Evasion differential game of infinitely many evaders from infinitely many pursuers in Hilbert space

We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space ℓ2. Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed

Linear evasion differential game of one evader and several pursuers with integral constraints

AbstractAn evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn't exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible

Differential game with many pursuers when controls are subjected to coordinate-wise integral constraints

In this paper, we study a differential game of many pursuers and one evader in R2. The motions of all players are simple. An integral constraint is imposed on each coordinate of the control functions of players. We say that pursuit is completed if the state of a pursuer coincides with that of the evader at some time. The pursuers try to complete the pursuit, and the evader tries to avoid this. Sufficient conditions for completion of the differential game were obtained. The strategies of the pursuers are constructed based on the current values of control parameter of the evader. Also an illustrative example is provided

An evasion differential game problem on the plane

Evasion differential game problem with many pursuers and one evader is studied on the plane. The control functions of the players are subject to integral constraints on each coordinates. Sufficient conditions for evasion to be proposed from many pursuers are obtained. Moreover, evader’s strategy is constructed and illustrative example is given.Keywords: evasion, integral constraint, strategies

Convexity Applications in Single and Multi-Agent Control

The focus of this dissertation is in the application of convexity for control problems; specifically, single-agent problems with linear or nonlinear dynamics and multi-agent problems with linear dynamics. A mixture of convex and non-convex constraints for optimal control problems is also considered. The main contributions of this dissertation include: 1) a convexification of single-agent problems with linear dynamics and annular control constraint, 2) a technique for controlling bounded nonlinear single-agent systems, and 3) a technique for solving multi-agent pursuit-evasion games with linear dynamics and convex control and state constraints. The first result shows that for annularly constrained linear systems, controllability is a sufficient condition for a free or fixed time problem to be solvable as a sequence of convex optimization problems. The second result shows that if a nonlinear system is bounded and “ordered”, it is possible to use a convex combination of bounding linear systems to design a control for the nonlinear system. The third result takes advantage of a convex reachable set computation for each agent in solving games using a geometrical approach. Altogether, the theoretical and computational results demonstrate the significance of convex analysis in solving non-convex control problems

Analysis of multi-agent systems under varying degrees of trust, cooperation, and competition

Multi-agent systems rely heavily on coordination and cooperation to achieve a variety of tasks. It is often assumed that these agents will be fully cooperative, or have reliable and equal performance among group members. Instead, we consider cooperation as a spectrum of possible interactions, ranging from performance variations within the group to adversarial agents. This thesis examines several scenarios where cooperation and performance are not guaranteed. Potential applications include sensor coverage, emergency response, wildlife management, tracking, and surveillance. We use geometric methods, such as Voronoi tessellations, for design insight and Lyapunov-based stability theory to analyze our proposed controllers. Performance is verified through simulations and experiments on a variety of ground and aerial robotic platforms. First, we consider the problem of Voronoi-based coverage control, where a group of robots must spread out over an environment to provide coverage. Our approach adapts online to sensing and actuation performance variations with the group. The robots have no prior knowledge of their relative performance, and in a distributed fashion, compensate by assigning weaker robots a smaller portion of the environment. Next, we consider the problem of multi-agent herding, akin to shepherding. Here, a group of dog-like robots must drive a herd of non-cooperative sheep-like agents around the environment. Our key insight in designing the control laws for the herders is to enforce geometrical relationships that allow for the combined system dynamics to reduce to a single nonholonomic vehicle. We also investigate the cooperative pursuit of an evader by a group of quadrotors in an environment with no-fly zones. While the pursuers cannot enter the no-fly zones, the evader moves freely through the zones to avoid capture. Using tools for Voronoi-based coverage control, we provide an algorithm to distribute the pursuers around the zone's boundary and minimize capture time once the evader emerges. Finally, we present an algorithm for the guaranteed capture of multiple evaders by one or more pursuers in a bounded, convex environment. The pursuers utilize properties of the evader's Voronoi cell to choose a control strategy that minimizes the safe-reachable area of the evader, which in turn leads to the evader's capture