论文标题
无约束模型预测控制的局部稳定性和收敛性
Local Stability and Convergence of Unconstrained Model Predictive Control
论文作者
论文摘要
研究了基于线性时间存在植物模型的无约束非线性动力学模型预测控制（MPC）的局部稳定性和收敛性。根据Riccati微分方程（RDE）解决方案的长期行为，得出了明确的误差估计，该误差估计明确证明了MPC中两个关键参数的影响：预测范围$ t $和控制范围$τ$。特别是，如果MPC控制器可以访问精确的（线性）植物模型，则MPC控制和相应的最佳状态轨迹在$ T-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-traption $ t-t-τ\ rightArrow \ rightarrow \ infty $时，将无限 - horizon-Horizon Optimal最佳控制问题的解决方案呈指数收敛。当线性模型和非线性植物之间的差异在原点附近足够小时，MPC策略正在局部稳定，并且可以通过选择控制范围$τ$较小来减少建模误差的影响。获得的收敛速率在数值模拟中得到验证。
The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based on a linear time-invariant plant model is studied. Based on the long-time behavior of the solution of the Riccati Differential Equation (RDE), explicit error estimates are derived that clearly demonstrate the influence of the two critical parameters in MPC: the prediction horizon $T$ and the control horizon $τ$. In particular, if the MPC-controller has access to an exact (linear) plant model, the MPC-controls and the corresponding optimal state trajectories converge exponentially to the solution of an infinite-horizon optimal control problem when $T-τ\rightarrow \infty$. When the difference between the linear model and the nonlinear plant is sufficiently small in a neighborhood of the origin, the MPC strategy is locally stabilizing and the influence of modeling errors can be reduced by choosing the control horizon $τ$ smaller. The obtained convergence rates are validated in numerical simulations.
