Observer design for stochastic time‐delayed Markovian jump systems with incomplete transition rates and actuator saturation

This article focuses on the finite‐time sampled‐data H∞ control problem of Markovian jumping linear system, which consists of mode‐dependent interval time‐varying delays. The delay‐dependent conditions of finite‐time sampled‐data control are obtained by adopting affine Bessel–Legendre inequality and appropriate mode‐dependent Lyapunov–Krasovskii functional. Finally, two examples are displayed to prove the feasibility of the proposed method.

Section: Introductionmentioning

confidence: 99%

“…Through Markovian chains, MJSs could realize the communication between the interconnected subsystems 4 . MJSs are used in several spheres, such as network control systems, mobile multi‐agent systems, and aerospace industry 5‐8 . Hence, the stability of MJSs with time‐varying delays has been investigated extensively.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time sampled‐data H∞ control of Markovian jumping linear systems with mode‐dependent time‐varying delays

Wang

et al. 2022

“…State estimation belongs to a kind of methodology that the internal state of a dynamic system is estimated by using measurable system measurement output 1 . Due to the well‐known effectiveness of state estimation, it has been playing an important role in a large number of control processes, for example, References 2,3.…”

Section: Introductionmentioning

confidence: 99%

“…State estimation belongs to a kind of methodology that the internal state of a dynamic system is estimated by using measurable system measurement output. 1 Due to the well-known effectiveness of state estimation, it has been playing an important role in a large number of control processes, for example, References 2,3. In the meantime, it also attracts a quantity of researchers to investigate the problem of state estimation of nonlinear systems, especially for the reason that most of industrial plants can be provided with complex nonlinear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Enhanced fuzzy state estimation of discrete‐time nonlinear systems via a multi‐instant united switch‐type observer

Xie

Liu

2021

The performance of state estimation of discrete‐time Takagi–Sugeno systems is enhanced by proposing a featured multiinstant united switch‐type observer. The novelty of the proposed observer lies in both the definition and application of a set of switching modes. Since different time‐variant free matrices can be for the first time introduced in accordance with each switching mode, both the current time and the past time normalized fuzzy weighting functions are together considered for designing the corresponding observer gain matrices with much less conservatism than those recent methods reported in the literature. Furthermore, there are only two tuning parameters which are both located in a limited candidate set and thus this fact does benefit for giving the optimal solution of our developed multiinstant united switch‐type candidates. Finally, numerical comparisons are provided in order to verify the technical superiority of the results developed in this article.

“…Nonlinear physical dynamics have been extended to regime‐switching counterparts 25 . Permanence and extinction of tumor under a randomly switching environment have been analyzed in Xia et al 26 Optimal control of delayed systems has been studied in Qin et al 27 Solute transport phenomena in vegetated watercourses have been considered as regime‐switching diffusion processes 28…”

Section: Introductionmentioning

confidence: 99%

A hybrid stochastic river environmental restoration modeling with discrete and costly observations

Yoshioka

Tsujimura

Hamagami

et al. 2020

Summary A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This setting harmonizes with real problems because continuously obtaining environmental and ecological information is difficult, and is often costly. The main problem is to decide when and how much of the sediment should be supplied into a river environment to effectively suppress bloom of benthic algae. The interventions are allowed only at observation times. Finding the optimal river restoration policy ultimately reduces to solving an optimality equation in an unconventional form due to the observation cost and discrete observations. We show its unique solvability and present a connection with degenerate parabolic partial differential equations, with which we can construct an effective algorithm for its approximation. An uncertainty‐averse optimization problem is also considered as an advanced problem. Coefficients and parameter values are identified from experimental and observation results to numerically compute the optimal restoration policy of an existing river environment with and without uncertainty.