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It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs).
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G. Wu and K. Sreenath, “Safety-critical and constrained geometric control synthesis using control lyapunov and control barrier functions for systems evolving on manifolds,” in Proc. of the American Control Conference , 2015, pp. 2038–2044
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