Resilient Integral Control for Regulating Systems with Convex Input Constraints

In this paper, a novel integral control that can maintain the control input vector trajectory of a generic ISS linear or nonlinear plant within a prescribed compact and convex set is proposed. During normal operating conditions, the proposed controller can regulate the plant to the desired setpoint, while in the case of abnormal conditions, e.g. sensor faults, unrealistic reference input command, the controller introduces an inherent resilience property by maintaining the entire control input vector of the plant within a desired convex set. The boundedness of the control input vector is analytically proven using invariant set theory and vector field analysis (Nagumo's theorem). Opposed to conventional and more advanced integral controllers that either restrict each element of the control input vector independently or bound its Euclidean norm, in this paper, a detailed methodology for designing a resilient integral control to guarantee a generic compact and convex input constraint for a plant with unknown structure or dynamics is presented for the first time. A practical example of an underwater vehicle is investigated to validate the efficiency and resilience of the proposed controller under changes of the reference signal and under sensor faults.