Fault tolerant control of uncertain dynamical systems using interval virtual actuators

Abstract

This is the peer reviewed version of the following article: Rotondo D, Cristofaro A, Johansen TA. Fault tolerant control of uncertain dynamical systems using interval virtual actuators. Int J Robust Nonlinear Control. 2018;28:611–624, which has been published in final form at https://doi.org/10.1002/rnc.3888. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, a model reference fault tolerant control strategy based on a reconfiguration of the reference model, with the addition of a virtual actuator block, is presented for uncertain systems affected by disturbances and sensor noise. In particular, this paper (1) extends the reference model approach to the use of interval state observers, by considering an error feedback controller, which uses the estimated bounds for the error between the real state and the reference state, and (2) extends the virtual actuator approach to the use of interval observers, which means that the virtual actuator is added to the control loop to preserve the nonnegativity of the interval estimation errors and the boundedness of the involved signals, in spite of the fault occurrence. In both cases, the conditions to assure the desired operation of the control loop are provided in terms of linear matrix inequalities. An illustrative example is used to show the main characteristics of the proposed approach.Peer ReviewedPostprint (author's final draft

A virtual actuator approach for the secure control of networked LPV systems under pulse-width modulated DoS attacks

“…Let us now consider a jammer which has less available energy to perform the attack, represented by a lower valueτ = 5 s. In this case, Corollary 1 can be applied with α * = 0, α 0 = −40, α 1 = 10, α 2 = 20 and µ 0 = µ 1 = µ 2 = 5, thus allowing for instability of the closed-loop system when even only one of the two actuators is being attacked. For these values, (29) is verified with ∑ n u k=0 ln (µ k ) + α h = −0.17 ≤ 0 (presentation of the symmetric matrices P γ * and virtual actuator gains, which provide feasibility of (30)- (31) and (42), is omitted). For this case, the following scenario will be considered in order to assess the performance of the proposed secure control technique.…”

“…To this end, the active FTC technique known as virtual actuator might be of interest, since it is based on the idea of performing a reconfiguration of the plant when an unexpected situation occurs, such that the nominal controller can still be used without need of retuning it. Initially proposed for linear time invariant (LTI) systems [34], virtual actuators were later extended to linear parameter varying (LPV) [35,36], hybrid [37], Takagi-Sugeno [38], piecewise affine [39], Hammerstein-Weiner [40], Lipschitz [41] and uncertain [42] systems. Note that the virtual actuator technique belongs to the wider class of fault-hiding reconfiguration approaches, among which there is the dual technique known as virtual sensors, that is employed when the considered faults affect the sensor outputs [43].…”

disturbance attenuation for a class of Lipschitz nonlinear systems with large input delay

“…Different control methods have been used to deal with external disturbances and faults (see References 1‐18 and the references therein). In Reference 1, an adaptive fault tolerant protocol is proposed for a class of Lipschitz nonlinear systems using adaptive gain technique.…”

“…An adaptive integral sliding mode fault tolerant controller is proposed in Reference 13 for nonlinear systems with actuator faults, mismatched disturbance, and time‐varying delay. Interval virtual actuators are designed in Reference 14 for uncertain systems under disturbances and sensor faults with known bounds. Recently, a nonzero‐sum game reinforcement learning based method is developed in Reference 15 to achieve performance optimization for large‐scale industrial processes using only data, which gets rid of the model uncertainties and faults.…”

Fault-tolerant Control of Discrete-time Descriptor Systems using Virtual Actuators

“…This active FTC strategy has been extended successfully to many classes of systems, e.g. linear parameter varying (LPV) systems [26], hybrid systems [27], Takagi-Sugeno systems [28], piecewise affine systems [29] and uncertain systems [30]. To the best of our knowledge, this approach has not been extended yet to descriptor systems, which are often used to model cyber-physical systems and other critical infrastructures, such as water distribution networks [5].…”