Fault tolerant control
Two main fault-tolerant methodologies are the active and passive methods. The passive methods are based on robust-ﬁxed-structure control systems considering bounds of uncertainty. Control allocation is an appealing approach to the design of active fault-tolerant control systems when the degrees of redundancy increases. Most of the control allocation methods require fault identification and persistent excitation assumption. Please see the adaptive control allocation section of website which introduces a novel method without fault identification and persistent excitation assumption requirements.
Null space of the control matrix
Hardware redundancy, for example, actuator or sensor redundancy, is commonly used in industrial applications to increase system maneuverability, flexibility, safety, and fault tolerability. This leads to rank deficiency of the control matrix. This means that the null space of the control matrix is not empty. This provides some degrees of freedom to design control allocation methods.
Control allocation based on the pseudo inverse along the control matrix null space
This method requires Recursive Least Squares (RLS) method for fault identification. While the information about actuator fault is in hand, this method uses the freedom provided by the null space of the control matrix and modifies the pseudo inverse approach. The main properties of the proposed methodology are 1) low computational cost compare to the optimization based methods, 2) considering actuator magnitude constraint.
Shahab Tohidi, Ali Khaki Sedigh, and David Buzorgnia, “Fault tolerant control design using adaptive control allocation based on the pseudo inverse along the null space,” International Journal of Robust and Nonlinear Control, 2016.
Shahab Tohidi, and Ali Khaki Sedigh, “Adaptive fault tolerance in automotive vehicle using control allocation based on the pseudo inverse along the null space for yaw stabilization,” International Conference on Control, Instrumentation, and Automation, 2013.
Shahab Tohidi, and Ali Khaki Sedigh, “Fault tolerant fuzzy control allocation for overactuated systems,” Iranian Conference on Fuzzy Systems (IFSC), 2013.