Decentralized Optimization, with Application to Multiple Aircraft Coordination

We present a decentralized optimization method for solving the coordination problem of interconnected nonlinear discrete-time dynamic systems with multiple decision makers. The optimization framework embeds the inherent structure in which each decision maker has a mathematical model that captures only the local dynamics and the associated interconnecting global constraints. A globally convergent algorithm based on sequential local optimizations is presented. Under assumptions of differentiability and linear independence constraint qualification, we show that the method results in global convergence to 2-feasible Nash solutions that satisfy the Karush-KuhnTucker necessary conditions for Pareto-optimality. We apply this methodology to a multiple unmanned air vehicle system, with kinematic aircraft models, coordinating in a common airspace with separation requirements between the aircraft.