2020/03/17 by Matthew Abate, Abate, Matthew, Maxence Dutreix +3
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #Extremum Seeking Control Systems #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2003.07975
openalex publication_date 2020/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The vector field of a mixed-monotone system is decomposable via a\ndecomposition function into increasing (cooperative) and decreasing\n(competitive) components, and this decomposition allows for, e.g., efficient\ncomputation of reachable sets and forward invariant sets. A main challenge in\nthis approach, however, is identifying an appropriate decomposition function.\nIn this work, we show that any continuous-time dynamical system with a\nLipschitz continuous vector field is mixed-monotone, and we provide a\nconstruction for the decomposition function that yields the tightest\napproximation of reachable sets when used with the standard tools for\nmixed-monotone systems. Our construction is similar to that recently proposed\nby Yang and Ozay for computing decomposition functions of discrete-time systems\n[1] where we make appropriate modifications for the continuous-time setting and\nalso extend to the case with unknown disturbance inputs. As in [1], our\ndecomposition function construction requires solving an optimization problem\nfor each point in the state-space; however, we demonstrate through example how\ntight decomposition functions can sometimes be calculated in closed form. As a\nsecond contribution, we show how under-approximations of reachable sets can be\nefficiently computed via the mixed-monotonicity property by considering the\nbackward-time dynamics.\n