Simultaneous state and input estimation with partial information on the inputs

Abstract

This paper investigates the problem of simultaneous state and input estimation (SSIE) for discrete-time linear stochastic systems when the information on the inputs is partially available. To incorporate the partial information on the inputs, matrix manipulation is used to obtain an equivalent system with reduced-order inputs. Then Bayesian inference is drawn to obtain a recursive filter for both state and input variables. The proposed filter is an extension of the recently developed state filter with partially observed inputs to the case where the input filter is also of interest, and an extension of the SSIE to the case where the information on the inputs is partially available. A numerical example is given to illustrate the proposed method. It is shown that, due to the additional information on the inputs being incorporated in the filter design, the performances of both state and input estimation are substantially improved in comparison with the conventional SSIE without partial input information.

Anti‐disturbance control for nonlinear system via adaptive disturbance observer

“…In practical engineering, it is worth pointing out that various disturbances are inevitable, which may affect the control precision and even destabilize the system. Hence, the problems of disturbance attenuation and anti-disturbance control have been widely researched [1][2][3], and many methods have been proposed, such as H 1 control [4][5][6], filter design [7][8][9], adaptive algorithm [10][11][12], and internal model approach [13].…”

Reduced-order disturbance observer design for discrete-time linear stochastic systems

“…On the other hand, to relax the assumption on disturbances and incorporate noise information for stochastic systems, Gillijns and De Moor (2007) proposed a simultaneous state and disturbance observer on the basis of Darouach and Zasadzinski (1997) using the Minimum-VarianceUnbiased-Estimation (MVUE) method. Later, Su et al (2015b) extends the results to the case where information on the disturbances is available at an aggregate level (Li (2013)). The assumption that the states are fully estimable inevitably restricts the applications of the FODOs (see, Su et al (2015a) for the existing condition of this kind of filter).…”

“…The conventional disturbance observers assume that all the system states are estimable or even directly measurable (e.g., Chen et al (2000); Kim et al (2010); Su et al (2015b)), and consequently the disturbance estimation is dependent on the estimated system states. For example, the researchers in Ohishi et al (1987) proposed a DO by treating the disturbances as additional states and estimating them using a deadbeat function observer (Kimura (1978)) under the assumption that the augmented systems are completely observable and the disturbances can be approximated by known transition dynamics.…”

“…Based on the availability of the state information, the existing DOs can be broadly classified into three categories: (a) full measurable state based DOs (e.g., Chen et al (2000); Kim et al (2010)); (b) full state estimation based DOs (termed as FODOs) (e.g., Gillijns and De Moor (2007) ;Fang et al (2013); Su et al (2015b)); and (c) reduced-order state function estimation based DOs (termed as RODOs) (e.g., Xiong and Saif (2003); Kim and Rew (2013)). …”

On Relationship Between Time-Domain and Frequency-Domain Disturbance Observers and Its Applications

“…There are two distinct approaches for linear systems including time-domain DOBs [9][10][11] and frequency-domain DOBs [1,12,13]. The time-domain DOB firstly appeared in the late 1960s when Johnson [9] first developed the Disturbance Accommodating Control by proposing Unknown Input Disturbance Observer (UIDO).…”