Abstract We consider a finite-horizon continuous-time optimal control problem with nonlinear dynamics, an integral cost, control constraints and a time-varying parameter which represents perturbations or uncertainty. After discretizing the problem we employ a Model Predictive Control (MPC) approach by first solving the problem over the entire remaining time horizon and then applying the first element of the optimal discrete-time control sequence, as a constant in time function, to the continuous-time system over the sampling interval. Then the state at the end of the sampling interval is measured (estimated) with certain error, and the process is repeated at each step over the remaining horizon. As a result, we obtain a piecewise constant function of time representing MPC-generated control signal. Hence MPC turns out to be an approximation to the optimal feedback control for the continuous-time system. In our main result we derive an estimate of the difference between the MPC-generated state and control trajectories and the optimal feedback generated state and control trajectories, both obtained for the same value of the perturbation parameter, in terms of the step-size of the discretization and the measurement error. Numerical results illustrating our estimate are reported.

中文翻译：

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通过模型预测控制逼近最优有限水平反馈

摘要 我们考虑具有非线性动力学、积分成本、控制约束和表示扰动或不确定性的时变参数的有限范围连续时间最优控制问题。在对问题进行离散化后，我们采用模型预测控制 (MPC) 方法，首先在整个剩余时间范围内解决问题，然后将最优离散时间控制序列的第一个元素（作为时间函数的常数）应用于连续- 采样间隔内的时间系统。然后以一定的误差测量（估计）采样间隔结束时的状态，并在剩余范围内的每一步重复该过程。结果，我们获得了代表 MPC 生成的控制信号的分段常数函数。因此 MPC 被证明是连续时间系统最优反馈控制的近似。在我们的主要结果中，我们推导出了 MPC 生成的状态和控制轨迹与最佳反馈生成的状态和控制轨迹之间的差异的估计，两者都是针对相同的扰动参数值获得的，就扰动参数的步长而言离散化和测量误差。报告了说明我们估计的数值结果。在离散化的步长和测量误差方面。报告了说明我们估计的数值结果。在离散化的步长和测量误差方面。报告了说明我们估计的数值结果。