How Optimal Control is used part2(Advanced Programming)
- Bilinear optimal control for a fractional diffusive equation(arXiv)
Author : Cyrille Kenne, Gisèle Mophou, Mahamadi Warma
Abstract : We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order 0<s<1. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some weak maximum principle results allowing us to obtain more regularity of our state equation. Then, we consider an optimal control problem which consists to bring the state of the system at final time to a desired state. We show that this optimal control problem has a solution and we derive the first and second order optimality conditions. Finally, under additional assumptions on the initial datum and the given target, we prove that local uniqueness of optimal solutions can be achieved.
2. Optimal Control for Wind Turbine Wake Mixing on Floating Platforms(arXiv)
Author : Maarten J. van den Broek, Daniel van den Berg, Benjamin Sanderse, Jan-Willem van Wingerden
Abstract : Dynamic induction control is a wind farm flow control strategy that utilises wind turbine thrust variations to accelerate breakdown of the aerodynamic wake and improve downstream turbine performance. However, when floating wind turbines are considered, additional dynamics and challenges appear that make optimal control difficult. In this work, we propose an adjoint optimisation framework for non-linear economic model-predictive control, which utilises a novel coupling of an existing aerodynamic wake model to floating platform hydrodynamics. Analysis of the frequency response for the coupled model shows that it is possible to achieve wind turbine thrust variations without inducing large motion of the rotor. Using economic model-predictive control, we find dynamic induction results that lead to an improvement of 7% over static induction control, where the dynamic controller stimulates wake breakdown with only small variations in rotor displacement. This novel model formulation provides a starting point for the adaptation of dynamic wind farm flow control strategies for floating wind turbines.
3.Validation of Stochastic Optimal Control Models for Goal-Directed Human Movements on the Example of Human Driving Behavior(arXiv)
Author : Philipp Karg, Simon Stoll, Simon Rothfuß, Sören Hohmann
Abstract : Stochastic Optimal Control models represent the state-of-the-art in modeling goal-directed human movements. The linear-quadratic sensorimotor (LQS) model based on signal-dependent noise processes in state and output equation is the current main representative. With our newly introduced Inverse Stochastic Optimal Control algorithm building upon two bi-level optimizations, we can identify its unknown model parameters, namely cost function matrices and scaling parameters of the noise processes, for the first time. In this paper, we use this algorithm to identify the parameters of a deterministic linear-quadratic, a linear-quadratic Gaussian and a LQS model from human measurement data to compare the models’ capability in describing goal-directed human movements. Human steering behavior in a simplified driving task shown to posses similar features as point-ot-point human hand reaching movements serves as our example movement. The results show that the identified LQS model outperforms the others with statistical significance. Particularly, the average human steering behavior is modeled significantly better by the LQS model. This validates the positive impact of signal-dependent noise processes on modeling human average behavior
