2014/02/27 by Mihai Sîrbu, Sîrbu, Mihai
Mathematics · #49L20 #49L25 #91A05 #91A15 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:49L20 #msc:49L25 #msc:91A05 #msc:91A15
paper · pdf · doi:10.48550/arxiv.1402.7030
some modifications and some typos fixed
arxiv created 2015/02/19 · arxiv updated 2015/02/20
We introduce a modification of Perron's method, where semi-solutions are considered in a carefully defined asymptotic sense. With this definition, we can show, in a rather elementary way, that in a zero-sum game or a control problem (with or without model uncertainty), the value function over all strategies coincides with the value function over Markov strategies discretized in time. Therefore, there are always discretized Markov ε-optimal strategies, (uniform with respect to the bounded initial condition). With a minor modification, the method produces a value and approximate saddle points for an asymmetric game of feedback strategies vs. counter-strategies.