Zonotope-based Symbolic Controller Synthesis for Linear Temporal Logic Specifications
arxiv(2024)
摘要
This paper studies the controller synthesis problem for nonlinear control
systems under linear temporal logic (LTL) specifications using zonotope
techniques. A local-to-global control strategy is proposed for the desired
specification expressed as an LTL formula. First, a novel approach is developed
to divide the state space into finite zonotopes and constrained zonotopes,
which are called cells and allowed to intersect with the neighbor cells.
Second, from the intersection relation, a graph among all cells is generated to
verify the realization of the accepting path for the LTL formula. The
realization verification determines if there is a need for the control design,
and also results in finite local LTL formulas. Third, once the accepting path
is realized, a novel abstraction-based method is derived for the controller
design. In particular, we only focus on the cells from the realization
verification and approximate each cell thanks to properties of zonotopes. Based
on local symbolic models and local LTL formulas, an iterative synthesis
algorithm is proposed to design all local abstract controllers, whose existence
and combination establish the global controller for the LTL formula. Finally,
the proposed framework is illustrated via a path planning problem of mobile
robots.
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