HMM‐based H_∞ filtering for Markov jump systems with partial information and sensor nonlinearities

Abstract

This work examines the H ∞ filtering issue for Markov jump systems in the circumstances of partial information on Markov chain and randomly occurring sensor nonlinearities. The partial information considered in this work includes partial information on the Markov state, on transition probabilities and on detection probabilities. A hidden Markov model with partially known transition probabilities and detection probabilities is introduced to describe the above partial information phenomenon. The randomly occurring sensor nonlinearities considered in this work depend on the system operating mode. Based on the Lyapunov methodology and the introduced hidden Markov model, some effective H ∞ performance analysis criteria are derived for the filtering error system under the circumstances of partial information and sensor nonlinearities. In addition, the design procedure of the desired hidden Markov model-based filter is established, and finally two examples are used to verify the theoretical results.

Mixed H∞‐based finite‐time passive filtering for a class of uncertain nonlinear singular systems

“…Robust finite‐time sliding mode control, $$$ {H}_{\infty } $$$ controller and observer dynamics of singular system have been studied in References 18 and 19. Robust finite‐time control and dissipative control of singular Markovian jump systems have been concerned in References 20 and 21, respectively. Significantly, the behavior of systems is inseparable within a fixed finite time interval.…”

Finite‐time exponentially extended dissipative filtering for singular time‐delay Markov jump systems with quantized outputs based on hidden Markov mode

“…Some well‐known asynchronous robust control performance such as $$$ {H}_{\infty } $$$, $$$ {l}_2-{l}_{\infty } $$$ and extended dissipativity were reported one after another, see, for example, References 17‐19. The exploration of asynchronous filters for discrete time Markov jump neural networks can be found in References 20 and 21 and for switched systems in References 22 and 23. The corresponding counterpart of continuous time asynchronous filter was shown in Reference 24.…”

Extended dissipative-based state estimation for Markov jump coupled neural networks with reaction-diffusion terms

“…On another research forefront, Markov jump systems, an important stochastic models composed of a limited number of dynamical modes, that can more accurately describe real systems with random changes in structure and parameters, such as the broken components, suddenly aggravated environmental disturbances, and changes in subsystem interconnections, and so forth. Markov jump systems have been studied in many works, for example control issues (Jiang et al, 2020; Li et al, 2019; Wu et al, 2019c), stability and stabilization (Yan et al, 2017), H ∞ filtering (Li et al, 2020; Wu et al, 2019a), and so on. Similarly, many NNs have finite number discrete modes, and the switching law among these different modes satisfies the Markov property.…”