手把手教做无人驾驶算法（二十七）--关于MPC扰动不变集的分析

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已于 2022-05-08 18:07:04 修改 · 3.4k 阅读

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#算法 #自动驾驶

于 2022-05-08 18:00:30 首次发布

该博客探讨了在控制系统中计算扰动不变集的问题，它涉及到无限的Minkowski加法和近似计算。作者通过示例代码展示了如何使用Matlab进行扰动线性系统的建模，并利用LQR控制器确保状态始终保持在扰动不变集内。此外，还引用了相关论文作为更复杂计算的参考。

Disturbance invariant set

I think one may get stuck at computation of what paper [1] called "disturbance invariant set". The disturbance invariant set is an infinite Minkowski addition Z = W ⨁ Ak*W ⨁ Ak^2*W..., where ⨁ denotes Minkowski addition. Obtaining this analytically is impossible, and then, what comes ones' mind first may be an approximation of that by truncation: Z_approx = W ⨁ Ak*W...⨁ Ak^n*W. This approximation, however, leads to Z_approx ⊂ Z, which means Z_approx is not disturbance invariant. So, we must multiply it by some parameter alpha and get Z_approx = alpha*(W ⨁ Ak*W...⨁ Ak^n*W) so that Z ⊂ Z_approx is guaranteed. (see example/Disturban