Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance

This paper explores the design of hybrid feedback for a class of affine nonlinear systems with topological constraints that prevent global asymptotic stability. A new hybrid control strategy is introduced, which differs conceptually from the commonly used synergistic hybrid approaches. The key idea involves the construction of a generalized synergistic Lyapunov function whose switching variable can either remain constant or dynamically change between jumps. Based on this new hybrid mechanism, a generalized synergistic hybrid feedback control scheme, endowed with global asymptotic stability guarantees, is proposed. This hybrid control scheme is then improved through a smoothing mechanism that eliminates discontinuities in the feedback term. Moreover, the smooth hybrid feedback is further extended to a larger class of systems through the integrator backstepping approach. The proposed hybrid feedback schemes are applied to solve the global obstacle avoidance problem using a new concept of synergistic navigation functions. Finally, numerical simulation results are presented to illustrate the performance of the proposed hybrid controllers.