VALUE OF INFORMATION ON HIDDEN SENSOR DEGRADATION FOR RELIABILITY-BASED CONTROL DESIGN
DOI:
https://doi.org/10.35546/kntu2078-4481.2025.2.2.51Keywords:
reliability-based control, survival probability, hidden sensor degradation, Markov chain, Kalman filter, phase-type distribution, unmanned aerial vehicle, pitot-static sensorAbstract
The paper considers reliability-based control design for a linear plant whose sensor degrades episodically: the measurement noise level switches according to a hidden Markov chain, while the controller and the Kalman filter receive no information about the current sensor condition. The performance index is the survival probability – the probability that the state vector does not leave the admissible region during a mission of given duration. The aim of the work is to determine what a reliability-based design must know about sensor degradation and under which conditions the degradation significantly affects the result. A phase-type estimate of the survival probability for a system with hidden sensor modes is proposed; it combines the per-mode boundary-crossing probabilities, computed through Owen’s function for a Gaussian sequence with correlation between neighbouring samples, with the transition matrix of the Markov chain. It is proved that knowing only the set of sensor modes changes the averaged exit intensity by no more than log(1/πmin) natural-logarithm units, where πmin is the smallest stationary mode probability; that noise-level switches keep the error covariance between the stationary values of the modes; and that a second-moment criterion averaged over the modes can prefer a design whose survival probability tends to zero. The computational experiment uses the linearised longitudinal model of the Aerosonde unmanned aerial vehicle with Dryden turbulence and degradation of the pitot-static airspeed sensor; the key conclusions are verified on a nonlinear twin model. A design that ignores the degradation loses up to 0.94 of survival probability compared with a design that accounts for it; a design that knows only the modes, without the chain statistics, falls behind by no more than 0.03; a design for the averaged noise can be worse than ignoring the degradation (by up to 0.12). The impact of the same fault depends on flight speed, controller structure and the estimator’s sensor set: for one of the controllers the loss decreases from 0.135 to 0.002 when the speed increases from 20 to 22 m/s, and with accurate accelerometers the degradation considered becomes harmless.
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