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In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems. As special cases, this class of systems includes both jump linear stochastic systems and linear stochastic hybrid automata. In the proposed framework, an approximation is itself a stochastic hybrid system, which can be used as a replacement of the...
For deterministic nonlinear dynamical systems, approximate dynamic programming based on Pontryagin's maximum principle provides a systematic way to solve optimal control problems. However, in the presence of noise, this approach becomes cumbersome. Hence, in current optimal control solution methodologies noise effect is typically ignored in the adjoint equations. Alternatively, in the Hamilton-Jacobi...
The applicability and usefulness of implicit sampling in stochastic optimal control is explored. The basic idea is to solve the stochastic Hamilton-Jacobi-Bellman equation with a Monte Carlo solver. This approach avoids the need for a grid of the domain (which is infeasible for problems of moderate dimension), however the sampling must be done carefully or else the Monte Carlo approach also becomes...
In order to understand how populations of neurons control movement, several phenomena beyond the realm of classical control theory must be addressed. These include the effect of variability in control due to stochastic firing, the effect of large partially unlabeled cooperative controllers, the effect of bandlimited control due to finite neural resources, and the effect of variation in the number...
The estimation of statistical momenta of the stochastic systems dx/dt = f(x, {ξi}i), where {ξi}i is the set of random parameters, is an important problem in computations. The direct solution consists in integration of evolution equations followed by the Monte-Carlo averaging. Recently a method of estimation statistical momenta of such systems, the so-called intrusive method, based on the expansion...
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