|عنوان فارسی مقاله:||برنامه ناظر وضعيت فاصله برای سیستمهای متفاوت غیرخطی زمان|
|عنوان انگلیسی مقاله:||Interval State Observer for Nonlinear Time Varying Systems|
|رشته های مرتبط:||مهندسی صنایع، تحلیل سیستم ها و بهینه سازی سیستم ها|
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This paper is devoted to design of interval observers for Linear Time Varying (LTV) systems and a class of nonlinear time-varying systems in the output canonical form. An interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable. It is shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The efficiency of the proposed approach is demonstrated through numerical simulations.
The problem of unmeasurable state vector estimation is very challenging and its solution is demanded in many applications , , . In some situations due to presence of uncertainty (parametric or/and signal) the design of a conventional pointwise estimator, converging in the noise-free case to the ideal value of the state, is not possible. However, an interval estimation remains feasible. By interval or set-membership estimation we understand an observer that, using input-output information, computes an outer-approximation of the set of admissible values (interval) for the state at each instant of time. Another group of applications deals directly with evaluation of the set of admissible values for the state of an uncertain system (it can be the estimation goal in some fault detection systems, in biology or chemistry), the interval observers were proposed as a solution of this problem . There are several approaches to design interval observers , , , . This paper continues the framework of interval observer design based on the monotone system theory , . That approach has been recently extended in  to nonlinear systems using Linear-Parameter-Varying (LPV) representation with known minorant and majorant matrices, and in  for observable nonlinear systems. One of the most complex assumptions for the interval observer design, dealing with cooperativity of the interval estimation error dynamics, was relaxed in , . It was shown that under some mild conditions applying similarity transformation, a Hurwitz matrix could be transformed to Hurwitz and Metzler (cooperative). The transformation matrix is a solution of the Sylvester equation, a constructive procedure for this solution calculation was also given in . The objective of this work is to develop the approach of interval observer design to the systems with non-constant matrices dependent on measurable input-output signals and time. In order to solve this problem an extension of the result from  is presented, that allows us to calculate a constant similarity transformation matrix representing a given interval of matrices to an interval of Metzler matrices. This result can be used to design interval observers for LPV systems with measurable vector of scheduling parameters , ,  or LTV systems, that is the main novelty of the work. Two examples of such systems are considered in this work: LTV system and the Lorenz chaotic model (as a nonlinear system in the output canonical form).