Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

Abstract

In this article, the H∞ state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the H∞ performance requirement is satisfied. According to the obtained analysis results, the desired H∞ state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.

LMI-Based Stubborn and Dead-Zone Redesign in Linear Dynamic Output Feedback

“…Summing up the above sector condition with inequality (22) and with (21), we obtain the following bound…”

“…In fact, [13] and [16] initially motivated the construction of these nonlinear redesigns in the context of linear observers. Later, the stubborn paradigm was extended to synchronization of multi-agent systems [17], [18], setmembership estimation [19], low-power high-gain observers [20], extended Kalman filtering [21], estimation for distributed parameter systems [22], nonlinear filtering [23]. Here instead, we extend the approach to a generic linear output feedback (possibly dynamic) controller, exploiting linear matrix inequalities (LMIs) [24] for the parameter tuning, generalizing the output injection scenarios of [13] and [16].…”

Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks

“…3 Usually, the model of the distributed parameter CPSs can be expressed as partial differential equations (PDEs). Researches like [4][5][6] have reported numerous noteworthy results to the DPSs throughout the past few decades. However, the control of distributed parameter CPSs still faces numerous difficulties because of the complexity of nonlinear system structures, external and internal disturbances, multi-coupling of the undetermined control parameters, and the conservatism of the designed control conditions.…”

Digital H∞ filter design for a low frequency multiple‐input multiple‐output system with multirate measurements

“…6 Due to robustness of H ∞ filtering, it is further developed to estimate state variables much accurately over the last decade. 7 In virtue of information digitization, it attracts our attention on a digital form of H ∞ filtering. On the other hand, time delays exist in many practical applications, which results in impoverished performance for control systems.…”

“…A basic idea of filtering is to design filters by solving the minimum infinite norm of control systems composed from noises to error signals 6 . Due to robustness of filtering, it is further developed to estimate state variables much accurately over the last decade 7 . In virtue of information digitization, it attracts our attention on a digital form of filtering.…”