Numerical Methods for Minimax Control Problems: Deterministic and Uncertain Systems

PARENTE LISANDRO A.; ARAGONE LAURA; GIANATTI JUSTINA; LOTITO, PABLO ANDRÉS

Tandil

Workshop; V LAWOC 2016; 2016

CONICET-UNCPBA-ANPCyT

We consider minimax optimal control problems with lineardynamics. First, we study the deterministic case where, underconvexity assumptions, by using non-smooth optimizationtechniques, we derive a set of optimality conditions. Wedefine an approximated discretetime problem where analogousconditions hold. One of them allows us to design an easilyimplementable descent method whose accumulation points areoptimal. Then, we address an extension of the previousproblem to a setting with parameter uncertainty, where theobjective function is the expectation of a max operator andthe underlying trajectory depends on stochastic parametersin such way that, for each fixed sample in a completeprobability space, we recover the deterministic case. Weanalyze two possibles approaches and show some examples.