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从线性可解最优控制到轨迹优化(希望)返回

From linearly-solvable optimal control to trajectory optimization, and (hopefully) back
课程网址: http://videolectures.net/cyberstat2012_todorov_optimal_control/  
主讲教师: Emanuel Todorov
开课单位: 华盛顿大学
开课时间: 2012-10-16
课程语种: 英语
中文简介:
在指数最优值函数满足线性方程的意义上,我们已经确定了一类具有内在线性的随机最优控制问题。这些问题具有许多独特的性质,这使得数值方法比通用配方更有效。然而,经过几次尝试超越这个文献的简单数值例子和规模到现实世界的问题(特别是机器人技术),我们意识到维度的诅咒仍然是一个诅咒。然后我们绕道而行,开发了轨迹优化方法,可以完全自动地合成非常复杂的行为。由于现代计算机的并行处理能力,这些方法中的一些在模型预测控制(MPC)模式中实时工作,从而产生隐式定义的反馈控制定律。但并非所有问题都可以通过这种方式解决,而且以某种方式重新使用MPC生成的本地解决方案会更好。下一步是结合这两种方法的优势:使用轨迹优化来识别最佳控制的随机系统可能花费时间的状态空间区域,然后应用限制于这些区域的线性可解的最优控制。
课程简介: We have identified a general class of stochastic optimal control problems which are inherently linear, in the sense that the exponentiated optimal value function satisfies a linear equation. These problems have a number of unique properties which enable more efficient numerical methods than generic formulations. However, after several attempts to go beyond the simple numerical examples characteristic of this literature and scale to real-world problems (particularly in robotics), we realized that the curse of dimensionality is still a curse. We then took a detour, and developed trajectory optimization methods that can synthesize remarkably complex behaviors fully automatically. Thanks to the parallel processing capabilities of modern computers, some of these methods work in real time in model-predictive-control (MPC) mode, giving rise to implicitly defined feedback control laws. But not all problems can be solved in this way, and furthermore it would be nice to somehow re-use the local solutions that MPC generates. The next step is to combine the strengths of these two approaches: using trajectory optimization to identify the regions of state space where the optimally-controlled stochastic system is likely to spend its time, and then applying linearly-solvable optimal control restricted to these regions.
关 键 词: 线性方程; 随机最优控制; 机器人技术
课程来源: 视频讲座网
最后编审: 2020-06-29:cxin
阅读次数: 90