有限博弈的矩阵半张量积方法

矩阵半张量积被广泛地应用在有限博弈的研究中,例如:1)演化博弈; 2)势博弈; 3)有限博弈的向量空间分解; 4)基于势博弈的优化与控制; 5)合作博弈等.本文的目的,就是对上述各种应用做一个全面的介绍,包括其原理、主要成果、以及尚待解决的问题.     

Algebraic decompositions of DP problems with linear dynamics

We consider Dynamic Programming (DP) problems in which the dynamics are linear, the cost is a function of the state, and the state-space is finite dimensional but defined over an arbitrary field. Starting from the natural decomposition of the state-space into a direct sum of invariant subspaces consistent with the rational canonical form, and assuming the cost functions exhibit an additive structure compatible with this decomposition, we extract from the original problem two distinct families of smaller DP problems associated with the invariant subspaces. Each family constitutes a decomposition of the original problem when the optimal policy and value function can be reconstructed from the optimal policies and value functions of the smaller problems. We derive necessary and sufficient conditions for these decompositions to exist, propose a readily verifiable sufficient condition for the first decomposition, and establish a hierarchy relating the two notions of decomposition.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.     

Detection of heterogeneous samples based on loaded generalized inner product method

Non-homogeneity detector (NHD) is known for improving the detection performance of space time adaptive processing (STAP) in heterogeneous environment. To mitigate the finite sample effect in the generalized inner product (GIP) based NHD, a new type of GIP detector based on diagonal loading (LGIP) is proposed in this paper. We derive the theoretical mean value of LGIP detector based on random matrix theory. Moreover, an approximation of the theoretical mean value is provided for practical considerations. We then apply the derived theoretical mean value of LGIP to the detection of heterogeneous samples. Finally, by theoretical analysis and numerical simulations, we show the effectiveness of the proposed detector.     

Bayesian smoothing spline analysis of variance

Smoothing spline ANOVA (SSANOVA) provides an approach to semiparametric function estimation based on an ANOVA type of decomposition. Wahba et al. (1995) decomposed the regression function based on a tensor sum decomposition of inner product spaces into orthogonal subspaces, so the effects of the estimated functions from each subspace can be viewed independently. Recent research related to smoothing spline ANOVA focuses on either frequentist approaches or a Bayesian framework for variable selection and prediction. In our approach, we seek “objective” priors especially suited to estimation. The prior for linear terms including level effects is a variant of the Zellner–Siow prior (Zellner and Siow, 1980), and the prior for a smooth effect is specified in terms of effective degrees of freedom. We study this fully Bayesian SSANOVA model for Gaussian response variables, and the method is illustrated with a real data set.     

Quantifying structural attributes of system decompositions in 28 feature-oriented software product lines

A key idea of feature orientation is to decompose a software product line along the features it provides. Feature decomposition is orthogonal to object-oriented decomposition—it crosscuts the underlying package and class structure. It has been argued often that feature decomposition improves system structure by reducing coupling and by increasing cohesion. However, recent empirical findings suggest that this is not necessarily the case. In this exploratory, observational study, we investigate the decompositions of 28 feature-oriented software product lines into classes, features, and feature-specific class fragments. The product lines under investigation are implemented using the feature-oriented programming language Fuji. In particular, we quantify and compare the internal attributes import coupling and cohesion of the different product-line decompositions in a systematic, reproducible manner. For this purpose, we adopt three established software measures (e.g., coupling between units, CBU; internal-ratio unit dependency, IUD) as well as standard concentration statistics (e.g., Gini coefficient). In our study, we found that feature decomposition can be associated with higher levels of structural coupling in a product line than a decomposition into classes. Although coupling can be concentrated in very few features in most feature decompositions, there are not necessarily hot-spot features in all product lines. Interestingly, feature cohesion is not necessarily higher than class cohesion, whereas features are more equal in serving dependencies internally than classes of a product line. Our empirical study raises critical questions about alleged advantages of feature decomposition. At the same time, we demonstrate how our measurement approach of coupling and cohesion has potential to support static and dynamic analyses of software product lines (i.e., type checking and feature-interaction detection) by facilitating product sampling.     

Using commercial video games in flipped classrooms to support physical concept construction

Based on the flipped‐classroom model and the potential motivational and instructional benefits of digital games, we describe a flipped game‐based learning (FGBL) strategy focused on preclass and overall learning outcomes. A secondary goal is to determine the effects, if any, of the classroom aspects of the FGBL strategy on learning efficiency. Our experiments involved 2 commercial games featuring physical motion concepts: Ballance (Newton's law of motion) and Angry Birds (mechanical energy conservation). We randomly assigned 87 8th‐grade students to game instruction (digital game before class and lecture‐based instruction in class), FGBL strategy (digital game before class and cooperative learning in the form of group discussion and practice in class), or lecture‐based instruction groups (no gameplay). Results indicate that the digital games exerted a positive effect on preclass learning outcomes and that FGBL‐strategy students achieved better overall learning outcomes than their lecture‐based peers. Our observation of similar overall outcomes between the cooperative learning and lecture‐based groups suggests a need to provide additional teaching materials or technical support when introducing video games to cooperative classroom learning activities.     

