Multiobjective control

2. Multiobjective control Maneuver sequencing is accomplished by stringing together capture sets, starting from the target set and working backwards Target Set Unsafe Set Avoid sets can be combined with capture sets to guarantee safety

3. Example: Collision Avoidance • Pilots instructed to attempt to collide vehicles [Gabe Hoffmann]

4. Back-Flip: Results

5. Decentralized optimization based on dual decomposition Consider the following simple example: aircraft, each with dynamics Private (local) cost function: Global cost function:

6. Centralized Optimization

7. Dual Decomposition: Overview • One primal problem leads to many dual problems • The dual decomposition method • solves one instance of these many dual problems • breaks the primal problem into a set of small problems • provides a lower bound on the global optimal solution • If the problem is convex, dual decomposition returns the global optimal solution

8. 2’ 2 3 3’ 2 Dual Decomposition: Overview 2 Primal Problem 1 3 2’’ Decoupled Primal Problem 1’ 1 2’’ 2’ Dual Problem 1 1’ 3 3’

9. Decentralized results after 5 iterations