Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Chair in Aerodynamics



+44 (0)20 7594 5548s.chernyshenko Website




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BibTex format

author = {Huang, D and Jin, B and Lasagna, D and Chernyshenko, SI and Tutty, O},
doi = {10.1109/TCST.2016.2638881},
journal = {IEEE Transactions on Control Systems Technology},
pages = {2073--2086},
title = {Expensive control of long-time averages using sum of squares and Its application to a laminar wake flow},
url = {},
volume = {25},
year = {2017}

RIS format (EndNote, RefMan)

AB - The paper presents a nonlinear state-feedback con-trol design approach for long-time average cost control, where thecontrol effort is assumed to be expensive. The approach is basedon sum-of-squares and semi-definite programming techniques. Itis applicable to dynamical systems whose right-hand side is apolynomial function in the state variables and the controls. Thekey idea, first described but not implemented in (Chernyshenkoetal.Phil. Trans. R. Soc. A, 372, 2014), is that the difficult problemof optimizing a cost function involving long-time averages isreplaced by an optimization of the upper bound of the sameaverage. As such, controller design requires the simultaneousoptimization of both the control law and a tunable function,similar to a Lyapunov function. The present paper introducesa method resolving the well-known inherent non-convexity ofthis kind of optimization. The method is based on the formalassumption that the control is expensive, from which it followsthat the optimal control is small. The resulting asymptoticoptimization problems are convex. The derivation of all thepolynomial coefficients in the controller is given in terms ofthe solvability conditions of state-dependent linear and bilinearinequalities. The proposed approach is applied to the problemof designing a full-information feedback controller that mitigatesvortex shedding in the wake of a circular cylinder in the laminarregime via rotary oscillations. Control results on a reduced-ordermodel of the actuated wake and in direct numerical simulationare reported.
AU - Huang,D
AU - Jin,B
AU - Lasagna,D
AU - Chernyshenko,SI
AU - Tutty,O
DO - 10.1109/TCST.2016.2638881
EP - 2086
PY - 2017///
SN - 1558-0865
SP - 2073
TI - Expensive control of long-time averages using sum of squares and Its application to a laminar wake flow
T2 - IEEE Transactions on Control Systems Technology
UR -
UR -
VL - 25
ER -