Robust and optimal control
Necessary conditions for nonsmooth, infinite-horizon, optimal control problems
Journal of Optimization Theory and Applications
Vector-Valued Optimization Problems in Control Theory
Vector-Valued Optimization Problems in Control Theory
SIAM Journal on Control and Optimization
Technical communique: The regular convex cooperative linear quadratic control problem
Automatica (Journal of IFAC)
Necessary and Sufficient Conditions for Pareto Optimal Solutions of Cooperative Differential Games
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Hi-index | 22.14 |
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal control problems with a special structure. Next, we show that if the dynamical system is controllable, certain transversality conditions hold true, and as a result all the Pareto candidates can be obtained by solving a weighted sum optimal control problem. Further, exploiting the linear structure we investigate the relationship between Pareto optimality and weighted sum minimization. Finally, for the scalar case, we present an algorithm to find all the Pareto optimal solutions assuming mild conditions on the control space.