H_∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems

Abstract

Summary This paper addresses the problem of H∞ boundary control for a class of nonlinear stochastic distributed parameter systems expressed by parabolic stochastic partial differential equations (SPDEs) of Itô type. A simple but effective H∞ boundary static output feedback (SOF) control scheme with collocated boundary measurement is introduced to ensure the local exponential stability in the mean square sense with an H∞ performance. By using the semigroup theory, the disturbance‐free closed‐loop well‐posedness analysis is first given. Then, based on the SPDE model, a general linear matrix inequality based H∞ boundary SOF control design is provided via Lyapunov technique and infinite‐dimensional infinitesimal operator, such that the disturbance‐free closed‐loop system is locally exponentially stable in the mean square sense and the H∞ performance of disturbance attenuation can also be achieved in the presence of disturbances. Finally, simulation results on a stochastic Fisher‐Kolmogorov‐Petrovsky‐Piscounov equation illustrate the effectiveness of the proposed method.

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

“…The study of system stability has always been one of the most basic and important problems in distributed parameter systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] At present, several control methods have been proposed for various distributed parameter systems, such as robust control, 5 adaptive control, 6,7 sliding mode control, 8 pulse control, 9 boundary control, [11][12][13] and parallel control. 14 With the development of artificial intelligence, intermittent control 10,[19][20][21][22] has attracted more attention.…”

Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

“…It is worth noting that the subject IC condition is relatively loose. In [17], the issue of H ∞ boundary state output feedback control with collocated boundary measurements is explored. An adaptive neural network statefeedback controller was designed by building an appropriate Lyapunov function in [18].…”

A generalized exponential stabilization for a class of semilinear parabolic equations: Linear boundary feedback control approach

“…Based on linear matrix inequalities (LMIs) approach, the exponential stabilization is obtained with H ∞ boundary control 23 and sampled‐data control 24 . For stochastic DPSs, boundary control design is provided in Wu et al 25 and Zhang and Wu 25,26 . It should point out the aforementioned results are to get exponential stabilization, n ‐diffusion systems with spatial point measurements.…”

“…24 For stochastic DPSs, boundary control design is provided in Wu et al 25 and Zhang and Wu. 25,26 It should point out the aforementioned results are to get exponential stabilization, n-diffusion systems with spatial point measurements.…”