Observability of nonlinear systems with unmeasured inputs. (1st September 2019)

• Record Type: Journal Article
• Authors: Maes, K.; Chatzis, M.N.; Lombaert, G.
• Is Part Of: Mechanical systems and signal processing. Volume 130(2019)
• Page Start: 378
• Page End: 394
• Publication Date: 2019-09-01
• Subjects: System identification -- Geometric observability -- Observability -- Identifiability -- Invertibility; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.05.010
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: System identification techniques aim at estimating unmeasured states, parameters, and inputs. They can only be successful if the estimated quantities are observable. A method to investigate observability in presence of unmeasured inputs is presented. It applies to nonlinear systems whose state and measurement equations are affine in all inputs. Abstract: This paper presents a geometric algorithm to investigate the theoretical observability of nonlinear systems with partially measured inputs and outputs. The algorithm is based on Lie algebra and applies to systems whose state and measurement equations are analytical and affine in all inputs. It investigates whether the system satisfies a necessary observability condition that is named the Observability Rank Condition for systems with Direct Feedthrough (ORC-DF). The presented algorithm allows to assess the observability of the dynamic system states, the identifiability of constant-in-time parameters, and the ability to track unmeasured inputs, which is referred to as system invertibility. It is also shown how the developed methodology can be extended to investigate the observability of non-smooth systems that can be broken into different smooth branches, often encountered in mechanical applications related to sliding and damage. Possible applications are illustrated with several examples from structural engineering.