Lyapunov Theory

Exact Backstepping Control for Systems in Pure Feedback Form

Prof. Johann Reger, Computer Science and Automation Faculty, TU Ilmenau, Germany

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KAUST

Traditional backstepping approaches may struggle to asymptotically stabilize systems in pure feedback form, due to its inherent implicit equations. Approximation based designs only have a limited domain of validity and turn out sensitive to model uncertainty and disturbances. We propose a new design that circumvents the necessity of solving implicit algebraic equations by introducing new state variables. Additional augmentations to the backstepping Lyapunov design lead to explicit expressions for the associated differential equations. The result is a dynamic state feedback, capable of asymptotically stabilizing the origin of a general class of nonlinear systems, based on just standard assumptions.

Part 2 - Introduction to backstepping control

Prof. Johann Reger, Computer Science and Automation Faculty, TU Ilmenau, Germany.

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KAUST

Backstepping is a widely applicable control technique based on Lyapunov theory that under rather mild assumptions leads to families of control laws for a large class of nonlinear systems. Focusing on systems of ordinary differential equations, we introduce the basic concept (integrator backstepping), generalize it, among others, to systems in strict feedback form and pure feedback form, which all enjoy an inherent controllability property, captured in the system structure. The course ends with extending the setting to the adaptive backstepping case, resorting to the certainty equivalence principle and Barbalat's lemma. The course is furnished by a series of exercises to let the students gather experience on tailored examples.