论文标题
使用凸限制的非线性系统的强大模型预测控制
Robust Model Predictive Control for Nonlinear Systems Using Convex Restriction
论文作者
论文摘要
我们提出了一种算法，以考虑不确定性和安全性限制，用于鲁棒模型预测性控制。我们的框架考虑了一个非线性动力学系统，但受到未知但不确定性集的干扰。通过将系统视为操作员对轨迹作用的固定点，我们提出了一个控制措施的凸条件，以确保对不确定性集的安全性。提议的条件保证了国家轨迹的所有实现都满足安全限制。我们的算法解决了大小为n*n的凸二次约束优化问题的序列，其中n是状态的数量，n是模型预测性控制问题中的预测范围。与现有方法相比，我们的方法解决了凸问题，同时保证所有不确定性集的实现都不会违反安全限制。此外，我们考虑了系统动力学的隐式时间消费，以增加预测范围并提高计算准确性。车辆导航的数值模拟证明了我们方法的有效性。
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set. By viewing the system as a fixed point of an operator acting over trajectories, we propose a convex condition on control actions that guarantee safety against the uncertainty set. The proposed condition guarantees that all realizations of the state trajectories satisfy safety constraints. Our algorithm solves a sequence of convex quadratic constrained optimization problems of size n*N, where n is the number of states, and N is the prediction horizon in the model predictive control problem. Compared to existing methods, our approach solves convex problems while guaranteeing that all realizations of uncertainty set do not violate safety constraints. Moreover, we consider the implicit time-discretization of system dynamics to increase the prediction horizon and enhance computational accuracy. Numerical simulations for vehicle navigation demonstrate the effectiveness of our approach.
