A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

Abstract

This article addresses the problem of state and unknown inputs (UIs) estimation for nonlinear systems with arbitrary relative degree with respect to the UIs.For this purpose, a novel nonlinear unknown input observer (UIO) is proposed, which is able to decouple the UIs by using the derivatives of the output signal. The error dynamics is attained by an exact handling and a factorization of its gradient to obtain a local polytopic representation suitable for input-affine nonlinear systems. For that representation, a novel design condition based on convex optimization and linear matrix inequalities is proposed to exponentially stabilize the estimation error and to guarantee the validity of the proposed nonlinear UIO. Numerical simulations indicate the effectiveness of the proposed approach for different classes of nonlinear systems, for which the UIs could be totally decoupled from the state estimation.

Cascade Takagi–Sugeno fuzzy observer design for nonlinear uncertain systems with unknown inputs: A sliding mode approach

“…Recently, an alternative approach to DMVT has been proposed in References 41 and 42. However, the approach in References 41 and 42 requires the derivation of the polynomial forms and their corresponding TS models, which could be possibly confuse the readers if integrated into our TS fuzzy cascaded observer scheme. As a result, we prefer to use the classical DMVT approach to ensure the readability of this paper.…”

“…Remark The differential mean value theorem has been shown as an effective tool to deal with unmeasured nonlinearities in various estimation problems, see for instance 7,17,40 and related references. Recently, an alternative approach to DMVT has been proposed in References 41 and 42. However, the approach in References 41 and 42 requires the derivation of the polynomial forms and their corresponding TS models, which could be possibly confuse the readers if integrated into our TS fuzzy cascaded observer scheme.…”

“…Output: Cascade TS fuzzy observer ( 12), ( 33) and ( 40), UI estimator (44), and uncertainty estimator (42).…”

“…e x is estimated by ê x , and 𝜒 = v y is estimated by χ = χ + ê x accordingly. Furthermore, the unknown input d is estimated with (44), and the uncertainty w is estimated with (42).…”

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

“…State estimation of nonlinear systems in the presence of unknown inputs (UIs) has received increasing research attention. The main reason is that, within di↵erent application contexts, unknown inputs can be seen as unmodeled dynamics, faults in engineering systems, uncertain disturbances, and attack signals in secure communication or cyber-physical systems [1,2,3,4,5,6]. Consequently, simultaneous estimation of the state of a dynamical system and its unknown input has become a key aspect in several practical applications [7,8,9].…”