This paper proposes a computationally effective predictive control algorithm for continuous-time, constrained nonlinear systems. The basic idea of the algorithm is to construct off-line a feasible and stable direction for the predictive controller via control Lyapunov functions (CLFs); and solve on-line the optimal step of the direction. Thus, the computational demand of the online optimization relies on the dimension of the step and is independent on the predictive horizon when the optimization is solved by numerical approaches. Furthermore, the feasibility and stability properties of the algorithm are guaranteed by introducing the notion of regional stability. Finally, a numerical simulation is utilized to illustrate the effectiveness of the mentioned algorithm.
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