Explicit model predictive control is an established methodology for the offline determination of the optimal control policy for linear discrete time-invariant systems with linear constraints. Nevertheless, nonlinearities in the form of quadratic constraints naturally appear in process models or are imposed for stability purposes in model predictive control formulations. In this manuscript, we present the theoretical developments and propose an algorithm for the exact solution of explicit nonlinear model predictive control problems with convex quadratic constraints. Our approach is based on a second-order Taylor approximation of Fiacco’s Basic Sensitivity Theorem, which allows for the existence and the analytic derivation of the optimal control actions. The complete exploration of the parameter space is founded on an active set strategy, which employs a pruning criterion to eliminate infeasible active sets. Based on that, the optimal map of solutions is constructed along with the corresponding control actions. The proposed strategy is applied to an explicit nonlinear model predictive control problem with an ellipsoidal terminal set, and comparisons with approximate solutions are drawn to demonstrate the benefits of the presented approach. Furthermore, as a practical application, the optimal operation of a chemostat in the presence of disturbances is exhibited.

显式模型预测控制是一种离线确定具有线性约束的线性离散时不变系统的最优控制策略的方法。然而，二次约束形式的非线性自然会出现在过程模型中，或者出于稳定性目的在模型预测控制公式中被强加。在这份手稿中，我们介绍了理论发展并提出了一种用于精确求解具有凸二次约束的非线性模型预测控制问题的算法。我们的方法基于Fiacco基本灵敏度定理的二阶泰勒逼近，它允许最优控制动作的存在和解析推导。对参数空间的全面探索是建立在主动集策略的基础之上的，它采用修剪标准以消除不可行的活动集。在此基础上，构建了最优解图以及相应的控制动作。将所提出的策略应用于具有椭圆形终端集的显式非线性模型预测控制问题，并与近似解进行比较，以证明所提出方法的优点。此外，作为实际应用，在存在干扰的情况下，显示了稳定器的最佳操作。并与近似解决方案进行了比较，以证明所提出方法的好处。此外，作为实际应用，在存在干扰的情况下，显示了稳定器的最佳操作。并与近似解决方案进行了比较，以证明所提出方法的好处。此外，作为实际应用，在存在干扰的情况下，显示了稳定器的最佳操作。