Passivity-based control design frameworks for hybrid nonlinear time-varying dynamical systems

This article proposes two novel passivity-based control design frameworks for hybrid nonlinear dynamical systems involving an interacting mixture of continuous-time and discrete-time dynamics whose dynamical properties evolve periodically over time. By deriving the Kalman-Yakubovich-Popov (KYP) conditions characterizing dissipativeness for hybrid nonlinear time-dependent dynamical systems, a hybrid computational algorithm, which alternates between continuous-time and discrete-time subsystems at an appropriate sequence of time instants, is then proposed to solve the resultant equations in an interacting manner. Two passivity-based control schemes are then developed by utilizing the foregoing KYP conditions in tandem with the passivity theorem. The overall framework consists mainly of three steps. The hybrid output dynamics of the plant are first determined judiciously to satisfy the passivity specifications. A hybrid nonlinear controller is then designed to meet the input strict passivity requirements. The stability of the closed-loop system is finally established by interconnecting the plant and the controller through negative feedback. Practical considerations for appropriately implementing the derived hybrid algorithms are then discussed in detail. The efficacy of the proposed control schemes is ultimately assessed via a multi-dimensional system with a hybrid source of actuation.