- ▪E.D. Sontag, "A general approach to path planning for systems without drift", In Essays on mathematical robotics (Minneapolis, MN, 1993), pp. 151–168, 1998. pdfpath-planning · systems without drift · nonlinear control · controllability · real-analytic functions · gradient dynamics · gradient descent · gradient systems · gradient descent · numerical methods · dynamics of algorithms
Abstract
This paper proposes a generally applicable technique for the control of analytic systems with no drift. The method is based on the generation of "nonsingular loops" that allow linearized controllability. One can then implement Newton and/or gradient searches in the search for a control. A general convergence theorem is proved.
- ▪E.D. Sontag, "Control of systems without drift via generic loops", IEEE Trans. Automat. Control, vol. 40, no. 7, pp. 1210–1219, 1995. pdfstabilization · non-holonomic systems · path-planning · systems without drift · nonlinear control · controllability · real-analytic functions
Abstract
This paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift. It is based on the generation of "nonsingular loops" which allow linearized controllability along suitable trajetories. Once such loops are available, it is possible to employ standard Newton or steepest descent methods, as classically done in numerical control. The theoretical justification of the approach relies on recent results establishing the genericity of nonsingular controls, as well as a simple convergence lemma.
- ▪E.D. Sontag, "Gradient techniques for systems with no drift: A classical idea revisited", In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pp. 2706–2711, 1993. pdfpath-planning · systems without drift · nonlinear control · controllability · real-analytic functions · gradient dynamics · gradient descent · gradient systems · gradient descent · numerical methods · dynamics of algorithms
Abstract
This paper proposes a technique for the control of analytic systems with no drift. It is based on the generation of "nonsingular loops" which allow linearized controllability. Once such loops are available, it is possible to employ standard Newton or steepest descent methods. The theoretical justification of the approach relies on results on genericity of nonsingular controls as well as a simple convergence lemma.