Fault-Tolerant Control of Markovian Jump Systems
Summary
Fault-tolerant control of Markovian jump systems addresses the design of controllers that ensure stability and acceptable performance in the presence of abrupt, random changes in system dynamics as well as component failures. Such systems are characterised by a finite set of operating modes and transition probabilities governed by a Markov chain. In practical terms, actuator faults, sensor degradations or abrupt parameter variations may occur without warning, yet critical applications—from power networks and aerospace vehicles to robotic manipulators—must continue to operate safely. The challenge lies in simultaneously estimating or detecting faults and reconfiguring the control law in real time, all while accommodating stochastic switching and modelling uncertainties. Contemporary approaches employ augmented observers for joint state and fault estimation, sliding-mode or H∞ synthesis for robustness against disturbances, and convex optimisation via linear matrix inequalities to derive mode-dependent controllers. By exploiting stochastic Lyapunov functions and coupling conditions across modes, modern designs can offer guaranteed levels of performance even under time-delays, nonlinearity or partial mode availability. The global significance of this field is underscored by its applications in networked control systems, energy management, automated transport and industrial automation, where uninterrupted operation is paramount.
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Fault-Tolerant Control of Markovian Jump Systems publication trend
The graph below shows the total number of articles in fault-tolerant control of markovian jump systems across all publications each year (not limited to Nature Index journals).
Technical terms
Markovian jump system: A dynamic system whose parameters or structure switch among predefined modes according to a Markov chain.
Fault-tolerant control: Control strategies that maintain system stability and performance in the presence of component faults or failures.
Linear matrix inequality (LMI): A convex constraint used in control synthesis, enabling computation of controllers that satisfy stability and performance criteria.
Lyapunov function: A scalar function used to assess the stability of a system by demonstrating that it decreases along system trajectories.
Observer: An algorithm or filter that estimates unmeasured states or faults from available outputs and inputs.
References
- Robust fault estimation and fault-tolerant control for nonlinear Markov jump systems with time-delays. Automatika (2020).
- Robust Redundant Input Reliable Tracking Control for Omnidirectional Rehabilitative Training Walker. Mathematical Problems in Engineering (2014).
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