Tuesday, November 6, 2007 - 8:55 AM

A Moving Horizon Estimation Algorithm Based on Nlp Sensitivity

Victor M. Zavala and Lorenz T. Biegler. Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213

Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the theoretical and practical advantages of this method, its application in industrial settings has been rather limited. Industrial MHE applications involve the solution of large-scale problems with many degrees of freedom (number of parameters, disturbance sequences and initial states). As expected, computational efficiency plays a crucial role. In this context, simultaneous collocation-based approaches coupled to full-space NLP solvers present an attractive alternative since they give rise to a favorable computational complexity and can be benefited from the availability of exact first and second order derivative information. Unfortunately, the advantages of this approach are usually not sufficient to allow efficient implementations of large-scale MHE applications in industrial settings.

In NMPC strategies, the estimated state of the system is required for the solution of the NMPC or regulator problem from which feedback is obtained. An important observation is that, in order to retain the stabilizing properties of the controller, both the large-scale MHE and NMPC problems should be solved in real-time. However, this is not currently possible in most practical applications. In this work, we revisit a previously proposed real-time MHE algorithm [1]. Here, the main idea is to provide instantaneous state estimates obtained from NLP sensitivity approximations constructed around the solution of a continuously updated nominal MHE problem. This fast optimization strategy allows for the implementation of large-scale MHE applications while avoiding undesired effects of computational delays. We extend these ideas further through a deeper analysis of the Karush-Kuhn-Tucker conditions of the MHE problem. As a result, we propose a common stability analysis framework for fast MHE algorithms and develop fast strategies for the computation of large-scale covariance information. Finally, we discuss implementation details of fast optimization capabilities in large-scale NLP algorithms.

[1] Zavala, V. M.; Laird, C.D. and Biegler, L.T. A Fast Computational Framework for Large-Scale Moving Horizon Estimation. Proceedings of the 8th International Symposium on Dynamics and Control of Process Systems, 2007.

Web Page: www.andrew.cmu.edu/user/vzavala/index.html