Session: 07-12-01 Control Theory and Applications I

Paper Number: 67484

Start Time: Tuesday, 01:00 PM

67484 - An Adaptive Control Framework for Unknown Input Estimation 

Many dynamic systems experience disturbances which must be considered when selecting successful

control strategies. While these disturbances act as unknown and uncontrollable inputs, they often

contain both deterministic and stochastic information. We model these unknown inputs as a

combination of independent waveforms, such as a Fourier series in Hilbert space. In this work, we

are interested in treating a class of systems with unknown inputs which have some uncertainty in

the model. Since all models are inherently only approximations of the true plant, it is natural to

expect some difference in the identified model and the true plant dynamics. Therefore, an adaptive

scheme is employed in parallel with an unknown input observer to correct the state estimation

while also converging the unknown input estimation.

A composite observer for both internal states and disturbance states is proposed for systems

with uncertainty in the state estimation. Proofs using Lyapunov analysis show that the error in the

internal states and unknown waveform converge to zero in the presence of bounded inputs using

the notion of almost strict dissipativity (ASD). The ASD propert is equivalent to the plant and

composite observer open loops have a positive definite high-frequency gain and stable minimum

phase transmission zeros.

The control architecture contains an internal model of the unknown input process, which is

critical to this approach. These input generators are in state space form and introduce marginally

stable blocks to the composite error dynamics. Strategies to stabilize the error dynamics given these

marginally stable input generators are discussed by solving linear matrix inequalities. Even though

the input estimator alone is often unobservable, the composite system can be completely observable,

which implies that estimates of both the state and input can be implemented in real time. Further,

it is shown that if a significant waveform is not included in the disturbance generator, the control

architecture orthogonally projects the unknown input onto the remaining available waveforms.

Illustrative examples are presented and will be made publicly available online.

Unknown adaptive input observers of this type offer robust methods to generate reliable esti-

mates of the internal state and unknown input simultaneously. Proofs of convergence and perfor-

mance are presented, along with simulated examples. This architecture offers the unique ability to

utilize or minimize the unknown input if it is identified as useful to the performance of the system,

rather than simply canceling it. Extensions are under consideration to consider weak non-linearities

and complex state vectors.

Presenting Author: Tristan Griffith Texas A&M University

Authors:

Tristan D. Griffith Texas A&M University
Mark J. Balas Texas A&M University