Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

Cooperative maneuver decision making for multi-UAV air combat based on incomplete information dynamic game

Cooperative autonomous air combat of multiple unmanned aerial vehicles(UAVs)is one of the main combat modes in future air warfare,which becomes even more complicated with highly changeable situation and uncertain information of the opponents.As such,this paper presents a cooperative decision-making method based on incomplete information dynamic game to generate maneuver strategies for multiple UAVs in air combat.Firstly,a cooperative situation assessment model is presented to measure the overall combat situation.Secondly,an incomplete information dynamic game model is proposed to model the dynamic process of air combat,and a dynamic Bayesian network is designed to infer the tactical intention of the opponent.Then a reinforcement learning framework based on multiagent deep deterministic policy gradient is established to obtain the perfect Bayes-Nash equilibrium solution of the air combat game model.Finally,a series of simulations are conducted to verify the effectiveness of the proposed method,and the simulation results show effective synergies and cooperative tactics.

Iterative Learning Control With Incomplete Information： A Survey

Abstract--This paper conducts a survey on iterative learn- ing control （ILC） with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects： the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.

Remanufacturing Scheme Design for Used Parts Based on Incomplete Information Reconstruction

The different conditions of use of a component result in a variety of damage levels.Therefore,excluding differences in shape and size,used parts show a high degree of uncertainty regarding failure characteristics,quality conditions,and remaining life,which seriously affects the efficiency of a remanufacturing scheme design.Aiming to address this problem,a remanufacturing scheme design method based on the reconstruction of incomplete information of used parts is proposed.First,the remaining life of the reconstructed model is predicted by finite element analysis,and the demand for the next life cycle is determined.Second,the scanned 3D damage point cloud data are registered with the original point cloud data using the integral iterative method to construct a missing point cloud model to achieve the restoration of geometric information.Then,according to reverse engineering and laser cladding remanufacturing,the tool remanufacturing process path can be generated by the tool contact point path section line method.Finally,the proposed method is adopted for turbine blades to evaluate the effectiveness and feasibility of the proposed scheme.This study proposes a remanufacturing scheme design method based on the incomplete reconstruction of used part information to solve the uncertain and highly personalized problems in remanufacturing.

Threat sequencing of multiple UCAVs with incomplete information based on game theory

The threat sequencing of multiple unmanned combat air vehicles(UCAVs) is a multi-attribute decision-making(MADM)problem. In the threat sequencing process of multiple UCAVs,due to the strong confrontation and high dynamics of the air combat environment, the weight coefficients of the threat indicators are usually time-varying. Moreover, the air combat data is difficult to be obtained accurately. In this study, a threat sequencing method of multiple UCAVs is proposed based on game theory by considering the incomplete information. Firstly, a zero-sum game model of decision maker( D) and nature(N)with fuzzy payoffs is established to obtain the uncertain parameters which are the weight coefficient parameters of the threat indicators and the interval parameters of the threat matrix. Then,the established zero-sum game with fuzzy payoffs is transformed into a zero-sum game with crisp payoffs(matrix game) to solve. Moreover, a decision rule is addressed for the threat sequencing problem of multiple UCAVs based on the obtained uncertain parameters. Finally, numerical simulation results are presented to show the effectiveness of the proposed approach.

Fuzzy multi-criteria decision-making approach with incomplete information based on evidential reasoning

The weights of criteria are incompletely known and the criteria values are incomplete and uncertain or even default in some fuzzy multi-criteria decision-making problems.For those problems,an approach based on evidential reasoning is proposed,in which the criteria values are integrated on the basis of analytical algorithm of evidential reasoning,and then nonlinear programming models of each alternative are developed with the incomplete information on weights.The genetic algorithm is employed to solve the models,producing the weights and the utility interval of each alternative,and the ranking of the whole set of alternatives can be attained.Finally,an example shows the effectiveness of the method.

Consistency and Asymptotic Normality of MLE of Parameter Vector in a Randomly Censored GLM with Incomplete Information

The generalized linear model（GLM） based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator（MLE） βn^-, are proved.

Mining association rules in incomplete information systems

Based on the rough set theory which is a powerful tool in dealing with vagueness and uncertainty, an algorithm to mine association rules in incomplete information systems was presented and the support and confidence were redefined. The algorithm can mine the association rules with decision attributes directly without processing missing values. Using the incomplete dataset Mushroom from UCI machine learning repository, the new algorithm was compared with the classical association rules mining algorithm based on Apriori from the number of rules extracted, testing accuracy and execution time. The experiment results show that the new algorithm has advantages of short execution time and high accuracy.

