SIAM Journal on Control and Optimization, Volume 58, Issue 5, Page 2979-2996, January 2020.
We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed---even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose constructing the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymptotically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability---a condition relating the current state, the stage cost, and the growth of the value function with respect to time---for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.

中文翻译：

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模型预测控制，成本可控制性和同质性

SIAM控制与优化杂志，第58卷，第5期，第2979-2996页，2020年1月。
我们关注模型预测控制（MPC）方案的设计，以确保最终闭环的渐近稳定性-即使在所需设定点处的线性化无法稳定也是如此。因此，我们建议基于齐次逼近构造阶段成本，并严格证明，如果齐次逼近是渐近零可控制的，则应用MPC会产生渐近稳定的闭环行为。为此，我们验证此类系统的成本可控制性-一种与当前状态，阶段成本和价值函数相对于时间的增长相关的条件-以便为以下系统提供稳定性和性能保证建议的MPC方案，而不会稳定终端成本或限制。