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Alternative strategies for designing stabilizing model predictive controllers

In this article, we propose two stabilizing discrete-time model predictive control (MPC) strategies, which are alternatives to other classical (e.g. terminal cost/constraint-based) approaches. Both proposed strategies take advantage of a known stabilizing controller and its associated Lyapunov function. The first strategy allows optimization of an arbitrary cost function at each stage, but guarantees stability by enforcing a decrease in the known Lyapunov function at the first step of each MPC state. The second strategy uses an averaged/summed Lyapunov function as the objective function. A combined strategy that enforces a decrease in a summed Lyapunov function while optimizing an arbitrary cost is also considered. The proposed strategies are applied to an example drawn from the class of linear systems subject to actuator saturation constraints.