Kalman Filter

Fault Detection and Isolation (FDI), also called Fault Detection and Diagnosis (FDD), is a discipline of control engineering concerned with automatic detection, isolation, and characterisation of faults in dynamic systems. FDI comprises three phases: (1) detection — determining that a fault has occurred (by residual threshold crossing); (2) isolation — identifying the fault location (which sensor/actuator/component); (3) identification — characterising the fault (type, magnitude, time profile). Model-based methods include state observers (Luenberger, KF), parity equations, observer banks, Dedicated Observer Scheme (DOS), and Generalised Observer Scheme (GOS). Data-driven methods use ML classifiers (SVM, neural networks, autoencoders) trained on fault data. FDI is a prerequisite for Active FTC — without reliable diagnosis, controller reconfiguration cannot happen in time. Key FDI metrics: False Alarm Rate (FAR), Missed Detection Rate (MDR), detection time T_d, and isolation time T_i. Standards: IEC 61511 (SIS), ISO 13849 (machinery), DO-178C (aviation).

Model Predictive Control (MPC), also called Receding Horizon Control, is a control paradigm introduced in industrial form in the late 1970s–1980s (IDCOM 1978, DMC 1980). At each controller step an optimization is solved: minimise a cost function (state/output trajectory deviations from reference plus input cost) over a prediction horizon N, subject to state and input constraints. Only the first step of the optimal sequence is applied to the plant; at the next step the horizon shifts by one and the optimisation repeats. MPC handles constraints natively (actuator saturation, safe state ranges), making it especially useful in robotics (manipulators, biped locomotion, drones, autonomous vehicles). In FTC, after fault identification the MPC internal model is updated to the faulty-plant model and the constraints are updated to the healthy actuator limits. Key variants: Linear MPC (convex QP, guaranteed convergence), Nonlinear MPC (NMPC, NLP, higher compute cost), Stochastic MPC, Robust MPC (explicit uncertainty modelling), Learning-based MPC (data-driven models). Tools: ACADO, CasADi, do-mpc, Acados, OSQP.

Fault-Tolerant Control (FTC) is a branch of control theory concerned with systems capable of preserving stability and acceptable control performance in the presence of faults. It is divided into two main classes: Passive FTC (PFTC), where the controller is designed to be robust against a predefined fault set without explicitly detecting it, and Active FTC (AFTC), where a Fault Detection and Diagnosis (FDD) module detects and isolates the fault and a reconfiguration mechanism then alters the controller structure or parameters. In robotics, FTC is applied to redundant manipulators, multirotor drones, humanoid robots, and autonomous vehicles — anywhere a single actuator or sensor failure must not result in loss of control. Typical methods include Control Allocation with redistribution onto healthy actuators, Multiple Model Adaptive Control, Sliding Mode Control, and Model Predictive Control with an updated faulty-plant model. FTC is tightly coupled with FDI (Fault Detection and Isolation) — without reliable diagnosis, the controller cannot be reconfigured in time. Key performance metrics include detection time, reconfiguration time, the bound on performance degradation, and the share of faults the system can handle. Standards such as ISO 26262 (automotive), DO-178C/DO-254 (aviation), and IEC 61508 (industry) mandate the use of FTC techniques in safety-critical applications.