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To assess the performance of a control loop based on the minimum variance (MV) benchmark, we need to calculate MV lower bound (MVLB). Even though there is a plethora of literature available for calculating MVLB for the linear systems, these methods are not suitable for nonlinear systems. Furthermore, almost all of the realworld applications have been encountered with input variance constraints. These constraints limit controllers' abilities in decreasing the output variability. Therefore, existing MVLB computation methods, which do not account for input constraints, are not realistic when applied to constrained systems. The authors propose a novel approach to estimate MVLB by employing properties of dual Lagrangian functions to address these issues simultaneously in this study. Furthermore, to design the constrained nonlinear MV controller (MVC), they propose to use the recurrent neural network for accommodating nonlinearities and the input constraints. Then, control loop stability, optimality with respect to MVLB as well as the global convergence of the proposed controller are analytically proved for convexnonlinear systems with input constraints. The proposed control strategy is verified through simulations performed on a nonlinear quadrupletank system. The results indicate that the proposed design provides satisfactory results in decreasing output variance while satisfying the constraints.
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