Universal controllers of V.A. Yakubovich: a systematic approach to LQR problems with uncertain external signals∗∗The paper was partially supported by RFBR, grants 13-08-01014 and 14-08-01015, and St. Petersburg State University, grant 6.38.230.2015. Theorems 6 and 13 are obtained at Institute for Problems of Mechanical Engineering RAS and supported solely by Russian Scientific Foundation (RSF), grant 14-29-00142.

Proskurnikov, Anton V.

doi:10.1016/j.ifacol.2015.09.245

Cited by 2 publications

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Optimal universal controllers for roll stabilization

2020

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Roll damping is an important problem of ship motion control since excessive roll motion may cause motion sickness of human occupants and damage fragile cargo. Actuators used for roll damping (fins, rudders and thrusters) inevitably create a rotating yaw moment, interfering thus with the vessel's autopilot (heading control system). To reach and maintain the "trade-off" between the concurrent goals of accurate vessel steering and roll damping, an optimization procedure in general needs to take place where the cost functional penalizes the roll angle, the steering error and the control effort. Since the vessel's motion is influenced by the uncertain wave disturbance, the optimal value of this functional and the resulting optimal process are also uncertain. Standard approaches, prevailing in the literature, approximate the wave disturbance by the "colored noise" with a known spectral density, reducing the optimization problem to conventional loop-shaping, LQG or H ∞ control. In this paper, we propose a novel approach to optimal roll damping, approximating the disturbance by a polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. For this class of external disturbances, an optimal universal controller (OUC) can be found, delivering the optimal solution for any uncertain parameters of the signal. Using numerical simulations, we compare our design method with classical approaches to optimal roll damping and show that OUC controllers exhibit better performance.

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