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arXiv 2104.01385eess.SYcs.SY
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非线性系统时序逻辑控制的规范指导框架

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

Yinan Li, Zhibing Sun, Jun Liu

摘要:

提出了一种基于线性时序逻辑(LTL)规范的非线性系统控制规范指导框架。与众所周知的基于抽象的方法相比,所提出的框架直接表征获胜集,即,通过单调算子在系统的连续状态空间上实现给定LTL公式的初始条件集。根据这一特征,提出了一种算法,通过自适应区间细分方案,产生一个有限的记忆控制策略,实际上近似的运营商。我们表明,该算法是健全的完整的LTL规格,和鲁棒完整的规格可识别的确定性Büchi自动机(DBA),后者在这个意义上说,控制策略可以找到只要给定的规格可以满足额外的有界干扰。该方法不需要DBA计算和存储抽象和生成的产品系统,具有更高的内存效率,复杂性分析和性能测试证明了这一点。一个预处理阶段也被设计来减少计算成本,通过分解的规格。我们表明,所提出的方法可以有效地解决现实世界的控制问题,如喷气发动机压缩机控制和运动规划的机械手和移动机器人。

英文摘要:

This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and robustly complete for specifications recognizable by deterministic Büchi automata (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A pre-processing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems such as jet engine compressor control and motion planning for manipulators and mobile robots.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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