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Second-order statistics of nonlinear dynamical systems can be obtained from experiments or numerical simulations. These statistics are relevant in understanding the fundamental physics, e.g., of fluid flows, and are useful for developing low-complexity models. Such models can be used for the purpose of control design and analysis. In many applications, only(More)
State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. In the present paper, we study the problem of completing partially known state statistics. Our aim is to develop tools that can be used in the context of control-oriented modeling of large-scale(More)
Second-order statistics of turbulent flows can be obtained either experimentally or via high fidelity numerical simulations. The statistics are relevant in understanding fundamental flow physics and for the development of low-complexity models. For example, such models can be used for control design in order to suppress or promote turbulence. Due to(More)
We consider a class of structured covariance completion problems which aim to complete partially known sample statistics in a way that is consistent with the underlying linear dynamics. The statistics of stochastic inputs are unknown and sought to explain the given correlations. Such inverse problems admit many solutions for the forcing correlations, but(More)
In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation(More)
We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate a convex optimization problem to match(More)
For a turbulent channel flow with zero-net-mass-flux surface actuation in the form of streamwise traveling waves we develop a model-based approach to design control parameters that can reduce skin-friction drag. In contrast to the traditional approach that relies on numerical simulations and experiments, we use turbulence modeling in conjunction with(More)
State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. These statistics are relevant in understanding the fundamental physics and can be used to develop control-oriented models for large-scale dynamical systems, e.g., stochastically forced linearized(More)
Low-complexity approximations of the Navier-Stokes (NS) equations are commonly used for analysis and control of turbulent flows. In particular, stochastically-forced linearized models have been successfully employed to capture structural and statistical features observed in experiments and high-fidelity simulations. In this work, we utilize(More)
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