Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement

We design an estimator for the position of a rocket car. The scheme is based on a novel idea of delay measurements in a realistic scenario. Ultrasonic sensors are used to give the measurement of the delay. The delay depends implicitly on the state of the system. This gives rise to a time delay system with a state-dependent delay which is a challenging research avenue. The central theme is to use inversion of the delay model and to extract the state vector given the delay. The overall system is nonlinear because of the state-dependent delay. We design an asymptotic observer for estimating the position of the system using delay information. We call or refer to this new technique as Delay Injection. We show that the error dynamics involve a time-varying delay instead of a state-dependent delay and this makes the problem tractable. A brief outline of the nonlinear observation for the autonomous system is also given. Though rocket car is a particular motivating example, the approach presented in this article can be used for the on-line estimation of states of generic systems from state-dependent delays affecting the system dynamics. Simulation results are given at the end which demonstrate the effectiveness, validity and usefulness of the proposed scheme.