Jeffrey H. Ahrens

High-gain observers in the presence of measurement noise: A switched-gain approach

This paper considers output feedback control using high-gain observers in the presence of measurement noise for a class of nonlinear systems. We study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other. Based on this tradeoff we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness and ultimate boundedness of the closed-loop system under switched-gain output feedback.

Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems

We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the measurement sampling rate is made faster than the control update rate. We show that, in the presence of bounded disturbances, given a sampled data state feedback controller that achieves stabilization with respect to a closed set, the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast. As an application we consider the control of smart material actuated systems. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

Closed-Loop Behavior of a Class of Nonlinear Systems Under EKF-Based Control

We study the closed-loop behavior of the extended Kalman filter (EKF) for a class of deterministic nonlinear systems that are transformable to the special normal form with linear internal dynamics. We argue that the closed-loop system is asymptotically stable and the estimation error exponentially converges to zero. We compare the performance of the EKF to a high-gain observer through simulation

Multirate Sampled-Data Output Feedback Using High-Gain Observers

We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the analog-to-digital sampling rate is faster than the digital-to-analog sampling rate. We show that if a single-rate sampled-data state feedback controller globally stabilizes the origin, then the multirate output feedback controller achieves semiglobal practical stabilization

Multirate Sampled-Data Output Feedback Control of Smart Material Actuated Systems

We consider multirate sampled-data output feedback control of smart material actuated systems where the measurement sampling rate is made faster than the control update rate. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. We show that the sampled-data output feedback controller achieves stabilization with respect to a closed set in the presence of hysteresis modeling uncertainty. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

High-Gain Observers in the Presence of Measurement Noise: A Switched-Gain Approach

Abstract This paper considers output feedback control using high-gain observers in the presence of measurement noise for a class of nonlinear systems. We study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other. Based on this tradeoff we propose a high-gain observer that switches between two gain values. This scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error. We argue boundedness and ultimate boundedness of the closed-loop system under switched-gain output feedback.

Asymptotic Properties of Extended Kalman Filters for a Class of Nonlinear Systems

We study the closed-loop behavior of the ex-tended Kalman filter for a class of deterministic nonlinear systems that are transformable to the special normal form with linear internal dynamics. We argue that the closed-loop system is asymptotically stable and the estimation error exponentially converges to zero. We compare the performance of the extended Kalman filter to a high-gain observer through the use of numerical examples.