Mathematical Cybernetics: Hybrid, Stochastic and Decentralized Systems

We consider partially observed stochastic dynamical systems whose state equations are of McKean-Vlasov type SDE and hence contain a measure term where the measure term is also random. Such SDEs are used to model the state dynamics of the agents in Mean Field Games framework with Major and Minor agents. We present nonlinear filtering equations in both normalized and unnormalized forms and, for some cases, for the conditional densities. Joint work with Peter E. Caines. 8. Mohamed Helwa, In-Block Controllability of Affine Systems on Polytopes. Abstract. In this talk, we first introduce the study of in-block controllability (IBC) of affine systems on polytopes, which formalizes controllability under state constraints. In particular, for a given affine system and a given full-dimensional polytope, representing the safety and performance state constraints, we study whether all the states in the interior of the given polytope are mutually accessible through its interior by applying uniformly bounded control inputs. By exploring the geometry of the problem, we provide easily checkable necessary and sufficient conditions for IBC of affine systems on polytopes. Then, we briefly discuss how to use this result to study controllability and build hierarchical control structures of piecewise affine hybrid systems, and to systematically solve approximate mutual accessibility problems of nonlinear systems on polytopes. We conclude the talk by presenting some future directions on IBC. 9. Bozenna Pasik-Duncan, Discrete Time Linear Exponential Quadratic Gaussian Control. Abstract. An explicit optimal control for the discrete time linear exponential quadratic Gaussian control problem is obtained which does not use the methods of dynamic programming or stochastic maximum principle and provides some insight into the terms that occur in the Riccati difference equation that determines the optimal feedback control. The method to obtain the explicit optimal control and optimal cost is algebraic. 10. Aditya Mahajan, Fundamental limits of remote estimation of Markov processes under communication constraints. Abstract. The fundamental limits of remote estimation of Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time Markov process, which is a symmetric countable state Markov source or a GaussMarkov process. At each time, the sensor either transmits the current state of the Markov process or does not