Adaptive variable structure state estimation for uncertain systems with persistently bounded disturbances

Abstract

SUMMARYThis paper develops an adaptive state estimator design methodology for nonlinear systems with unknown nonlinearities and persistently bounded disturbances. In the proposed estimation scheme, the boundary layer strategy in variable structure techniques is utilized to design a continuous state estimator such that the undesirable chattering phenomenon is avoided; and the adaptive bounding technique is used for online estimation of the unknown bounding parameter. The existence condition of the adaptive estimators is provided in terms of linear matrix inequality (LMI). Since the orthogonal projection of the state estimation error onto the null space of the linear measurement distribution matrix is used in the derivation process, the update law of bounding parameter estimate is represented in terms of the available measurement error. The proposed estimator can ensure that the state estimation error is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal adaptive state estimator can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method.

Stability Analysis of a Multilink Flexible Manipulator: Nonlinear Observers

“…We can choose some sufficient small positive constants ε 5 = 0.8055, ε 6 = 10.1072, ε 7 = 12.4537, ε 8 …”

“…At many special situations, without some consideration of these dynamics problems in the total control system design, the measurements used for feedback control will often be not adequate enough for acceptable control system performance. However, the relevant robust state estimation (filtering) problem [1,8,9] has been studied extensively for nonlinear systems.…”

“…More recently, it is worth noting that for FMs, the system uncertainties, nonlinearities, and disturbances are unavoidable in modeling of dynamic system [9,[16][17][18], so the robust observer design problems are not easy to derive. In order to preserve the observer action under system uncertainties as well as nonlinearities, various methods to design of robust state observers (estimation or filtering), such as algebraic, geometric, generalized inverse, and variable structure observer (VSO) techniques have been used to the observer design in [8,12,19,20]. In many practice applications, the design of robust nonlinear observers is close to the actual dynamic behavior of nonlinear systems with uncertainty disturbance rather than linear observers.…”

A variational characterization of the sliding mode control processes

“…Moreover, the developed analytic tool and results related to the variable structures systems (VSSs) constitute a valuable part of the modern systems theory. We refer to [9], [12], [13], [20], [25], [29], [30], [33], [35], [36], [37], [38], [39], [40] for the basic facts and also for some interesting real world uses of the sliding mode techniques.…”

State estimation for asynchronous multirate multisensor nonlinear dynamic systems with missing measurements

“…In recent years, networked control systems and sensor technology has witnessed extraordinary growth [1][2][3][4]. The state estimation problem for time delay [1][2][3], asynchronous [5], or uncertain system with bounded noises [6] are studied for effective networked control, whereas most of the literatures assumed that the systems are linear. In engineering, most of the real systems are nonlinear.…”