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=== Fault modelling ===
The figure to the right shows a plant controlled by a controller in a standard control loop.
The nominal linear model of the plant is
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\mathbf{y}_f & = \mathbf{C}_f\mathbf{x}_f\end{cases}</math>
where the subscript <math>f</math> indicates that the system is faulty. This approach models multiplicative faults by modified system matrices. Specifically, actuator faults are represented by the new input matrix <math>\mathbf{B}_f</math>, sensor faults are represented by the output map <math>\mathbf{C}_f</math>, and internal plant faults are represented by the system matrix <math>\mathbf{A}_f</math>.
The upper part of the figure shows a supervisory loop consisting of ''fault detection and isolation'' (FDI) and ''reconfiguration'' which changes the loop by
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# State trajectory recovery
# Transient time response recovery
Internal stability of the reconfigured closed loop is usually the minimum requirement. The equilibrium recovery goal (also referred to as weak goal) refers to the steady-state output equilibrium which the reconfigured loop reaches after a given constant input. This equilibrium must equal the nominal equilibrium under the same input (as time tends to infinity). This goal ensures steady-state reference tracking after reconfiguration. The output trajectory recovery goal (also referred to as strong goal) is even stricter. It requires that the dynamic response to an input must equal the nominal response at all times. Further restrictions are imposed by the state trajectory recovery goal, which requires that the state trajectory be restored to the nominal case by the reconfiguration under any input.
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| last=Maciejowski | first=J. | last2=Jones | first2=C. | year=2003
| chapter=MPC Fault-Tolerant Flight Control Case Study: Flight 1862
| title=
| publisher=IFAC | place=Washington D.C., USA | pages=265–276}}
* {{Citation
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| last=Zhang | first=Y. | last2=Jiang | first2=J. | year= 2003
| chapter=Bibliographical review on reconfigurable fault-tolerant control systems
| title=
| publisher=IFAC | place=Washington D.C., USA | pages=265–276}}
* {{Citation
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