@article { author = {Mansourinasab, Sara and Sojoodi, Mahdi and Moghadasi, Seyed Reza}, title = {Model Predictive Control for a 3D Pendulum on SO(3) Manifold Using Convex Optimization}, journal = {Control and Optimization in Applied Mathematics}, volume = {4}, number = {2}, pages = {69-80}, year = {2019}, publisher = {Payame Noor University (PNU)}, issn = {2383-3130}, eissn = {2538-5615}, doi = {10.30473/coam.2021.50933.1134}, abstract = {Conventional model predictive control (MPC) methods are usually implemented to systems with discrete-time dynamics laying on smooth vector space $ \mathbf{R}^n$‎. ‎In contrast‎, ‎the configuration space of the majority of mechanical systems is not expressed as Euclidean space‎. ‎Therefore‎, ‎the MPC method in this paper has developed on a smooth manifold as the configuration space of the attitude control of a 3D pendulum‎. ‎The Lie Group Variational Integrator (LGVI) equations of motion of the 3D pendulum have been considered as the discrete-time update equations since the LGVI equations preserve the group structure and conserve quantities of motion‎. ‎The MPC algorithm is applied to the linearized dynamics of the 3D pendulum according to its LGVI equations around the equilibrium using diffeomorphism‎. ‎Also‎, ‎as in standard MPC algorithms‎, ‎convex optimization is solved at each iteration to compute the control law‎. ‎In this paper‎, ‎the linear matrix inequality (LMI) is used to solve the convex optimization problem under constraints‎. ‎A numerical example illustrates the design procedure‎.}, keywords = {Model predictive control‎,‎Convex optimization‎,‎Linear matrix inequality‎,‎Lie group variational integrator}, url = {https://mathco.journals.pnu.ac.ir/article_7505.html}, eprint = {https://mathco.journals.pnu.ac.ir/article_7505_e3b99cc15a646523035f85832fcef2aa.pdf} }