A Differential Game Approach to Multi-Agent Systems
E-Mail: prima.aditya@tuhh.de
The multi-agent formation control problem has been widely studied as an essential application of cooperative control theory. Because it involves more than one agent and each has its
own strategy, issues in multi-agent systems, especially formation control, can be modeled as a
game. Game theory is a concept of strategical scenarios by players who understand that their
decisions will affect other agents’ decisions. We are interested in Linear Quadratic Discrete-Time Games (LQDTG). In an LQDTG, players will have different cost functions. The optimal control theory employed for a single cost function cannot resolve the problem. As an alternative, Nash equilibria have been studied,
which require solving coupled Riccati difference equations. A challenge is the implementation
of distributed controllers, as the states and control signals are coupled through the cost. By
relocating the coupling terms that initially appear in the cost function to the dynamics, we can
design a decoupling framework for solving the LQDTG in a distributed manner. The advantage of working in discrete-time is that one does not require solving a series of ODEs. Besides the time efficiency, a second benefit is that modeling the problem in discrete time will allow the development of a receding horizon strategy (predictive control). In this project, the role of Nash equilibrium solutions in the cooperative control of MAS will be explored, and a decoupling framework for formation control will be developed.
Tasks:
1. Familiarization with the concept of a Nash equilibrium and its Riccati solution
2. Design and implementation of a formation control problem as an LQDTG with trajectory
tracking
3. Design and implementation of a decoupling framework for LQDTG
4. Implementation of a receding horizon technique based on the open-loop solution
5. Evaluation and discussion
Requirement:
A background in optimal control (ORC) or the willingness
to familiarize with the material