Superlinear Convergence Using Control Based on Second-Order Needle Variations

TitleSuperlinear Convergence Using Control Based on Second-Order Needle Variations
Publication TypeConference Paper
Year of PublicationSubmitted
AuthorsMamakoukas, G., M. A. MacIver, and T. D. Murphey
PublisherConference on Decision and Control
Abstract

This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first- and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations,  the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model  verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Through the benchmark example of the cart pendulum,  this paper further demonstrates the superior convergence in a closed-loop, receding horizon implementation.

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This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first- and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations,  the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model  verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Through the benchmark example of the cart pendulum,  this paper further demonstrates the superior convergence in a closed-loop, receding horizon implementation.