Towards fully probabilistic control design
Automatica (Journal of IFAC)
The variational formulation of the Fokker-Planck equation
SIAM Journal on Mathematical Analysis
A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
SIAM Journal on Optimization
Existence and Uniqueness of Optimal Control for a Distributed-Parameter Bilinear System
Journal of Dynamical and Control Systems
Multigrid methods for parabolic distributed optimal control problems
Journal of Computational and Applied Mathematics
Solution of lambda-omega systems: Theta-schemes and multigrid methods
Numerische Mathematik
Multigrid for High-Dimensional Elliptic Partial Differential Equations on Non-equidistant Grids
SIAM Journal on Scientific Computing
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An efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker-Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The resulting optimality system is discretized by the Chang-Cooper scheme that guarantees positivity of the forward solution. The effectiveness of the proposed computational framework is validated with a stochastic Lotka-Volterra model and a noised limit cycle model.