Stochastic uncertainties in complex dynamical systems lead to variability ofsystem states, which can in turn degrade the closed-loop performance. Thispaper presents a stochastic model predictive control approach for a class ofnonlinear systems with unbounded stochastic uncertainties. The control approachaims to shape probability density function of the stochastic states, whilesatisfying input and joint state chance constraints. Closed-loop stability isensured by designing a stability constraint in terms of a stochastic controlLyapunov function, which explicitly characterizes stability in a probabilisticsense. The Fokker-Planck equation is used for describing the dynamic evolutionof the states' probability density functions. Complete characterization ofprobability density functions using the Fokker-Planck equation allows forshaping the states' density functions as well as direct computation of jointstate chance constraints. The closed-loop performance of the stochastic controlapproach is demonstrated using a continuous stirred-tank reactor.
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