Stochastic Systems Seminar
Abstract: This talk will consider some recent results on the finite horizon minimax optimal output feedback control for a class of discrete-time stochastic uncertain systems. The uncertainty description for the class of stochastic uncertain systems to be considered involves a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic constraint uncertainty description which is commonly used in the robust control literature.
The minimax optimal control problem is solved by converting it into an equivalent (parameter dependent) risk sensitive control problem. In the case of linear stochastic uncertain systems, this leads to a linear output feedback risk sensitive control problem. The solution to this risk sensitive control problem is well known and given in terms of a pair of Riccati difference equations which are of the type which occurs in the finite horizon H infinity control problem. This (parameter dependent) Riccati equation solution to the minimax optimal control problem reduces to the stamdard LQG optimal controller in the case in which the uncertainty is set to zero in the linear stochastic uncertain system.
The talk will also explore the connection between the solution to the minimax LQG control problem and H infinity control. It follows from the solution to the risk sensitive control problem in terms of a pair Riccati differential equations that this problem is equivalent to a certain finite horizon H infinity control problem. Taking the limit as the time horizon approaches infinity, it can be concluded that the minimax optimal control problem has a solution if and only if a corresponding deterministic uncertain system with a sum quadratic constraint uncertainty description is absolutely stabilizable.
Joint Seminar, Center for Fluid Mechanics & Division of Engineering
Abstract: Turbulence has attracted the attention of some of the best minds in engineering, physics, and mathematics because of its intellectual challenges as well as its importance in many practical engineering applications. Despite all of the attention, however, turbulence has been incredibly resistant to studies that would reveal its nature, and progress has been painfully slow. A brief overview of the recent progress achieved by the author's research group on turbulence control for drag reduction in turbulent boundary layers will be presented. Examples include applications of neural networks, suboptimal control theory, the Goore scheme, systems control theory. Numerical experiments illustrate that substantial drag reduction can be achieved from these approaches. Practical issues concerning implementation of these control schemes in practice will be discussed.
Brown University Graduate School Dissertation Defense Information
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