Observer design for nonlinear systems with discrete-time measurements

Abstract

Abstract-This paper focuses on the development of asymptotic observers for nonlinear discrete-time systems. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that the discrete Newton method, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems, while the continuous Newton method may be employed to obtain a global observer. Furthermore, it is analyzed how the use of Broyden's method in the observer structure affects the observer's performance and its computational complexity. An example illustrates some aspects of the proposed methods; moreover, it serves to show that these methods apply equally well to discrete-time systems and to continuous-time systems with sampled outputs.

Nonlinear PID Predictive Controller

“…Lemma 1 : If the disturbance relative degree, ρ, is well-defined, then there exists a constant, p 0 , such that the estimation,b(t), yielded by the observer (20) and (21) with the design function (25) approaches b(t) exponentially.…”

“…Once the offset estimation is given by the nonlinear observer (20) and (21), the offset b in the NGPC (9) is replaced by its estimateb. Then the NGPC (9) becomes…”

“…The whole closed-loop system consists of the nonlinear observer (20) and (21), the NGPC (9) and the nonlinear system (1). Substituting the NGPC (9) into the nonlinear system (1) and after a series of manipulations, the closed-loop system error equation is given by…”

“…Although the state-space observer/ state feedback approach for GPC advocated by Bitmead, Gevers and Wertz [16] can be adopted, nonlinear GPC at present is a state feedback control strategy since, in general, to design an observer for a nonlinear system is not trivial [19,20].…”

Observers for interconnected nonlinear and linear systems

“…constraints (Açıkmeşe and Corless, 2011); sliding observers (Slotine, Hedrick, and Misawa, 1987;Drakunov, 1992); and moving-horizon estimation (Moraal and Grizzle, 1995). This list is by no means exhaustive, and in addition to general methodologies, application-specific designs proliferate throughout the literature.…”