Approximate optimal monitoring: Preliminary results

2014 American Control Conference

2014

Self Cite

The problem of steering a team of agents from their initial positions to a predefined end-configuration while avoiding collisions is formulated as a differential game. A method for approximating the solution of the differential game is then presented, providing -Nash strategies. It is shown that approximate solutions are sufficient to guarantee that the task of reaching the final configuration while avoiding collisions is achieved. The theory is illustrated by simulations.

Section: Introductionmentioning

confidence: 99%

“…Thus, it appears natural that many problems involving multi-agent systems can be formulated as a differential game. In [24] the problem of monitoring a region has been formulated as a bimatrix game, whereas a similar problem has been formulated in [19] as a differential game.…”

Section: Introductionmentioning

confidence: 99%

A constructive differential game approach to collision avoidance in multi-agent systems

Mylvaganam

Sassano

2014 American Control Conference

2014

Self Cite

“…The problem of monitoring an area using a team of UAVs, referred to as agents, was studied in [8]. There, the problem of continuously monitoring a region has been formulated as a differential game and approximated as a sequence of optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

Approximate optimal monitoring

Mylvaganam¹,

2014 European Control Conference (ECC)

2014

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The problem of continuously monitoring a region using a team of agents, for example unmanned aerial vehicles equipped with sensors, is formulated as a differential game. This allows for the use of heterogeneous agents. The differential game is approximated as a sequence of optimal control problems, for which approximate solutions are found using dynamic feedback and the notion of algebraicP solution. A general form for such a solution is presented assuming the agents have single-integrator dynamics. The results can be interpreted as a trajectory plan for agents with more general dynamics. The case in which the agents have unicycle dynamics and are to track the generated trajectory plan is presented.

“…Typical areas are economics and management, defense, and robust control [2], [7]- [9]. Additionally, differential games play a role in many other areas, including problems involving multi-agent systems and biological systems [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions to a class of nonlinear Stackelberg differential games

Mylvaganam

53rd IEEE Conference on Decision and Control

2014

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A two-player nonlinear Stackelberg differential game with player 1 and player 2 as leader and follower, respectively, is considered. The feedback Stackelberg solutions to such games rely on the solution of two coupled partial differential equations (PDEs) for which closedform solutions cannot in general be found. A method for constructing strategies satisfying partial differential inequalities in place of the PDEs is presented. It is shown that these constitute approximate solutions to the differential game. The theory is illustrated by a numerical example.