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 /spl epsiv/-feasible Nash solutions that satisfy the Karush-Kuhn-Tucker 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.

[1]  Umit Ozguner,et al.  Optimal control of multilevel large-scale systems† , 1978 .

[2]  Tamer Basar,et al.  Distributed algorithms for the computation of noncooperative equilibria , 1987, Autom..

[3]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[4]  Harri Ehtamo,et al.  Distributed computation of Pareto solutions inn-player games , 1996, Math. Program..

[5]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[6]  Michael P. Wellman,et al.  The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes , 1998 .

[7]  Pirja Heiskanen,et al.  Decentralized method for computing Pareto solutions in multiparty negotiations , 1999, Eur. J. Oper. Res..

[8]  Srdjan S. Stankovic,et al.  Decentralized overlapping control of a platoon of vehicles , 2000, IEEE Trans. Control. Syst. Technol..

[9]  Timothy W. McLain,et al.  A decomposition strategy for optimal coordination of unmanned air vehicles , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[10]  Claire J. Tomlin,et al.  Nonlinear Inverse Dynamic Control for Mode-based Flight * , 2000 .

[11]  C. Hillermeier Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach , 2001 .

[12]  E. Feron,et al.  Resolution of Conflicts Involving Many Aircraft via Semidefinite Programming , 2001 .

[13]  Walter Murray,et al.  Two decomposition algorithms for nonconvex optimization problems with global variables , 2001 .

[14]  S. Shankar Sastry,et al.  OPTIMAL COORDINATED MANEUVERS FOR THREE DIMENSIONAL AIRCRAFT CONFLICT RESOLUTION , 2001 .

[15]  Angel-Victor DeMiguel,et al.  Two decomposition algorithms for nonconvex optimization problems with global variables , 2001 .