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On Compatibility and Region of Attraction for Safe Stabilizing Control Laws

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Document pages: 10 pages

Abstract: A novel control method is proposed to ensure compatibility of safe,stabilizing control laws, i.e., simultaneous satisfaction of asymptoticstability and constraint satisfaction for nonlinear affine systems. The resultsare dependent on an asymptotically stabilizing control law and a zeroingcontrol barrier function (ZCBF), but do not require a control Lyapunov function(CLF). Sufficient conditions for a region of attraction are defined for whichthe proposed control safely stabilizes the system, while preserving thedecrescent Lyapunov function of the original stabilizing control law. Theproposed methodology for nonlinear affine systems requires checking conditionsof the system dynamics over a substantial portion of the state space, which maybe computationally expensive. To facilitate the search for compatibility, weextend the results to a class of nonlinear systems including mechanical systemsfor which a novel controller is designed to guarantee passivity, safety, andstability. Numerical examples are used to demonstrate the proposed technique.

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