A. Azemi

Variable structure observer with a boundary-layer for correlated noise/disturbance models and disturbance minimization

We present a design methodology for state estimation of nonlinear stochastic systems and measurement models with coloured noise processes. The method is based on the extension of variable structure observer schemes. The deterministic versions of these results are also included, a new approach for obtaining the required parameters in the observer design is provided, together with the design of a dynamic feedback controller to minimize the effect of known waveform-type disturbances with unknown magnitudes and arrival times. Two simulation examples illustrate the design procedures.

Sliding mode observers for nonlinear models with unbounded noise and measurement uncertainties

This work extends the applicability of variable structure observers designed for nonlinear systems in two ways. First, it is proved that these observers using a boundary-layer scheme can be applied to system models described by Ito differential equations, resulting in almost sure and mean square exponential estimation error. Second, the use of variable structure observers is extended to nonlinear measurement models containing disturbance effects. Also, a novel approach for obtaining the required parameters in the observer design is provided. Finally, two examples are given to illustrate the application and favorable convergence properties of these generalizations.

Robust/adaptive observers for systems having uncertain functions with unknown bounds

A novel robust/adaptive observer is presented for state reconstruction of nonlinear systems with uncertainty having unknown bounds. The observer uses a nonlinear gain which is continuously adapted to guarantee a uniformly bounded and convergent observation error. Some generalizations to known waveform type disturbances and measurement uncertainties are pointed out.

Design of covariance controllers and estimators with prescribed pole locations

Pole placement features of continuous-time covariance controllers are considered. First, a qualitative property of pole placement as a function of the chosen design covariance is provided. Then, two design techniques for assignment of closed-loop poles to specific regions in the complex plane are described. The necessary and sufficient conditions for assignability, complete characterization of the necessary control gains for assignment, and results on the satisfaction of covariance upper bounds are provided. Examples illustrate the proposed techniques; estimation counterparts of these design techniques are given; and further extensions are pointed out. The results obtained make it possible to satisfy performance criteria like transient response and stability robustness in addition to guaranteeing bounds on the mean square values of the state variables.<<ETX>>

Variable Structure Observers for Nonlinear Models with Unbounded Noise and Measurement Uncertainties

This work extends the applicability of variable structure observers designed for nonlinear systems in two ways. First, it is proved that these observers using a boundary layer scheme can be applied to system models described by Ito differential equations resulting in almost sure and mean square exponential estimation error. Second, the use of variable structure observer is extended to nonlinear measurement models containing disturbance effects. Finally, two examples are given to illustrate the application of these generalizations.

Lyapunov-based nonlinear observer, design for stochastic systems

An observer design methodology which is applicable to more general nonlinear stochastic system models is given. The method relies not on the optimization theory but on Lyapunov-type stochastic stability results which can guarantee a mean square exponential rate of convergence for the estimation error. It is proved that discrete- and continuous-time state estimation is possible using the method. An example is given to illustrate the performance of this observer relative to some of the most commonly used filters in this field.<<ETX>>

A numerical procedure for discrete-time nonlinear stochastic observer design

An observer design methodology which is applicable to a general class of nonlinear stochastic system and measurement models is considered. It is shown that, under the conditions given in the paper, a systematic numerical approach to discrete-time nonlinear state estimation is possible with guaranteed exponential rate of convergence.<<ETX>>

Exponentially convergent robust and adaptive observers for uncertain stochastic systems

We present mean square exponentially convergent state observers for nonlinear stochastic systems driven by Wiener noise. The method is based on extension of variable structure observer schemes using exponential nonlinear gain. The adaptive version of the results are provided to be used when the matching uncertainty has unknown bounds. It is also shown how these results can be applied to system and measurement equations having colored noise processes.

Extensions of Estimation and Control by Covariance Assignment

Four extensions of the state and estimation error covariance assignment algorithms are presented in this work.