基于Microblaze处理器的浮点内积运算设计

浮点内积运算在信号处理与图像处理中有着广泛的应用,本文利用软核处理器灵活性和可扩展性的特点,介绍了基于Microblaze处理器的浮点内积运算结构,设计采用IEEE-754双精度浮点数,通过对DSA电路改进设计出了适合于内积运算的累加电路结构。通过EDK设计平台,在SOPC系统中把内积运算单元通过FSL总线挂载到Microblaze软核处理器上,实现了硬件单元的调用。     

A Matrix Approach to the Analysis and Control of Networked Evolutionary Games with Bankruptcy Mechanism

This paper investigates the evolutionary dynamic and control problem for a kind of networked evolutionary games with bankruptcy mechanism by using semi‐tensor product of matrices, and presents a number of new results. First, this kind of games are expressed as logical dynamic networks and converted into their algebraic forms, based on which, the evolutionary dynamics of the given games can be discussed. Second, the control problem is considered, and a control sequence is designed to guarantee that none of players goes bankrupt as the control target requires. Finally, an illustrative example is given to show the effectiveness of our main results.     

Minimality of an Automaton Cascade Decomposition for Learning System Environments

We already know how to decompose any finite automaton with a strongly connected state diagram into a strongly connected version of what we call a synchronizable cascade decomposition. This is a two component cascade decomposition whose first component has a synchronizer and whose second component is a permutation automaton. Here, we give a simpler procedure for constructing such a decomposition and show that the constructed decomposition is a homomorphic image of a subautomaton of any other synchronizable cascade decomposition. The constructed decomposition is then of minimal size, and all minimal synchronizable cascade decompositions are isomorphic, including all decompositions constructed by the old procedure. This means that their first components are isomorphic, but their second components need not be. In analyzing learning systems, we can use a synchronizable cascade decomposition to model a finite automaton environment, and in these analytical applications, the second component has equiprobable states and can often be ignored in analysis. There are many ways of constructing synchronizable cascade decompositions and we will want to use the construction that is easiest for the analytical application. The isomorphism result says that two different construction methods produce isomorphic decompositions provided the decompositions produced have the minimal number of states, and it is often easy to show this by a simple counting argument. This paper confines itself to giving the simpler procedure and proving the homomorphism result. It does not discuss analytical applications.     

Safe reinforcement learning for dynamical games

This article presents a novel actor‐critic‐barrier structure for the multiplayer safety‐critical systems. Non‐zero‐sum (NZS) games with full‐state constraints are first transformed into unconstrained NZS games using a barrier function. The barrier function is capable of dealing with both symmetric and asymmetric constraints on the state. It is shown that the Nash equilibrium of the unconstrained NZS guarantees to stabilize the original multiplayer system. The barrier function is combined with an actor‐critic structure to learn the Nash equilibrium solution in an online fashion. It is shown that integrating the barrier function with the actor‐critic structure guarantees that the constraints will not be violated during learning. Boundedness and stability of the closed‐loop signals are analyzed. The efficacy of the presented approach is finally demonstrated by using a simulation example.     

Unbiased estimation of inner product via higher order count sketch

Count sketch [1] is one of the popular sketching algorithms widely used for frequency estimation in data streams, and pairwise inner product for real-valued vectors [2]. Recently, Shi et al. [3] extended the count sketch (CS) and suggested a higher-order count sketch (HCS) algorithm that compresses input tensors (or vectors) into succinct tensors which closely approximates the value of queried features of the input. The major advantage of HCS is that it is more space-efficient than count sketch. However, their paper didn't comment on estimating pairwise inner product from the sketch. This note demonstrates that HCS also closely approximates the pairwise inner product. We showed that their sketch gives an unbiased estimate of the pairwise inner product, and gives a concentration analysis of the estimate.     

实时格斗游戏的智能决策方法

格斗游戏作为实时双人零和对抗博弈的代表性问题,具有实时对抗和快速响应的重要研究特性.相应针对性方法的提出有效反映了游戏人工智能领域的重要研究进展及发展方向.本文以格斗游戏人工智能竞赛作为研究背景,将智能决策方法分为启发式规则型、统计前向规划型与深度强化学习型三大类型,介绍相应的智能决策方法在实时格斗游戏中的研究进展.为分析格斗游戏智能决策方法的表现性能,本文提出了胜率、剩余血量、执行速率、优势性和伤害性的5个性能因子,系统分析智能决策方法的性能优势及不足.最后,对未来的在格斗游戏中研究发展趋势进行展望.     

