Team decision theory and information structures in optimal control problems--Part I

Information structures of organizations are studied and applied to problems of dynamic team decisions. For a causal system it is shown that there is a partially ordered precedence relation existing among the decision makers. The team decision problem with linear information structure and quadratic payoff function is dealt with. The primitive random variables are assumed to be jointly Gaussian. The optimal solutions for the teams in which precedents' information is available for the followers are obtained. It is shown that the well-known linear-quadratic-Gaussian stochastic control problem and static team decision problem are special cases of the structure considered.     

Relationship between decentralized controller design usingH∞ and stochastic risk-averse criteria

Considers discrete-time decentralized risk-averse LEQG (linear exponential of quadratic cost Gaussian) teams, and shows that the team-optimal solutions are identical to one of the solutions for minimax team problems. The author first gives the result for static teams, and extends the result to dynamic teams, with a quasi-classical information pattern, using a dynamic programming argument. In the process, the author also establishes differences between the two problems by pointing out the existence of multiple solutions to the minimax team problem, while there exists a unique solution to the LEQG team problem     

Team-optimal closed-loop Stackelberg strategies in hierarchical control problems

This paper is concerned with the derivation of closed-loop Stackelberg (CLS) solutions of a class of continuous-time two-player nonzero-sum differential games characterized by linear state dynamics and quadratic cost functionals. Explicit conditions are obtained for both the finite and infinite horizon problems under which the CLS solution is a representation of the optimal feedback solution of a related team problem which is defined as the joint minimization of the leader's cost function. First, a specific class of representations is considered which depend linearly on the current and initial values of the state, and then the results are extended to encompass a more general class of linear strategies that also incorporate the whole past trajectory. The conditions obtained all involve solutions of linear matrix equations and are amenable to computational analysis for explicit determination of CLS strategies.     

Ultrafuzzy team decisions in a dynamic environment

In this paper, the concept of fuzzy sets of type 2 is introduced and the team decision processes which contain ultrafuzzy states, ultrafuzzy information structures, ultrafuzzy information signals, ultrafuzzy decision rules, and ultrafuzzy actions are formulated. After some definitions of fuzzy relations of type 2, fuzzy sets of type 2 induced by mappings, composition, Cartesian product, ultrafuzzy mappings, and ultrafuzzy functions, a model of ultrafuzzy team decision in a dynamic environment is proposed. The team decision problem under ultrafuzzy constraints is dealt with. Some results on fuzzy sets of type 2 induced by mappings are given.     

On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem

In this paper, a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered. First, we show that the efficient solutions fuzzy quadratic multiobjective programming problems series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. An application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given. At the end, numerical examples are illustrated in the support of the obtained results.     

A set partitioning based goal programming model for the team formation problem

In this paper, we offer a multi-objective set-partitioning formulation for team formation problems using goal programming. Instead of selecting team members to teams, we select suitable teams from a set of teams. This set is generated using a heuristic algorithm that uses the social network of potential team members. We then utilize the proposed multi-objective formulation to select the desired number of teams from this set that meets the skill requirements. Therefore, we ensure that selected teams include individuals with the required skills and effective communication with each other. Two real datasets are used to test the model. The results obtained with the proposed solution are compared with two well-known approaches: weighted and lexicographic goal programming. Results reveal that weighted and lexicographic goal programming approaches generate almost identical solutions for the datasets tested. Our approach, on the other hand, mostly picks teams with lower communication costs. Even in some cases, better solutions are obtained with the proposed approach. Findings show that the developed solution approach is a promising approach to handle team formation problems.     

A decision approach with multiple interactive qualitative objectives for product conceptual schemes based on noncooperative-cooperative game theory

Product development based on a morphological matrix involves the process of decision-based design. Although the decision process can generate conceptual schemes under the guidance of qualitative decision objectives, analysis of the interactions among the qualitative objectives is seldom considered, which can lead to unreliable optimal solutions by combining conflicting principle solutions. In addition, due to the ambiguity of the constraints among the qualitative objectives, multiple feasible schemes with equilibrium states are not considered in the concept decision stage. To solve these problems, a decision approach with multiple interactive qualitative objectives is developed for conceptual schemes based on noncooperative-cooperative game theory to consider the tradeoffs among objectives (e.g., cost, quality and operability) using discrete principle solution evaluation data. First, the morphological analysis method can obtain feasible schemes and determine the principle solutions for each subfunction. Second, the principle solutions are quantified using linguistic terms. Then, the subfunctions are categorized through cluster analysis to determine the suitable principle solution. Third, based on the clustering results, a noncooperative game decision model is constructed to identify multiple Nash equilibrium solutions that satisfy the constraints among the objectives. Fourth, a cooperative game decision model is constructed to obtain the optimal scheme as screened by the noncooperative game model. The case study proves that this approach can choose a relatively superior scheme under the existing technical conditions, thereby preventing inconsistency with the actual design expectations.     

