Composition of Dynamic Control Objectives Based on Differential Games

We present a divide and conquer design approach for handling control problems with dynamically changing objectives. The approach is based on associating each objective with a virtual input and then considering a game between a set of (virtual) players, each trying to achieve an objective by controlling the associated virtual input. By guarantying a Nash equilibrium for this game, we synthesize a combined controller that establishes a stable balance between the objectives. To demonstrate the use of the approach, we describe how a controller for a non-linear system (quadrotor) can be designed to handle competing objectives that change in time. The example shows how our approach allows to model each of the objectives separately and to combine them using game theory.