Strategy Selection for Moving Target Defense in Incomplete Information Game

As a core component of the network,web applications have become one of the preferred targets for attackers because the static configuration of web applications simplifies the exploitation of vulnerabilities by attackers.Although the moving target defense(MTD)has been proposed to increase the attack difficulty for the attackers,there is no solo approach can cope with different attacks;in addition,it is impossible to implement all these approaches simultaneously due to the resource limitation.Thus,the selection of an optimal defense strategy based on MTD has become the focus of research.In general,the confrontation of two players in the security domain is viewed as a stochastic game,and the reward matrices are known to both players.However,in a real security confrontation,this scenario represents an incomplete information game.Each player can only observe the actions performed by the opponent,and the observed actions are not completely accurate.To accurately describe the attacker’s reward function to reach the Nash equilibrium,this work simulated and updated the strategy selection distribution of the attacker by observing and investigating the strategy selection history of the attacker.Next,the possible rewards of the attacker in each confrontation via the observation matrix were corrected.On this basis,the Nash-Q learning algorithm with reward quantification was proposed to select the optimal strategy.Moreover,the performances of the Minimax-Q learning algorithm and Naive-Q learning algorithm were compared and analyzed in the MTD environment.Finally,the experimental results showed that the strategy selection algorithm can enable defenders to select a more reasonable defensive strategy and achieve the maximum possible reward.

A rule induction algorithm for incomplete information system

Incompleteness of information about objects may be the greatest obstruct to performing induction learning from examples. In this paper, the concept of limited-non-symmetric similarity relation is used to formulate a new definition of approximation to an incomplete information system. With the new definition of approximation to an object set and the concept of attribute value pair, rough-setsbased methodology for certain rule acquisition in an incomplete information system is developed. The algorithm can deal with incomplete data directly and does not require changing the size of the original incomplete system. Experiments show that the algorithm provides precise and simple certain decision rules and is not affected by the missing values.

Extension of information entropy-based measures in incomplete information systems

It is helpful for people to understand the essence of rough set theory to study the concepts and operations of rough set theory from its information view. In this paper we address knowledge expression and knowledge reduction in incomplete infolvnation systems from the information view of rough set theory. First, by extending information entropy-based measures in complete information systems, two new measures of incomplete entropy and incomplete conditional entropy are presented for incomplete information systems. And then, based on these measures the problem of knowledge reduction in incomplete information systems is analyzed and the reduct definitions in incomplete information system and incomplete decision table are proposed respectively. Finally, the reduct definitions based on incomplete entropy and the reduct definitions based on similarity relation are compared. Two equivalent relationships between them are proved by theorems and an in equivalent relationship between them is illustrated by an example. The work of this paper extends the research of rough set theory from information view to incomplete information systems and establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in incomplete information systems.

Local mine production safety supervision game analysis based on incomplete information

Utilized fundamental theory and analysis method of Incomplete Information repeated games, introduced Incomplete Information into repeated games, and established two stages dynamic games model of the local authority and the coal mine owner. The analytic result indicates that： so long as the country established the corresponding rewards and punishments incentive mechanism to the local authority departments responsible for the work, it reports the safety accident in the coal mine on time. The conclusion that the local government displays right and wrong cooperation behavior will be changed with the introduction of the Incomplete Information. Only has the local authority fulfill their responsibility, can the unsafe accident be controlled effectively. Once this kind of cooperation of local government appears, the costs of the country on the safe supervise and the difficulty will be able to decrease greatly.

CONSISTENCY OF MLE OF THE PARAMETER OF EXPONENTIAL LIFETIME DISTRIBUTION FOR RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.

Cooperative coalition for formation flight scheduling based on incomplete information

This study analyzes the cooperative coalition problem for formation scheduling based on incomplete information. A multi-agent cooperative coalition framework is developed to optimize the formation scheduling problem in a decentralized manner. The social class differentiation mech- anism and role-assuming mechanism are incorporated into the framework, which, in turn, ensures that the multi-agent system （MAS） evolves in the optimal direction. Moreover, a further differen- tiation pressure can be achieved to help MAS escape from local optima. A Bayesian coalition nego- tiation algorithm is constructed, within which the Harsanyi transformation is introduced to transform the coalition problem based on incomplete information to the Bayesian-equivalent coali- tion problem based on imperfect information. The simulation results suggest that the distribution of agents＇ expectations of other agents＇ unknown information approximates to the true distribution after a finite set of generations. The comparisons indicate that the MAS cooperative coalition algo- rithm produces a significantly better utility and possesses a more effective capability of escaping from local optima than the proposal-engaged marriage algorithm and the Simulated Annealing algorithm.

Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems

In this paper we address information measures of roughness of knowledge and rough sets for incomplete information systems. The definition of rough entropy of knowledge and its important properties are given. In particular, the relationship between rough entropy of knowledge and the Hartley measure of uncertainty is established. We show that rough entropy of know1edge decreases monotonously as granularity of information become smaller. This gives an information interpretation for roughness of knowledge. Based on rough entropy of knowledge and roughness of rough set. a definition of rough entropy of rough set is proposed, and we show that rough entropy of rough set decreases monotonousIy as granularity of information become smaller. This gives more accurate measure for roughness of rough set.

Generalized binary discernibility matrix for attribute reduction in incomplete information systems

To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.

An approach to quality assessment for web service selection based on the analytic hierarchy process for cases of incomplete information

Since web services intended for the same application environment tend to be functionally homogeneous, researchers have turned to their non-functional aspects in order to constructively compare web services and choose an appropriate one. In general, quality of service is very important to users. Many schemes that consider quality assessment have been proposed for web service selection. With the increasing number of qualityrelated attributes, an effective quality assessment method needs satisfactory scalability. Schemes based on the analytic hierarchy process(AHP) meet this requirement. However, prevalent methods in this vein overlook the fact that the traditional AHP needs a complete judgment matrix. In practice, all the information needed to construct a judgment matrix is often unavailable for a variety of reasons, due to which certain judgments cannot be made. In this paper, for an incomplete judgment matrix, we propose an improved AHP approach to consistency verification and the subsequent ordering. Our method can deal with situations where information is insufficient,and inherits all the merits of the traditional AHP approach. A case study establishes the effectiveness of our proposed method.

Rough set extensions in incomplete information systems

All eight possible extended rough set models in incomplete information systems are proposed.By analyzing existing extended models and technical meth-ods of rough set theory,the strategy of model extension is found to be suitable for processing incomplete information systems instead of filling possible values for missing attributes.After analyzing the definitions of existing extended models,a new general extended model is proposed.The new model is a generalization of indiscernibility relations,tolerance relations and non-symmetric similarity relations.Finally,suggestions for further study of rough set theory in incomplete informa-tion systems are put forward.

Public Opinion Dissemination with Incomplete Information on Social Network: A Study Based on the Infectious Diseases Model and Game Theory

Given the fragmentation of public opinion dissemination and the lag of network users’cognition,the paper analyzes public opinion dissemination with incomplete information,which can provide reference for us to control and guide the spread of public opinion.Based on the derivative and secondary radiation of public opinion dissemination with incomplete information,the Susceptible-Susceptible-Infected-Recovered-Recovered-Infected(SSIRR-I)model is proposed.Given the interaction between users,the Deffuant opinion dynamics model and evolutionary game theory are introduced to simulate the public opinion game between dissemination and immune nodes.Finally,the numerical simulation and results analysis are given.The results reveal that the rate of opinion convergence significantly affects disseminating public opinion,which is positively correlated with the promotion effect of the dissemination node and negatively correlated with the suppression effect of the immune node of public opinion dissemination.Derivative and secondary radiations have different effects on public opinion dissemination in the early stage,but promote public opinion dissemination in the later stage.The dominant immune nodes have an apparent inhibitory effect on the spread of public opinion;nevertheless,they cannot block the dissemination of public opinion.

HYPERGAMES AND BAYESIAN GAMES:A THEORETICAL COMPARISON OF THE MODELS OF GAMES WITH INCOMPLETE INFORMATION

The present study discusses the relationships between two independently developed models of games with incomplete information, hypergames （Bennett, 1977） and Bayesian games （Harsanyi, 1967）. The authors first show that any hypergame can naturally be reformulated in terms of Bayesian games in an unified way. The transformation procedure is called Bayesian representation of hypergame. The authors then prove that some equilibrium concepts defined for hypergames are in a sense equivalent to those for Bayesian games. Furthermore, the authors discuss carefully based on the proposed analysis how each model should be used according to the analyzer＇s purpose.