This paper introduces hysteretic control Lyapunov functions (HCLFs) for hybrid feedback control of a class of continuous-time systems. A family of HCLFs consists of local control Lyapunov functions defined on open domains, and include finite collections of open and closed sets that cover the state-space, implicitly defining a hysteresis-based switching mechanism. Given an HCLF family, we derive sufficient conditions for the existence of globally asymptotically stabilizing hybrid control laws. Moreover, we provide a constructive design procedure for synthesis of optimization-based feedback laws under mild conditions on the objective functions. We construct HCLFs for an underwater vehicle and demonstrate their applicability to hybrid control design for global asymptotic trajectory tracking for underwater vehicles.
Autonomous surface vehicles (ASVs) are safetycritical systems that must provide strict safety guarantees such as collision avoidance to enable fully autonomous operations. This paper presents a unified framework for safety-critical control of ASVs for maneuvering, dynamic positioning, and control allocation with safety guarantees in the presence of unknown ocean currents. The framework utilizes control Lyapunov function (CLF)-and control barrier function (CBF)-based quadratic programs (QPs), and is applicable to a general class of nonlinear affine control systems. The stabilization objective is formulated as a maneuvering problem and integral action is introduced in the CLFs to counteract the effect of unknown irrotational ocean currents. Furthermore, ocean current estimates are constructed for robust CBF design, and analytic conditions under which the estimates guarantee safety are derived. Subsequently, robust CBFs are designed to achieve collision avoidance of static obstacles. The paper concludes by verifying the framework in simulation for a double-ended passenger ferry.
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