Plant and control optimization in the context of chaotic dynamical systems

Abstract

The combined plant and control design (co-design) of complex systems governed by chaotic dynamics presents many unique and interesting challenges associated with the multidisciplinary nature of the design problem and the chaotic behavior of the system dynamics. The challenges investigated in this work are 1) the relationship between design space complexity and system multidisciplinary optimality; 2) the failure of conventional sensitivity analysis methods to produce usable derivatives; and 3) the optimality and stability guarantees for the final design. Typically, co-design problems are dealt with in a sequential (segregated fashion), where the control is designed after all operational and optimality conditions for the plant design have been achieved. Furthermore, there is no existing literature where optimal co-design is applied to problems where chaotic dynamics dominates, such as active control of chaotic flows. This thesis aims for the development of a co-design methodology capable of handling nonlinear dynamical systems that exhibit chaotic behavior. The purpose of such a methodology is to assist engineers in the initial stages of a product development cycle in order to help improve the overall efficiency of the final design. More narrowly, the goal of this research is to help further the development of active flow control design methodologies which in turn can be used to improve overall efficiency and/or mission capability of future aircraft designs. Towards that goal, firstly, a gradient-based algorithm capable of handling chaotic dynamics and simple bound constraints is developed for (generic) chaotic co-design problems. Secondly, two co-design approaches are investigated and their results analyzed. Finally, optimal active-flow control is explored as a means to improve aerodynamic performance of aeronautical systems; more specifically, a methodology for optimization of closed-loop active-flow control systems that avoids the shortcomings of the previously discussed methods, and that guarantees, at every optimization iteration, a form of nonlinear stability and robustness. This thesis proposes and studies solutions to address all main 3 challenges, previously mentioned, associated with co-design and active flow control.