Power Control Algorithm of Cognitive Radio Based on Non-Cooperative Game Theory

This paper addresses the power con- trol problems of Cognitive Radio （CR） trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the Quality of Service （QoS） standards for primary users is considered and a non-cooperative game power control model. Based on the proposed model, we developed a logical utility function based on the Signal-to-Interference-Noise Ratio （S/NR） and a novel algorithm network power control. that is suitable for CR Then, the existence and uniqueness of the Nash Equilibrium （NE） in our utility function are proved by the principle of game theory and the corresponding optimi- zations. Compared to traditional algorithms, the proposed one could converge to an NE in 3-5 iterative operations by setting an appropriate pricing factor. Finally, simulation results ver- ified the stability and superiority of the novel algorithm in flat-fading channel environments.

A Game Theoretic Approach for Inter-Network Interference Mitigation in Wireless Body Area Networks

Wireless Body Area Network(WBAN) is an emerging technology to provide real-time health monitoring and ubiquitous healthcare services. In many applications, multiple wireless body area networks have to coexist in a small area, resulting in serious inter-network interference. This not only reduces network reliability that is especially important in emergency medical applications, but also consumes more power of WBANs. In this paper, an inter-network interference mitigation approach based on a power control algorithm is proposed. Power control is modeled as a non-cooperative game, in which both inter-network interference and energy efficiency of WBANs are considered. The existence and uniqueness of Nash Equilibrium in the game are proved, and an optimal scheme based on best response is proposed to find its Nash Equilibrium. By coordinating the transmission power levels among networks under interference environment, the total system throughput can be increased with minimum power consumed. The effectiveness of the proposed method has been illustrated by simulation results, where the performance of the proposed approach is evaluated in terms of overall utility and power efficiency and convergence speed.

Multimodal collaborative BCI system based on the improved CSP feature extraction algorithm

Background As a novel approach for people to directly communicate with an external device,the study of brain-computer interfaces(BCIs)has become well-rounded.However,similar to the real-world scenario,where individuals are expected to work in groups,the BCI systems should be able to replicate group attributes.Methods We proposed a 4-order cumulants feature extraction method(CUM4-CSP)based on the common spatial patterns(CSP)algorithm.Simulation experiments conducted using motion visual evoked potentials(mVEP)EEG data verified the robustness of the proposed algorithm.In addition,to freely choose paradigms,we adopted the mVEP and steady-state visual evoked potential(SSVEP)paradigms and designed a multimodal collaborative BCI system based on the proposed CUM4-CSP algorithm.The feasibility of the proposed multimodal collaborative system framework was demonstrated using a multiplayer game controlling system that simultaneously facilitates the coordination and competitive control of two users on external devices.To verify the robustness of the proposed scheme,we recruited 30 subjects to conduct online game control experiments,and the results were statistically analyzed.Results The simulation results prove that the proposed CUM4-CSP algorithm has good noise immunity.The online experimental results indicate that the subjects could reliably perform the game confrontation operation with the selected BCI paradigm.Conclusions The proposed CUM4-CSP algorithm can effectively extract features from EEG data in a noisy environment.Additionally,the proposed scheme may provide a new solution for EEG-based group BCI research.

Solution of a zero-sum linear quadratic differential game with singular control cost of minimiser

We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.

Mean field games of controls:Propagation of monotonicities

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control.It is well known that,for standard mean field games,certain monotonicity conditions are crucial to guarantee the uniqueness of mean field equilibria and then the global wellposedness for master equations.In the literature the monotonicity condition could be the Lasry–Lions monotonicity,the displacement monotonicity,or the anti-monotonicity conditions.In this paper,we investigate these three types of monotonicity conditions for Mean Field Games of Controls and show their propagation along the solutions to the master equations with common noises.In particular,we extend the displacement monotonicity to semi-monotonicity,whose propagation result is new even for standard mean field games.This is the first step towards the global wellposedness theory for master equations of Mean Field Games of Controls.

Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

Mass concentrations and temporal profiles of PM10, PM2.5 and PM1 near major urban roads in Beijing

Mass concentrations of PM10, PM2.5 and PM1 were measured near major roads in Beijing during six periods： summer and winter of 2001, winter of 2007, and periods before, during and after the 2008 Beijing Olympic Games. Since the control efforts for motor vehicles helped offset the increase of emissions from the rapid growth of vehicles, the averaged PM2.5 concentrations at roadsides during the sampling period between 2001 and 2008 fluctuated over a relatively small range. With the implementation of temporary traffic control measures during the Olympics, a clear “V” shaped curve showing the concentrations of particulate matter and other gaseous air pollutants at roadsides over time was identified. The average concentrations of PM10, PM2.5, CO and NO decreased by 31.2%, 46.3%, 32.3% and 35.4%, respectively, from June to August; this was followed by a rebound of all air pollutants in December 2008. Daily PM10 concentrations near major roads exceeded the National Ambient Air Quality Standard （Grade II） for 61.2% of the days in the non-Olympic periods, while only for 12.5% during the Olympics. The mean ratio of PM2.5/PM10 near major roads remained relatively stable at 0.55 （±0.108） on non-Olympic days. The ratio decreased to 0.48 （±0.099） during the Olympics due to a greater decline in fine particles than in coarse-mode PM. The ratios PM1/PM2.5 fluctuated over a wide range and were statistically different from each other during the sampling periods. The average ratios of PM1/PM2.5 on non-Olympic days were 0.71.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.