Stochastic control of drill-heads driven by Levy processes

This paper considers the feedback tracking control problem of drill-heads with the bit-rock interaction modeled by drifts and jump-diffusions (Levy processes). A Lyapunov-type theorem is developed to study well-posedness, stability in moment, and almost sure stability of nonlinear stochastic differential equations driven by Levy processes. This theorem and the backstepping method are applied to design robust and adaptive controllers that guarantee both global practical K-infinity-exponential p-stability and almost sure global practical K-infinity-exponential stability of the tracking errors for the drill-heads. (C) 2019 Elsevier Ltd. All rights reserved.