Robust MHE - Moving horizon estimation: robust stability, robust performance and interaction with model predictive control

From 01-01-2008 to 31-12-2011

Description

The aim of this project is the development of robust moving horizon estimation (MHE) methods.  

• Estimating model states and model parameters is crucial for a successful model predictive control (MPC) strategy.  They need to be estimated based on measurements and a model. The performance of the closed loop system is directly influenced by the quality of the state estimates.  
• The idea behind moving horizon estimation (MHE) is to estimate a sequence of unknown parameters based on a weighted least squares cost function and using a finite optimization window. In the case of a linear system and in the absence of constraints, one can show that MHE is equivalent to the Kalman filter for certain weighting matrices. MHE methods have been developed to overcome the limitations of the widely used Kalman filter, being (i) its inability to incorporate constraints on state and disturbance variables and (ii) the assumptions of Gaussian disturbances and a linear model.
• Over the last years the research of MHE has resulted in important theoretical advances with proofs of stability and optimality. For a successful application of MHE, it is very important to guarantee stability and performance even in the presence of external disturbances.
• Furthermore, our research group is experienced in the simultaneous estimation of states and unknown inputs. Extensions of these recursive formulations towards moving horizon formulations form the second main objective of this project. 
• Because of their mutual dependence, state estimation and control cannot be seen separately. The third main objective of this project is therefore the connection of the robust MHE techniques with the control problem.

More specifically, we opt to investigate the combination of MHE and MPC because both methods allow for the incorporation of constraints and nonlinear dynamics. Furthermore, MPC has become the most widely used multivariable control strategy in industry and it is expected that MHE will be increasingly applied for state estimation where today the (Extended) Kalman filter is still used. 
 
Objectives
This project has the following main objectives: 
a. Develop MHE algorithms with guaranteed robust stability and performance in the presence of   model uncertainties. 
b. Develop MHE algorithms for the simultaneous estimation of states and unknown inputs with guaranteed robust stability and performance. 
c. Develop algorithms for MPC that consider the interaction with MHE explicitly.

Team

• Moritz Diehl, Co-promoter
• Bart De Moor, Promoter

Financing

Funding: FWO - Research Foundation - Flanders

Program/Grant Type: FWO Research Grant - FWO Research Grant