Towards fully probabilistic control design
Automatica (Journal of IFAC)
Brief paper: Optimal probability density function control for NARMAX stochastic systems
Automatica (Journal of IFAC)
IEEE Transactions on Circuits and Systems Part I: Regular Papers
PID controller design for output PDFs of stochastic systems using linear matrix inequalities
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t-~ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.