A Novel Distributed Optimal Adaptive Control Algorithm for Nonlinear Multi-Agent Differential Graphical Games

In this paper, an online optimal distributed learning algorithm is proposed to solve leader-synchronization problem of nonlinear multi-agent differential graphical games. Each player approximates its optimal control policy using a single-network approximate dynamic programming(ADP) where only one critic neural network(NN) is employed instead of typical actorcritic structure composed of two NNs. The proposed distributed weight tuning laws for critic NNs guarantee stability in the sense of uniform ultimate boundedness(UUB) and convergence of control policies to the Nash equilibrium. In this paper, by introducing novel distributed local operators in weight tuning laws, there is no more requirement for initial stabilizing control policies. Furthermore, the overall closed-loop system stability is guaranteed by Lyapunov stability analysis. Finally, Simulation results show the effectiveness of the proposed algorithm.

APPROXIMATE REPRESENTATION OF THE p-NORM DISTRIBUTION

In surveying data processing,we generally suppose that the observational errors distribute normally.In this case the method of least squares can give the minimum variance unbiased estimation of the parameters.The method of least squares does not have the character of robustness,so the use of it will become unsuitable when a few measurements inheriting gross error mix with others.We can use the robust estimating methods that can avoid the influence of gross errors.With this kind of method there is no need to know the exact distribution of the observations.But it will cause other difficulties such as the hypothesis testing for estimated parameters when the sample size is not so big.For non_normally distributed measurements we can suppose they obey the p _norm distribution law.The p _norm distribution is a distributional class,which includes the most frequently used distributions such as the Laplace,Normal and Rectangular ones.This distribution is symmetric and has a kurtosis between 3 and -6/5 when p is larger than 1.Using p _norm distribution to describe the statistical character of the errors,the only assumption is that the error distribution is a symmetric and unimodal curve.This method possesses the property of a kind of self_adapting.But the density function of the p _norm distribution is so complex that it makes the theoretical analysis more difficult.And the troublesome calculation also makes this method not suitable for practice.The research of this paper indicates that the p _norm distribution can be represented by the linear combination of Laplace distribution and normal distribution or by the linear combination of normal distribution and rectangular distribution approximately.Which kind of representation will be taken is according to whether the parameter p is larger than 1 and less than 2 or p is larger than 2.The approximate distribution have the same first four order moments with the exact one.It means that approximate distribution has the same mathematical expectation,variance,skewness and kurtosis with p _norm distribution.Because every density function used in the approximate formulae has a simple form,using the approximate density function to replace the p _norm ones will simplify the problems of p _norm distributed data processing obviously.

The Multivariate Saddlepoint Approximation to the Distribution of Estimators： A General Approach

We develop the theory of multivariate saddlepoint approximations. Our treatment differs from the one in Barndorff-Nielsen and Cox （1979, equation （4.7）） in two aspects： 1） our results are satisfied for random vectors that are not necessarily sums of independent and identically distributed random vectors, and 2） we consider that the sample is taken from any distribution, not necessarily a member of the exponential family of densities. We also show the relationship with the corresponding multivariate Edgeworth approximations whose general treatment was developed by Durbin in 1980, emphasizing that the basic assumptions that support the validity of both approaches are essentially similar.

Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle

In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents in a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent can only use information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurements of its neighbors＇ states are corrupted by random noises. By probability limit theory and the property of graph Laplacian matrix, it is shown that for a connected network, the static mean square error between the individual state and the average of the initial states of all agents can be made arbitrarily small, provided the sampling size is sufficiently small. Furthermore, by properly choosing the consensus gains, almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which implies that in the case of white Gaussian noises, no matter what the sampling size is, the product of the steady-state and transient performance indices is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.

Joint modeling of longitudinal proportional measurements and survival time with a cure fraction

In cancer clinical trials and other medical studies, both longitudinal measurements and data on a time to an event(survival time) are often collected from the same patients. Joint analyses of these data would improve the efficiency of the statistical inferences. We propose a new joint model for the longitudinal proportional measurements which are restricted in a finite interval and survival times with a potential cure fraction. A penalized joint likelihood is derived based on the Laplace approximation and a semiparametric procedure based on this likelihood is developed to estimate the parameters in the joint model. A simulation study is performed to evaluate the statistical properties of the proposed procedures. The proposed model is applied to data from a clinical trial on early breast cancer.

MOTIONS IN THE BOUNDARY LAYER UNDER THE GEOSTROPHIC MOMENTUM APPROXIMATION INCORPORATING A THREE-SECTION K DISTRIBUTION

By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the distribution of eddy transfer coefficient k is divided into three sections:k_1z(z_0≤z<h_1),k_2(h_1≤z<h_2), and k_3(h_2≤z).The results are in agreement with the observations.In particular,the wind profile in the surface layer(z_0≤z<h_1)coincides with the logarithmic distribution.The maximum angle between winds near the surface and at the bottom of the free atmosphere is only about 30°.This work improves the work of Wu and Blumen(1982)who introduced the geostrophic momentum approximation to the boundary layer.The solutions in barotropic and neutral conditions have been also extended to the baroclinic and stratified atmosphere.