Observers for interconnected nonlinear and linear systems

Abstract

In this paper we begin by assuming that an observer with a corresponding quadratic-type Lyapunov function has been designed for a given nonlinear system. We then consider the problem that arises when the output of that nonlinear system is not directly available; instead, it acts as an input to a second, linear system from which a partial-state measurement is in turn available. We develop an observer design methodology for the resulting cascade interconnection, based on estimating the unavailable output together with the states of the linear system. We also extend this methodology to a more general class of feedback-interconnected systems. Under a set of technical assumptions, the overall error dynamics is proven to be globally exponentially stable if the gains are chosen to satisfy an H ∞ condition. We illustrate application of the methodology by considering a navigation example based on integration of inertial and satellite measurements.

A uniformly semiglobally exponentially stable nonlinear observer for GNSS- and camera-aided inertial navigation

“…However, U is also function of P , that depends on γ. Given that γ → 0 as ∆ → ∞ and the eigenvalues of P have the same rate of convergence to zero [22], [24], both k 1 and k 2 are functions of γ of the same order for the scope of (15), which is thus verified. All hypotheses of theorem 2 from [23] are satisfied, so it can be concluded that the origin of the error dynamics (10)- (12) is USGES.…”

“…As reported in [22], there is a function W =w T Pw, with P positive definite, such thatẆ ≤ − w 2 + γ 2 d 2 , whered is defined as in (11) and…”

Decentralized Stabilization for a Class of Continuous-Time Nonlinear Interconnected Systems Using Online Learning Optimal Control Approach

“…, for the N isolated subsystems (4). In the following, we will show that by proportionally increasing some local feedback gains, a stabilizing decentralized control scheme can be established for the interconnected system (1).…”

Nonlinear observer with time-varying gains for inertial navigation aided by satellite reference systems in dynamic positioning

“…A direct attitude measurement was not needed in Hua [7] and Roberts and Tayebi [11] where the INS/GNSS integration was carried out with linear GNSS velocity measurements together with inertial and magnetometer measurements. More recently, Grip et al [12] estimated position, velocity and attitude by utilizing a rotation matrix as attitude representation with the framework of interconnected observers from [13]. The origin of the INS/GNSS integration error dynamics was proven to be global exponential stable.…”