A multimodel approach to stochastic team problems

This paper develops decentralized team strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.     

Parametric optimal control problems with weighted <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-norm in the cost function

In the paper, an optimal control problem with weighted L ₁-norm in the cost function is studied. The problem is considered as a parametric problem where L ₁-norm weight ratio is treated as a parameter. We analyze the dependence of solution to the mentioned optimization problem on values of the parameter. A theorem that describes properties of the solution under small parameter perturbations is proved. Differential properties of the solution are investigated. Under assumption that a solution to unperturbed problem is known, rules for construction of solutions to perturbed optimization problems are given.     

Multi-agent team cooperation: A game theory approach

The main goal of this work is to design a team of agents that can accomplish consensus over a common value for the agents’ output using cooperative game theory approach. A semi-decentralized optimal control strategy that was recently introduced by the authors is utilized that is based on minimization of individual cost using local information. Cooperative game theory is then used to ensure team cooperation by considering a combination of individual cost as a team cost function. Minimization of this cost function results in a set of Pareto-efficient solutions. Among the Pareto-efficient solutions the Nash-bargaining solution is chosen. The Nash-bargaining solution is obtained by maximizing the product of the difference between the costs achieved through the optimal control strategy and the one obtained through the Pareto-efficient solution. The latter solution results in a lower cost for each agent at the expense of requiring full information set. To avoid this drawback some constraints are added to the structure of the controller that is suggested for the entire team using the linear matrix inequality (LMI) formulation of the minimization problem. Consequently, although the controller is designed to minimize a unique team cost function, it only uses the available information set for each agent. A comparison between the average cost that is obtained by using the above two methods is conducted to illustrate the performance capabilities of our proposed solutions.     

A concept of compromise solutions and the method of the displaced ideal

In problems with multiple noncommensurable objectives, finding the set of nondominated solutions can be considered a sound first step of any decision making methodology. Such a set could however be too large to allow the decision maker to choose the final solution safely. So an effort is made to help the decision maker to reduce the set of nondominated solutions by eliminating some “obviously bad” solutions. Several complementary ways of reducing the nondominated set are discussed: weight space decomposition, fuzzy weight assessment and the ideal solution displacement. A new concept of the weight of importance based on attribute entropy measurement is introduced. Numerical examples are given throughout the text.     

Decomposition of heterogeneous classification problems

In some classification problems the feature space is heterogeneous in that the best features on which to base the classification are different in different parts of the feature space. In some other problems the classes can be divided into subsets such that distinguishing one subset of classes from another and classifying examples within the subsets require very different decision rules, involving different sets of features. In such heterogeneous problems, many modeling techniques (including decision trees, rules, and neural networks) evaluate the performance of alternative decision rules by averaging over the entire problem space, and are prone to generating a model that is suboptimal in any of the regions or subproblems. Better overall models can be obtained by splitting the problem appropriately and modeling each subproblem separately.This paper presents a new measure to determine the degree of dissimilarity between the decision surfaces of two given problems, and suggests a way to search for a strategic splitting of the feature space that identifies regions with different characteristics. We illustrate the concept using a multiplexor problem, and apply the method to a DNA classification problem.     

