Invariance of the Hamiltonian in Control Problems for Semilinear Parabolic Distributed Parameter Systems

1994 ◽  
pp. 115-130
Author(s):  
H. O. Fattorini
Keyword(s):  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Control Problems ◽  
Semilinear Parabolic ◽  
Parabolic Distributed Parameter Systems

Robust piecewise adaptive control for an uncertain semilinear parabolic distributed parameter systems

2022 ◽  
Vol 27 ◽  
pp. 1-20
Author(s):  
Yanfang Lei ◽  
Junmin Li ◽  
Ailiang Zhao
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Design Method ◽  
External Disturbance ◽  
Adaptive Controller ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Closed Loop System ◽  
Semilinear Parabolic ◽  
Parabolic Distributed Parameter Systems

In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.

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