The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods

The support operators method of discretizing partial differential equations produces discrete analogs of continuum initial boundary value problems that exactly satisfy discrete conservation laws analogous to those satisfied by the continuum system. Thus, the stability of the method is assured, but currently there is no theory that predicts the accuracy of the method on nonuniform grids. In this paper, we numerically investigate how the accuracy, particularly the accuracy of the fluxes, depends on the definition of the inner product for discrete vector fields. We introduce two different discrete inner products, the standard inner product that we have used previously and a new more accurate inner product. The definitions of these inner products are based on interpolation of the fluxes of vector fields. The derivation of the new inner product is closely related to the use of the Piola transform in mixed finite elements. Computing the formulas for the new accurate inner product requires a nontrivial use of computer algebra. From the results of our numerical experiments, we can conclude that using more accurate inner product produces a method with the same order of convergence as the standard inner product, but the constant in error estimate is about three times less. However, the method based on the standard inner product is easier to compute with and less sensitive to grid irregularities, so we recommend its use for rough grids.     

OPTIMAL REJECTION WITH ZERO STEADY‐STATE ERROR OF SINUSOIDAL DISTURBANCES FOR TIME‐DELAY SYSTEMS

This paper studies the problem of optimal rejection with zero steady‐state error of sinusoidal disturbances for linear systems with time‐delay. Based on the internal model principle, a disturbance compensator is constructed to counterbalance the external sinusoidal disturbances, so that the original system can be transformed into an augmented system without disturbances. Then, with the introduction of a sensitivity parameter and expanding power series around it, the optimal disturbance rejection problem can be simplified to the problem of solving an infinite sum of a linear optimal control series without time‐delay or disturbance. The optimal control law for disturbance rejection with zero steady‐state error consists of accurate linear state feedback terms and a time‐delay compensating term, which is an infinite sum of an adjoint vector series. In the presented approach, iteration is required only for the time‐delay compensation series. By intercepting a finite sum of the compensation series, we obtain an approximate physically realizable optimal control law that avoids complex calculation. A numerical simulation shows that the algorithm is effective and easy to implement.     

The effects of participation,performance, and interest in a game‐based writing environment

We have observed that many computer‐supported writing environments based on pedagogical strategies have only been designed to incorporate the cognitive aspects, but motivational aspects should also be included. Hence, we theorize that integrating game‐based learning into the writing environment may be a practical approach that can facilitate student participation, not only helping students learn how to write, but also sustaining their willingness to write. In this study, we investigate the effects of the game‐based writing environment on improving students' participation, performance, and interest in writing. An experiment was conducted to compare the effectiveness of 2 approaches to writing in language arts at an elementary school. Two hundred forty‐five third grade students participated in the experiment over a period of 1 year. One hundred thirty‐nine students were assigned to an experimental group and learned with a game‐based writing environment, and 106 students were in the contrast group and learned with an online writing environment. The empirical results show that the game‐based writing environment can effectively promote students' writing participation, writing performance, interest in writing, as well as their perceptions of the use of educational self‐management games. Some implications of the experimental results are also discussed.     

A fast inner product processor based on equal alignments

Inner product computation is an important operation, invoked repeatedly in matrix multiplications. A high-speed inner product processor can be very useful (among many possible applications) in real-time signal processing. This paper presents the design of a fast inner product processor, with appreciably reduced latency and cost. The inner product processor is implemented with a tree of carry-propagate or carry-save adders; this structure is obtained with the incorporation of three innovations in the conventional multiply/add tree: (1) The leaf-multipliers are expanded into adder subtrees, thus achieving an O(log Nb) latency, where N denotes the number of elements in a vector and b the number of bits in each element. (2) The partial products, to be summed in producing an inner product, are reordered according to their “minimum alignments.” This reordering brings approximately a 20% saving in hardware—including adders and data paths. The reduction in adder widths also yields savings in carry propagation time for carry-propagate adders. (3) For trees implemented with carry-save adders, the partial product reordering also serves to truncate the carry propagation chain in the final propagation stage by 2 log b − 1 positions, thus significantly reducing the latency further. A form of the Baugh and Wooley algorithm is adopted to implement two's complement notation with changes only in peripheral hardware.     

Non‐Zero Sum Differential Games of Backward Stochastic Differential Delay Equations Under Partial Information

In this paper, we study a new type of differential game problems of backward stochastic differential delay equations under partial information. A class of time‐advanced stochastic differential equations (ASDEs) is introduced as the adjoint process via duality relation. By means of ASDEs, we suggest the necessary and sufficient conditions called maximum principle for an equilibrium point of non‐zero sum games. As an application, an economic problem is putted into our framework to illustrate the theoretical results. In terms of the maximum principle and some auxiliary filtering results, an equilibrium point is obtained.     

A parallel decomposition for Kalman filters

A decomposition is given for the implementation of the Kalman filter as a collection of parallel processors. This decomposition is based on the representation of the system as a direct sum of observability subspaces     

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum‐of‐squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite‐time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite‐time convergence of the sliding surface to a pre‐chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.