基于状态空间搜索法的商人过河问题解决方案

商人过河问题可以视为一个多步决策的过程,通过确定每一步的决策,最终达到安全渡河的目标。将经典的商人过河问题进行了泛化讨论,在此基础上着重分析了安全渡河问题的状态空间,建立了满足问题需求的渡河规则,研究了相应的控制策略,得出了求解路径的搜索规则和搜索策略,给出了基于状态空间搜索法的问题解决方案。     

支持动态策略变化的ABAC决策回收

基于属性的访问控制(Attribute-Based Access Control, ABAC)因其灵活、表达能力丰富等特性,成为最常见的访问控制模型之一。然而,ABAC的策略决策点(Policy Decision Point, PDP)繁琐的策略查询任务以及PDP与策略执行点(Policy Enforcement Point, PEP)之间的网络通信影响其访问控制决策的效率。访问控制决策结果的回收利用是解决以上问题的有效方法之一。本文提出一种支持访问控制策略动态变化的、带策略的ABAC访问控制决策结果的回收利用方案。方案针对ABAC的3种变体模型给出如何创建和更新访问控制决策结果的缓存、如何由缓存内容进行精确和近似的访问控制决策。最终,通过原型系统对方案的可行性和有效性进行实验验证,实验结果显示本文提出的方法一定程度上能降低系统的访问控制决策时间并减少PDP的工作负荷。     

主子阵约束下矩阵方程AX=B的对称最小二乘解

本文主要讨论主子阵约束下矩阵方程AX=B的对称最小二乘解．基于投影定理,巧妙的把最小二乘问题转化为等式问题求解,并利用奇异值分解的方法,给出了该对称最小二乘解的一般表达式．此外,文章还考虑了此对称最小二乘解集合对任一给定矩阵的最佳逼近问题,得到了最佳逼近解,并给出了相应的算法步骤和数值例子．     

Optimization of queuing system via stochastic control

The problem of access and service rate control in queuing systems as a general optimization problem for controlled Markov process with finite state space is considered. By using the dynamic programming approach we obtain the explicit form of the optimal control in the case of minimizing cost given as a mixture of an average queue length, number of lost jobs, and service resources. The problem is considered on a finite time interval in the case of nonstationary input flow. In this case we suggest the general procedure of the numerical solution which can be applied to a problems with constraints.     

Optimal decision f usion given sens or rules

When all the rules of sensor decision are known ,the optimal distributed decision fusion ,which relies only on the joint conditional probability densities , can be derived for very general decision systems. They include those systems with interdependent sensor observations and any network structure. It is also valid for m-ary Bayesian decision problems and binary problems under the Neyman- Pearson criterion. Local decision rules of a sensor with communication from other sensors that are optimal for the sensor itself are also presented ,which take the form of a generalized likelihood ratio test . Numerical examples are given to reveal some interesting phenomena that communication between sensors can improve performance of a senor decision ,but cannot guarantee to improve the global fusion performance when sensor rules were given before fusing.     

Optimal decision fusion given sensor rules

When all the rules of sensor decision are known,the optimal distributed decision fusion,which relies only on the joint conditional probability densities, can be derived for very general decision systems. They include those systems with interdependent sensor observations and any network structure. It is also valid for m-ary Bayesian decision problems and binary problems under the Neyman-Pearson criterion. Local decision rules of a sensor withfrom other sensors that are optimal for the sensor itself are also presented, which take the form of a generalized likelihood ratio test. Numerical examples are given to reveal some interesting phenomem that communication between sensors can improve performance of a senor decision,but cannot guarantee to improve the global fusion performance when sensor rules were given before fusing.     

Asymptotics of the solutions of the generalized Hutchinson equation

The problem of the behavior of solutions of the Hutchinson equation and its generalizations is considered. Results regarding the estimation of the domain of the global stability of the positive equilibrium state in the parameter space are obtained. The problems of the existence, stability, and asymptotics of a slowly oscillating periodic solution are approached in the basic propositions. The problem of the dynamic properties of the system of ordinary differential equations that describes the well-known Belousov-Zhabotinsky reaction is considered as an application of the newly developed asymptotic methods.     

Numerical solutions of a nonlinear reaction-diffusion system

This paper is concerned with finite difference solutions of a coupled system of nonlinear reaction-diffusion equations. The investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. The existence and uniqueness of a non-negative finite difference solution and three monotone iterative algorithms for the computation of the solutions are given. It is shown that the time-dependent problem has a unique non-negative solution, whereas the steady-state problem may have multiple non-negative solutions depending on the parameters in the problem. The different non-negative steady-state solutions can be computed from the monotone iterative algorithms by choosing different initial iterations. Also discussed is the asymptotic behaviour of the time-dependent solution in relation to the steady-state solutions. The asymptotic behaviour result gives some conditions ensuring the convergence of the time-dependent solution to a positive or semitrivial non-negative steady-state solution. Numerical results are given to demonstrate the theoretical analysis results.