On properties of one functional used in software constructions for solving differential games

Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.

On a discrete game problem with non-convex control vectograms

In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.

Two-Stage Pursuit Strategy for Incomplete-Information Impulsive Space Pursuit-Evasion Mission Using Reinforcement Learning

This paper presents a novel and robust two-stage pursuit strategy for the incomplete-information impulsive space pursuit-evasion missions considering the J2 perturbation. The strategy firstly models the impulsive pursuit-evasion game problem into a far-distance rendezvous stage and a close-distance game stage according to the perception range of the evader. For the far-distance rendezvous stage, it is transformed into a rendezvous trajectory optimization problem and a new objective function is proposed to obtain the pursuit trajectory with the optimal terminal pursuit capability. For the close-distance game stage, a closed-loop pursuit approach is proposed using one of the reinforcement learning algorithms, i.e., the deep deterministic policy gradient algorithm, to solve and update the pursuit trajectory for the incomplete-information impulsive pursuit-evasion missions. The feasibility of this novel strategy and its robustness to different initial states of the pursuer and evader and to the evasion strategies are demonstrated for the sun-synchronous orbit pursuit-evasion game scenarios. The results of the Monte Carlo tests show that the successful pursuit ratio of the proposed method is over 91% for all the given scenarios.

The Principle-Agent Conflict Problem in a Continuous-Time Delegated Asset Management Model

This paper considers the principle-agent conflict problem in a continuous-time delegated asset management model when the investor and the fund manager are all risk-averse with risk sensitivity coefficients γ f and γ m , respectively. Suppose that the investor entrusts his money to the fund manager. The return of the investment is determined by the manager’s effort level and incentive strategy, but the benefit belongs to the investor. In order to encourage the manager to work hard, the investor will determine the manager’s salary according to the terminal income. This is a stochastic differential game problem, and the distribution of income between the manager and the investor is a key point to be solved in the custody model. The uncertain form of the incentive strategy implies that the problem is different from the classical stochastic optimal control problem. In this paper, we first express the investor’s incentive strategy in term of two auxiliary processes and turn this problem into a classical one. Then, we employ the dynamic programming principle to solve the problem.

A Study on Nash-Collative Differential Game of N -Players for Counterterrorism

In this work, by using the Nash-collative approach for a differential game problem between N -governments and terrorist organizations, we study governments’ cooperation and the role of each government for counterterrorism. Furthermore, we discuss the intertemporal strategic interaction of governments and terrorist organizations, where all world governments have to cooperate to fight terrorism. Also, we study the necessary conditions for finding the optimal strategies for each government to fight terrorism; we discuss the existence of the solution of the formulated problem and the stability set of the first kind of the optimal strategies.

Graphical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

In this paper, the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems (MASs) with spanning tree condition based on game theory and reinforcement learning. First, the graphical minimax game algebraic Riccati equation (ARE) is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors. The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically. Then, a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics. A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.

A Pollution Sensitive Fuzzy EPQ Model With Endogenous Reliability and Product Deterioration Under Lock Fuzzy Game Theoretic Approach

This article deals with a cost minimization objective function of an economic production quantity (EPQ) inventory model with production breakdown and deterioration. The process reliability and the environmental pollution due to over production have also been considered. The model has been split into two different scenarios according to the breaking time before and after the production period. In scenario 1, no machinery failure occurs during production run time and that of scenario 2 the failure occurs during production run time. We develop a deterministic cost minimization problem first then we fuzzify the model by considering the production rate, the demand rate and all the cost components as lock fuzzy numbers. We convert the fuzzy model into equivalent game problem by considering Gaussian normal strategic probabilities. The model has been solved with the help of different key vectors employed by the decision maker. We have shown that the value of the game might be changed with the change of different key vectors. A comparative study has been made with the numerical results of the general fuzzy and crisp models. Finally, graphical illustrations and sensitivity analysis have been done followed by a conclusion.