Funnel control of the Fokker-Planck equation for a multidimensional Ornstein-Uhlenbeck process. (English) Zbl 1479.35860
In this paper the feasibility of funnel control techniques for the Fokker–Planck equation corresponding to a multidimensional Ornstein-Uhlenbeck process on an unbounded spatial domain is explored. First, using weighted Lebesgue and Sobolev spaces, an auxiliary operator is defined via a suitable sesquilinear form. This operator is then transformed to the desired Fokker-Planck operator. The author shows that any mild solution of the controlled Fokker-Planck equation (which is a probability density) has a covariance matrix that exponentially converges to a constant matrix. After a simple feedforward control approach is discussed, the author establishes feasibility of funnel control in the presence of disturbances by exploiting semigroup theory. The results are illustrated by some simulations.
Reviewer: Sven-Ake Wegner (Hamburg)
MSC:
| 35Q84 | Fokker-Planck equations |
| 35K55 | Nonlinear parabolic equations |
| 93C40 | Adaptive control/observation systems |
Keywords:
adaptive control; Fokker-Planck equation; Ornstein-Uhlenbeck process; funnel control; bilinear control systems; robust controlReferences:
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