A structure exploiting interior-point method for moving horizon estimation

In this article a primal barrier interior-point method for moving horizon estimation (MHE) is presented. It exploits the structure of the KKT systems yielding an algorithm with linear complexity in the horizon length as opposed to cubically as in unstructured solvers. Ideas of square root covariance Kalman filtering are proposed in order to update covariance matrices occurring in the factorization of the KKT matrix efficiently and in a numerically stable way. The algorithm is able to compute - without any additional costs - the covariance of the last estimate within the horizon, which reflects the accuracy of the estimate.

[1]  Eric C. Kerrigan,et al.  Efficient robust optimization for robust control with constraints , 2008, Math. Program..

[2]  J. Potter,et al.  STATISTICAL FILTERING OF SPACE NAVIGATION MEASUREMENTS , 1963 .

[3]  Anders Hansson,et al.  A primal-dual interior-point method for robust optimal control of linear discrete-time systems , 2000, IEEE Trans. Autom. Control..

[4]  Lorenz T. Biegler,et al.  Efficient Solution of Dynamic Optimization and NMPC Problems , 2000 .

[5]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[6]  A. Hansson,et al.  Robust optimal control of linear discrete-time systems using primal-dual interior-point methods , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[7]  Steven Gillijns,et al.  Kalman filtering techniques for system inversion and data assimilation , 2007 .

[8]  Johan U. Backstrom,et al.  Quadratic programming algorithms for large-scale model predictive control , 2002 .

[9]  Jay H. Lee,et al.  A moving horizon‐based approach for least‐squares estimation , 1996 .

[10]  Marc C. Steinbach,et al.  A structured interior point SQP method for nonlinear optimal control problems , 1994 .

[11]  James B. Rawlings,et al.  Efficient moving horizon estimation and nonlinear model predictive control , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[12]  Stephen P. Boyd,et al.  ROBUST LINEAR PROGRAMMING AND OPTIMAL CONTROL , 2002 .

[13]  Stephen J. Wright,et al.  Application of Interior-Point Methods to Model Predictive Control , 1998 .

[14]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[15]  Hans Joachim Ferreau,et al.  Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation , 2009 .

[16]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[17]  James Demmel,et al.  LAPACK Users' Guide, Third Edition , 1999, Software, Environments and Tools.

[18]  Jay H. Lee,et al.  Constrained linear state estimation - a moving horizon approach , 2001, Autom..

[19]  David Q. Mayne,et al.  Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations , 2003, IEEE Trans. Autom. Control..

[20]  Torkel Glad,et al.  A Method for State and Control Constrained Linear Quadratic Control Problems , 1984 .

[21]  P. Dooren,et al.  Numerical aspects of different Kalman filter implementations , 1986 .

[22]  J. B. Jørgensen,et al.  Numerical Methods for Large Scale Moving Horizon Estimation and Control , 2004 .