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Fault-tolerant control for a class of switched parabolic systems. (English) Zbl 1430.35233

Summary: This paper addresses the fault tolerant control (FTC) problem for switched parabolic systems with process and boundary faults, described by partial differential equation (PDE). The boundary feedback controller is designed to guarantee the exponential stability of the systems. Both the accumulative and dissipative characteristics of faults are considered, respectively. Constructing the comparative system and using Lyapunov method, the non-switched parabolic systems are exponentially stable. The new result is further extended to the switched parabolic systems where the boundary controller in each mode and the switching law are designed comprehensively. It shows that the FTC goal can be achieved even if only some faulty modes are stabilizable. A heat propagation control of semiconductor power chips example is taken to illustrate the efficiency of obtained theoretical results.

MSC:

35Q93 PDEs in connection with control and optimization
93B52 Feedback control
93C20 Control/observation systems governed by partial differential equations
35B35 Stability in context of PDEs
80A19 Diffusive and convective heat and mass transfer, heat flow
35K20 Initial-boundary value problems for second-order parabolic equations
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