Minimax control of flexible structures using quadratically constrained programming
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The focus of this thesis is on the design of a control strategy for robust control of slewing flexible structures. The minimax problem is posed in a Quadratically Constrained Programming (QCP) framework for determination of the time-optimal control profile, which minimizes the maximum magnitude of the system's residual energy over the range of uncertain parameter values. A set of quadratic constraints are generated that merge state constraints with the quadratic form of the system's residual energy equation and incorporate multiple system plants to represent the range of parameter uncertainty. The new formulation utilizes the most powerful large-scale optimization problem solvers, exploits a convex optimization framework, and neither requires parameterization of the control profile and corresponding time-vector, nor approximation of the system's residual energy. The technique is tested on several benchmark problems. Results approximate traditional minimax solutions and illustrate potential for use in approximating the minimax control profile for large-scale systems with parameter uncertainties.