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Defense: Two Degree of Freedom Optimal Control of Nonlinear Systems with Parameter Uncertainty

Speaker Name: 
Richard Shaffer
Speaker Title: 
PhD Candidate (Advisor: Qi Gong)
Speaker Organization: 
Statistics & Applied Mathematics
Start Time: 
Friday, December 7, 2018 - 10:30am
End Time: 
Friday, December 7, 2018 - 12:30pm
Engineering 2, Room 280
Qi Gong

Abstract:  Standard nonlinear optimal control relies on precise knowledge of parameter values which are difficult to measure in many practical applications. The result of which is that, when implementing the designed controls, there is likely some error between the desired state trajectories and the actual observed state trajectories. Usually these errors are managed using feedback control which relies on sensor measurement to correct the state deviations on the fly. However, recently there has been promising work done for generating controls which operate in the open-loop for generating state trajectories which are inherently robust to uncertainty in the parameters. A two degree of freedom control, constructed of both a robust open-loop maneuver and a feedback contribution, can be designed which specifically addresses the effects of the parameter uncertainty on the ability of the controls to achieve a desired endpoint condition. Two main approaches, for systems where the uncertainty appears in both the objective function and the model dynamics, to the problem formulation, via series expansion and sampling, are outlined and conditions for which they achieve the same goal are defined according to the order of the expansion and the number of samples used. For the design of both feedforward and feedback controls a nonlinear neighboring type optimal control problem is constructed and demonstrated on a simulated nonlinear double gimbal and an experimental nonlinear flexible link robotic arm. In both cases a significant increase in robustness to uncertainty in the parameter that models the flexibility via a spring constant is observed.