DIFFERENTIAL GAME WITH A LIFELINE FOR THE INERTIAL MOVEMENTS OF PLAYERS

In this paper, we study the well-known problem of Isaacs called the "Life line" game when movements of players occur by acceleration vectors, that is, by inertia in Euclidean space. To solve this problem, we investigate the dynamics of the attainability domain of an evader through finding solvability conditions of the pursuit-evasion problems in favor of a pursuer or an evader. Here a pursuit problem is solved by a parallel pursuit strategy. To solve an evasion problem, we propose a strategy for the evader and show that the evasion is possible from given initial positions of players. Note that this work develops and continues studies of Isaacs, Petrosjan, Pshenichnii, Azamov, and others performed for the case of players' movements without inertia.

A Stackelberg game for the Italian tax evasion problem

In this paper, we consider the problem of tax evasion, which occurs whenever an individual or business ignores tax laws. Fighting tax evasion is the main task of the Economic and Financial Military Police, which annually performs fiscal controls to track down and prosecute evaders at national level. Due to limited financial resources, the tax inspector is unable to audit the population entirely. In this article, we propose a model to assist the Italian tax inspector (Guardia di Finanza, G.d.F.) in allocating its budget among different business clusters, via a controller-controlled Stackelberg game. The G.d.F. is seen as the leader, while potential evaders are segmented into classes according to their business sizes, as set by the Italian regulatory framework. Numerical results on the real Italian case for fiscal year 2015 are provided. Insights on the optimal number of controls the inspector will have to perform among different business clusters are discussed and compared to the strategy implemented by the G.d.F.

Pursuer Assignment and Control Strategies in Multi-Agent Pursuit-Evasion Under Uncertainties

We consider a pursuit-evasion problem with a heterogeneous team of multiple pursuers and multiple evaders. Although both the pursuers and the evaders are aware of each others’ control and assignment strategies, they do not have exact information about the other type of agents’ location or action. Using only noisy on-board sensors the pursuers (or evaders) make probabilistic estimation of positions of the evaders (or pursuers). Each type of agent use Markov localization to update the probability distribution of the other type. A search-based control strategy is developed for the pursuers that intrinsically takes the probability distribution of the evaders into account. Pursuers are assigned using an assignment algorithm that takes redundancy (i.e., an excess in the number of pursuers than the number of evaders) into account, such that the total or maximum estimated time to capture the evaders is minimized. In this respect we assume the pursuers to have clear advantage over the evaders. However, the objective of this work is to use assignment strategies that minimize the capture time. This assignment strategy is based on a modified Hungarian algorithm as well as a novel algorithm for determining assignment of redundant pursuers. The evaders, in order to effectively avoid the pursuers, predict the assignment based on their probabilistic knowledge of the pursuers and use a control strategy to actively move away from those pursues. Our experimental evaluation shows that the redundant assignment algorithm performs better than an alternative nearest-neighbor based assignment algorithm1.

Minmax fuzzy deterministic policy gradient for zero-sum differential game: Take pursuit-evasion problem as example

A novel actor-critic algorithm is introduced and applied to zero-sum differential game. The proposed novel structure consists of two actors and a critic. Different actors represent the control policies of different players, and the critic is used to approximate the state-action utility function. Instead of neural network, the fuzzy inference system is applied as approximators for the actors and critic so that the specific practical meaning can be represented by the linguistic fuzzy rules. Since the goals of the players in the game are completely opposite, the actors for different players are simultaneously updated in opposite directions during the training. One actor is updated updated toward the direction that can minimize the Q value while the other updated toward the direction that can maximize the Q value. A pursuit-evasion problem with two pursuers and one evader is taken as an example to illustrate the validity of our method. In this problem, the two pursuers the same actor and the symmetry in the problem is used to improve the replay buffer. At the end of this paper, some confrontations between the policies with different training episodes are conducted.

Compensation Control Strategy for Orbital Pursuit-Evasion Problem with Imperfect Information

This paper studies the orbital pursuit-evasion problem with imperfect information, including measurement noise and input delay. The presence of imperfect information will degrade the players’ control performance and lead to mission failure. To solve this problem, a compensation control strategy for the players is proposed. The compensation control strategy consists of two parts: the guaranteed cost strategy and the time delay compensation method. First, a near-optimal feedback strategy called guaranteed cost strategy with perfect information is proposed based on a Lyapunov-like function and matrix analysis theory. Second, a time delay compensation method based on an uncertainty set is proposed to compensate for delayed information. The compensation control strategy is derived by combining the time delay compensation method with the guaranteed cost strategy. While applying this strategy to the game, the input of the strategy is generated by processing the measured data with the state estimation algorithm based on the unscented Kalman filter (UKF). The simulation results show that the proposed strategy can handle the orbital pursuit-evasion problem with imperfect information effectively.

A Distributed Approach to the Evasion Problem

The Evasion Problem is the question of whether—given a collection of sensors and a particular movement pattern over time—it is possible to stay undetected within the domain over the same stretch of time. It has been studied using topological techniques since 2006—with sufficient conditions for non-existence of an Evasion Path provided by de Silva and Ghrist; sufficient and necessary conditions with extended sensor capabilities provided by Adams and Carlsson; and sufficient and necessary conditions using sheaf theory by Krishnan and Ghrist. In this paper, we propose three algorithms for the Evasion Problem: one distributed algorithm extension of Adams’ approach for evasion path detection, and two different approaches to evasion path enumeration.