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Technical Brief

# A Control Theoretic Approach for Solving Underdetermined Problems and Its Application to Control Allocation

[+] Author and Article Information

Department of Electrical Engineering,
National Institute of Technology,
Rourkela 769008, India

Sourav Patra

Department of Electrical Engineering,
Indian Institute of Technology,
Kharagpur 721302, India
e-mail: sourav@ee.iitkgp.ernet.in

Siddhartha Sen

Department of Electrical Engineering,
Indian Institute of Technology,
Kharagpur 721302, India
e-mail: ssen@ee.iitkgp.ernet.in

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 10, 2014; final manuscript received November 20, 2015; published online February 3, 2016. Assoc. Editor: Umesh Vaidya.

J. Dyn. Sys., Meas., Control 138(4), 044501 (Feb 03, 2016) (6 pages) Paper No: DS-14-1251; doi: 10.1115/1.4032063 History: Received June 10, 2014; Revised November 20, 2015

## Abstract

In this paper, a new iterative algorithm is developed using control theoretic approach to find the minimum norm solution of underdetermined problems. The minimum norm solution is obtained by applying the $H∞$ optimization technique. The accuracy and convergence rate of the proposed algorithm are ensured using the framework of linear feedback control theory. The performances of the proposed method, the QR decomposition method, and the least square minimal residue (LSMR) method are compared numerically. The number of iterations in the proposed algorithm is comparable with the LSMR method. Finally, the developed algorithm is applied to the control allocation problem and its effectiveness is demonstrated through a detailed simulation study.

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## Figures

Fig. 1

Closed-loop representation of Σ

Fig. 2

The errors (NORMERR) in iterative solution for Example 1 by the proposed method and the LSMR method

Fig. 3

Thrusters location and actuator directions

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