Optimal Control of Differentially Flat Systems is Surprisingly Simple
Optimal Control of Differentially Flat Systems is Surprisingly Simple
复制标题
差动平坦系统的最优控制出奇地简单
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Andreas A. Malikopoulos
中科院分区：
文献类型：
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作者：
Logan E. Beaver;Andreas A. Malikopoulos
随着我们转向日益复杂的网络物理系统（CPS），需要新的方法来实时规划有效的状态轨迹。在本文中，我们提出了一种方法，以显着降低解决一类CPS的最优控制问题的复杂性。我们利用微分不变性的性质来简化欧拉-拉格朗日方程，这种简化消除了一般情况下出现的数值不稳定性。我们还提出了一个显式的微分方程，描述了最优状态轨迹的演变，我们扩展我们的结果，考虑无约束和约束的情况下。此外，我们通过在有障碍物的环境中为双积分代理生成最佳轨迹来证明我们的方法的性能。在模拟中，我们的方法显示了30%的成本降低和近3倍的计算速度相比，现有的搭配为基础的最优控制库。
—As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS. We exploit the property of differential flatness to simplify the Euler-Lagrange equations, and this simplification eliminates the numerical instabilities that arise in the general case. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a double-integrator agent in an environment with an obstacle. In simulation, our approach shows a 30% cost reduction and nearly a 3-fold increase in computational speed compared to existing collocation-based optimal control libraries.