This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Following the first-order time discretization, the dynamic programming principle is used to find the multiobjective discrete dynamic programming equation equivalent to the resulting discrete multiobjective optimal control problem. The multiobjective discrete dynamic programming equation is finally discretized in the state space. The convergence of the approximation for both discretization steps is discussed.

Additional Metadata
Keywords Convergence of sequences of sets, Discrete approximation, Dynamic programming, External stability property, Multiobjective optimal control, Partial order generated by a cone, Topology of families of sets
Persistent URL dx.doi.org/10.1137/080720723
Journal SIAM Journal on Control and Optimization
Citation
Guigue, A. (A.), Ahmadi, M, Hayes, M.J.D, & Langlois, R.G. (2009). A discrete dynamic programming approximation to the multiobjective deterministic finite horizon optimal control problem. SIAM Journal on Control and Optimization, 48(4), 2581–2599. doi:10.1137/080720723