The problem of achieving a good trade-off in Stochastic Model PredictiveControl between the competing goals of improving the average performance andreducing conservativeness, while still guaranteeing recursive feasibility andlow computational complexity, is addressed. We propose a novel, lessrestrictive scheme which is based on considering stability and recursivefeasibility separately. Through an explicit first step constraint we guaranteerecursive feasibility. In particular we guarantee the existence of a feasibleinput trajectory at each time instant, but we only require that the inputsequence computed at time $k$ remains feasible at time $k+1$ for mostdisturbances but not necessarily for all, which suffices for stability. Toovercome the computational complexity of probabilistic constraints, we proposean offline constraint-tightening procedure, which can be efficiently solved viaa sampling approach to the desired accuracy. The online computationalcomplexity of the resulting Model Predictive Control (MPC) algorithm is similarto that of a nominal MPC with terminal region. A numerical example, whichprovides a comparison with classical, recursively feasible Stochastic MPC andRobust MPC, shows the efficacy of the proposed approach.
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机译：解决了在提高平均性能和降低保守性的竞争目标之间，同时仍保证递归的可行性和较低的计算复杂度之间，在随机模型PredictiveControl中实现良好折衷的问题。我们提出了一种新颖的，较少限制的方案，该方案基于分别考虑稳定性和递归可行性。通过明确的第一步约束，我们保证了递归的可行性。特别地，我们保证在每个时刻都存在可行的输入轨迹，但是我们只要求在时间$ k $上计算的输入序列在时间$ k + 1 $上对于大多数扰动而言仍然是可行的，但不一定对所有扰动都足够，这足以保证稳定性。为了克服概率约束的计算复杂性，我们提出了一种离线约束严格程序，可以通过采样方法有效地解决该问题，以达到所需的精度。最终的模型预测控制（MPC）算法的在线计算复杂性类似于带有终端区域的标称MPC的在线计算复杂性。数值示例提供了与经典的，递归可行的随机MPC和稳健MPC的比较，表明了该方法的有效性。
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