Abstract
We provide extensions to the new flexible-step model predictive control (MPC) scheme, which is based on the idea of generalized discrete-time control Lyapunov functions. These facilitate the implementation of a flexible number of control inputs in each iteration of the MPC scheme. We present relaxed recursive feasibility and stability results and provide a converse Lyapunov result. These results combined simplify the design of the flexible-step MPC scheme. We demonstrate the capabilities of the flexible-step MPC algorithm for a nonholonomic system, where the standard one-step implementation may suffer from lack of asymptotic convergence.
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