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In this paper, we study the quadratic model updating problems by using symmetric low-rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low-rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper extends the weighted low rank approximation (WLRA) approach to linearly structured matrices. In the case of Hankel matrices with a special block structure, an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper extends the weighted low rank approximation (WLRA) approach towards linearly structured matrices. In the case of Hankel matrices an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. The correctness of the latter algorithm is verified on a benchmark problem. Finally the statistical accuracy and numerical efficiency of the proposed algorithm is compared with that of STLNB, a previously proposed algorithm for solving Hankel WLRA problems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of extremum seeking in the presence of obstacles. The analytical expression of the cost function as well as locations and shapes of the obstacles are assumed to be partially or completely unknown. We describe a broad family of control algorithms for a unicycle type system, which provides a solution of the above problem based on Lie bracket approximation ideas. The obtained controllers generalize some known results and allow to construct new control strategies. Furthermore, it is shown that gradient‐free control algorithms can be used for excluding the attraction of trajectories to undesirable equilibriuma in obstacle avoidance problems. [ABSTRACT FROM AUTHOR]