Designing Resilient Linear Driftless Systems

Abstract: Critical systems must be designed resilient to all kinds of malfunctions. We are especially interested by the loss of control authority over actuators. This malfunction considers actuators producing uncontrolled and possibly undesirable inputs. We investigate the design of resilient linear systems capable of reaching their target even after such a malfunction. In contrast with the settings of robust control and fault-tolerant control, we consider undesirable but observable inputs of the same magnitude as controls since they are produced by a faulty actuator of the system. The control inputs can then depend on these undesirable inputs. Building on our previous work, we focus on designing resilient systems able to withstand the loss of one or multiple actuators. Since resilience refers to the existence of a control law driving the state to the target, we naturally continue with the synthesis of such a control law. We conclude with a numerical application of our theory on the ADMIRE fighter jet model.