This work addresses control for linear systems with Markov jump parameters (LMJP), which is an important class of systems that can be employed asmodels for several applications. Recently, we derived results concerning control of LMJP with additive noise, showing that the long run averagecost (LRAC) converges under some mild conditions on the system. Now, we are interested in studying the stochastic stability of the system with finite LRAC control, as well as to calculate the optimal LRAC control via different optimization methods. We are also interested in analytical results concerning the convergence of those methods, when applied to the LRAC optimal control problem. We believe that these issues are relevant for theory and application of dynamical systems.
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