Stéphane Le Ménec

Linear Differential Game with Two Pursuers and One Evader

We study the situation involving two pursuers and one evader in the framework of DGL/1 (Linear Differential Game with bounded controls and first order dynamics for both players). The criterion of the one-on-one DGL/1 game is the terminal miss distance (perpendicular to the initial pursuer/evader Line Of Sight). The pursuer is minimizing this outcome meantime the evader is maximizing the same criterion. We introduce one pursuer more and analyze the changes. A new optimal evasion strategy is then derived to compromise the terminal miss distance with respect to each pursuer. This trade-off strategy and the resulting 2 ×1 No Escape Zone have been computed when the pursuers have the same time-to-go as well as with different times-to-go (equal and different durations of the individual games).

A Swarm Intelligence Method Combined to Evolutionary Game Theory Applied to the Resources Allocation Problem

This paper addresses an allocation problem and proposes a solution using a swarm intelligence method. The application of swarm intelligence has to be discrete. This allocation problem can be modelled as a multi-objective optimization problem where the authors minimize the time and the distance of the total travel in a logistic context. This study uses a hybrid Discrete Particle Swarm Optimization DPSO method combined to Evolutionary Game Theory EGT. One of the main implementation issues of DPSO is the choice of inertial, individual, and social coefficients. In order to resolve this problem, those coefficients are optimised by using a dynamical approach based on EGT. The strategies are either to keep going with only inertia, only with individual, or only with social coefficients. Since the optimal strategy is usually a mixture of the three, the fitness of the swarm can be maximized when an optimal rate for each coefficient is obtained. Evolutionary game theory studies the behaviour of large populations of agents who repeatedly engage in strategic interactions. Changes in behaviour in these populations are driven by natural selection via differences in birth and death rates. To test this algorithm, the authors create a problem whose solution is already known. This study checks whether this adapted DPSO method succeeds in providing an optimal solution for general allocation problems.

Level Sets of the Value Function in Differential Games with Two Pursuers and One Evader. Interval Analysis Interpretation

An algorithm for numerical constructing level sets of the value function is shortly described for one class of linear differential games with fixed termination instant. Some model interception problems with one target and two interceptors are considered; all objects are weak maneuverable.

Cooperative Missile Guidance Strategies for Maritime Area Air Defence

Abstract Mid-course guidance phase classically refers to the procedure guiding the missile to a terminal handover point in order to acquire the target motion through its on-board sensor. The mid-course guidance law differs significantly from the guidance logic for the terminal homing phase due to the inherited characteristic of the midcourse guidance: it must not only find the best condition for the terminal homing phase, but also deliver the missile to that condition using only the target motion data updated by the external source such as a plane, ship, or ground base. In this paper we revisit the micourse guidance problem for maritime area air defense by mixing two contributions (one for mid course guidance law design and one for target allocation). The proposed solution is based on differential games (capturability considerations) for allocation of the missiles. The main idea is that a cooperative mid-course guidance strategy can defend the area as long as it assures that the depending area is always inside the defended area defined by earliest intercept geometry.

Cooperative Mid Course Guidance for Area Air Defence

In this paper, a cooperative mid course missile guidance law is proposed by using Earliest Intercept Geometry (EIG) concept and the optimal control theory for area air defence. In the cooperative mid course guidance problem, since there are many attacking and defending missiles, how to allocate the defending missiles to the attacking missiles is one of most important issues. Therefore, we focused on developing a best allocation plan by using the EIG concept. Each EIG between an attacking and defending missile is analytically generated for the range of all possible manoeuvre of the challenging missile using differential geometry concepts. All parameters to find an optimal allocation are also analytically derived by using simple algebra. Then, we formulate a simple optimal allocation problem and introduce a numerical approach to solve the problem. The computational

A Two-Step Optimisation Method for Dynamic Weapon Target Assignment Problem

The weapon target assignment (WTA) problem has been designed to match the Command & Control (C2) requirement in military context, of which the goal is to find an allocation plan enabling to treat a specific scenario in assigning available weapons to oncoming targets. The WTA always get into situation weapons defending an area or assets from an enemy aiming to destroy it. Because of the uniqueness of each situation, this problem must be solved in real-time and evolve accordingly to the aerial/ground situation. By the past, the WTA was solved by an operator taking all the decisions, but because of the complexity of the modern warfare, the resolution of the WTA in using the power of computation is inevitable to make possible the resolution in real time of very complex scenarii involving different type of targets. Nowadays, in most of the C2 this process is designed in order to be as a support for a human operator and in helping him in the decision making process. The operator will give its final green light to proceed the intervention.

Study of Linear Game with Two Pursuers and One Evader: Different Strength of Pursuers

The paper deals with a problem of pursuit-evasion with two pursuers and one evader having linear dynamics. The pursuers try to minimize the final miss (an ideal situation is to get exact capture), the evader counteracts them. Results of numerical construction of level sets (Lebesgue sets) of the value function are given. A feedback method for producing optimal control is suggested. The paper includes also numerical simulations of optimal motions of the objects in various situations.

Cooperative Guidance for Naval Area Defence

Abstract In this paper, we proposed a cooperative guidance strategy to consider many on many engagements for maritime area air defence. The main idea is that a cooperative missile guidance law can defend the area as long as it guarantees that the keep out zone is always within the defended area defined by Earliest Intercept Geometry (EIG) or a No Escape Zone (NEZ). Since one of the most important issues for the cooperative guidance is to allocate attacking missiles to defending missiles, we focused on developing an allocation plan. The cooperative guidance algorithm proposed in this paper consists of two main parts: a pre allocation algorithm designed by using the EIG guidance law and Differential Geometry Guidance Law (DGGL); in flight target allocation proposed based on the differential game theory. Whilst the pre allocation plan is activated during the mid course and deactivated after the mid course, the in flight target allocation is activated during all in flight phases to refine the initial allocation. Mathematical analysis for the allocation algorithms is carried out to check their characteristics and the performance of the proposed strategy is verified by some numerical examples.

Model Formulation of Pursuit Problem with Two Pursuers and One Evader

We study a model differential zero-sum game, which can be regarded as an idealized variant of the final stage of a space pursuit, in which two pursuing objects and one evader are involved. Results of numeric constructions of level sets of the value function for qualitatively different cases of the game parameters and results of simulation of optimal motions are presented.

Collaborative Interception of Moving Re-locatable Target

This paper is dealing with a team of autonomous vehicles using on-board sensors for tracking and intercepting a moving target. The team of autonomous vehicles is composed of a pursuing vehicle and of several Unmanned Aircraft Vehicles (UAVs). The on-board sensors we talk about have limited capabilities in terms of range. Before acquiring the target, the pursuing vehicle relies on external discrete time information. The target is a slow moving target with respect to the pursuer velocity. The pursuer and the evader are both ground mobile vehicles. The pursuer is able to decide when receiving target re-location information coming from UAVs. UAVs are flying in a cooperative manner with the pursuing vehicle. This situation has been described in terms of a zero-sum two-player pursuit-evasion differential game with costly information. The pursuer minimizes the time to reach the target, while the target tries to evade and to maximize the capture time. After solving this pursuit-evasion game for simple kinematics, test and evaluation simulations with more realistic kinematics have been performed. We also discuss the 4D guidance law and the coordination algorithm we implemented for managing the UAVs.