We propose a model predictive control (MPC) framework to generate feedback controls for time-varying nonlinear systems with input constraints. One of the main features of this framework is to allow the feedback laws to be discontinuous and thereby enlarge the class of nonlinear systems that can be stabilized by continuous-time MPC. We consider a continuous-time MPC framework and perform a continuous-time stability analysis while considering that the inter-sampling times are nonzero and that the open-loop optimal control problems are solved at every sampling instant. The feedback law generated by MPC is not a function of the state at every instant of time, rather it is a function of the state at the last sampling instant. The trajectories resulting from this "sampling-feedback" are well-defined even when the feedback is discontinuous. Important classes of nonlinear systems that could not be stabilized by a continuous feedback, such as nonholonomic systems, can now be addressed in a continuous-time MPC framework.
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