Sensor delay-compensated prescribed-time observer for LTI systems. (English) Zbl 1480.93156
Summary: We present an observer for linear time-invariant (LTI) systems with measurement delay. Our design ensures that the observer error converges to zero within a prescribed terminal time. To achieve this, we employ time-varying output gains that approach infinity at the terminal time, which can be arbitrarily short but no shorter than the sensor delay time. We model the sensor delay as a transport partial differential equation (PDE) and build upon the cascade ODE-PDE setting while accounting for the infinite dimensionality of the sensor. To construct our time-varying gains, the observer design needs to be conducted in a particular system representation. For this reason, we employ a sequence of state transformations (and their inverses) mapping the original observer error model into (1) the observer form, (2) a sensor delay-compensated observer error form via backstepping, and (3) a particular diagonal form that is amenable to the selection of time-varying gains for prescribed-time stabilization. Our construction of the time-varying observer gains uses (a) generalized Laguerre polynomials, (b) elementary symmetric polynomials, and (c) polynomial-based Vandermonde matrices. A simulation illustrates the results.
MSC:
| 93B53 | Observers |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C05 | Linear systems in control theory |
| 93C43 | Delay control/observation systems |
Keywords:
infinite dimensional systems; prescribed-time convergence; delay-compensation; observer designReferences:
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