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Dynamical system learning using extreme learning machines with safety and stability guarantees
International Journal of Adaptive Control and Signal Processing ( IF 3.9 ) Pub Date : 2021-03-26 , DOI: 10.1002/acs.3237
Iman Salehi 1 , Ghananeel Rotithor 1 , Gang Yao 1 , Ashwin P. Dani 1
Affiliation  

This article presents a continuous dynamical system model learning methodology that can be used to generate reference trajectories for the autonomous systems to follow, such that these trajectories are invariant to a given closed set and uniformly ultimately bounded with respect to an equilibrium point inside the closed set. The autonomous system dynamics are approximated using extreme learning machines (ELM), the parameters of which are learned subject to the safety constraints expressed using a reciprocal barrier function, and the stability constraints derived using a Lyapunov analysis in the presence of the ELM reconstruction error. This formulation leads to solving a constrained quadratic program (QP) that includes a finite number of decision variables with an infinite number of constraints. Theorems are developed to relax the QP with infinite number of constraints to a QP with a finite number of constraints which can be practically implemented using a QP solver. In addition, an active sampling methodology is developed that further reduced the number of required constraints for the QP by only evaluating the constraints at a smaller subset of points. The proposed method is validated using a motion reproduction task on a seven degree-of-freedom Baxter robot, where the task space position and velocity dynamics are learned using the presented methodology.

中文翻译:

使用极限学习机进行动态系统学习,安全稳定有保障

本文提出了一种连续动态系统模型学习方法,可用于为自治系统生成要遵循的参考轨迹,使得这些轨迹对于给定的闭集是不变的,并且最终一致地以闭集内的平衡点为界. 自治系统动力学使用极限学习机 (ELM) 进行近似,其参数根据使用互易障碍函数表示的安全约束以及在存在 ELM 重建误差的情况下使用 Lyapunov 分析得出的稳定性约束进行学习。此公式导致求解包含有限数量的决策变量和无限数量的约束的约束二次规划 (QP)。定理被开发以将具有无限数量约束的 QP 松弛为具有有限数量约束的 QP,这可以使用 QP 求解器实际实现。此外,还开发了一种主动采样方法,通过仅评估较小点子集上的约束,进一步减少了 QP 所需的约束数量。使用七自由度 Baxter 机器人上的运动再现任务验证所提出的方法,其中使用所提出的方法学习任务空间位置和速度动力学。开发了一种主动采样方法,通过仅评估较小点子集上的约束,进一步减少了 QP 所需的约束数量。使用七自由度 Baxter 机器人上的运动再现任务验证所提出的方法,其中使用所提出的方法学习任务空间位置和速度动力学。开发了一种主动采样方法,通过仅评估较小点子集上的约束,进一步减少了 QP 所需的约束数量。使用七自由度 Baxter 机器人上的运动再现任务验证所提出的方法,其中使用所提出的方法学习任务空间位置和速度动力学。
更新日期:2021-03-26
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