied by considering the joint effects of nonzero boresight pointing errors and atmospheric turbulence modeled by exponentiated Weibull(EW) distribution. The closed-form analytical expression of outage probability is derived, and the results are validated through Monte Carlo simulation. Furthermore, the detailed analysis is provided to evaluate the impacts of turbulence strength, receiver aperture size, boresight displacement, beamwidth and number of relays on the outage performance for the studied system.

BACKWARD LINEAR-QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO-SUM DIFFERENTIAL GAME PROBLEM WITH RANDOM JUMPS

This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).

部分可观测带跳倒向随机系统的非零和微分博弈及其应用

微分博弈是研究两个或多个局中人的控制作用同时施加于一个由微分方程描述的动态系统时实现各自最优目标的博弈过程的理论,因其有趣的数学性质和经济领域的应用价值得到了广泛的关注。研究了一类部分可观测带跳倒向随机系统的非零和微分博弈问题,其中博弈系统涉及跳过程,且每个参与者拥有不同的观测方程。对于这种部分可观测的随机微分博弈问题,在控制域为凸的条件下,采用凸变分和对偶技术,建立了博弈纳什均衡点的最大值原理;在适当的凹凸性假设下,证明了必要性最优条件也是充分性最优条件,得到了验证定理。应用上述最大值原理,研究了部分可观测带跳倒向随机系统的线性二次(Linear Quadratic,LQ)博弈问题,得到了LQ博弈问题的唯一最优控制,其中状态方程和伴随方程构成了一类带跳的正倒向随机微分方程。由于LQ模型通常被用于描述许多金融和经济现象,期望上述的部分可观测带跳倒向随机系统的LQ博弈结果能在这些领域得到广泛应用。