A Linear Quadratic Controller Design Incorporating a Parametric Sensitivity Constraint
The purpose of this paper is to propose a synthesis method of parametric sensitivity constrained linear quadratic (SCLQ) controller for an uncertain linear time invariant (LTI) system. System sensitivity to parameter variation is handled through an additional quadratic trajectory parametric sensitivity term in the standard LQ criterion to be minimized. The main purpose here is to find a suboptimal linear quadratic control taking explicitly into account the parametric uncertainties. The paper main contribution is threefold: 1) A descriptor system approach is used to show that the underlying singular linear-quadratic optimal control problem leads to a non-standard Riccati equation. 2) A solution to the proposed control problem is then given based on a connection to the so-called Lur’e matrix equations. 3) A synthesis method of multiple parametric SCLQ controllers is proposed to cover the whole parametric uncertainty while degrading as less as possible the intrinsic robustness properties of each local linear quadratic controller. Some examples are presented in order to illustrate the effectiveness of the approach.
KeywordsLinear quadratic control parametric uncertainties trajectory sensitivity non-standard Riccati equation Lur’e matrix equations linear time invariant (LMI) particle swarm optimization
Unable to display preview. Download preview PDF.
- M. Yagoubi. A parametric sensitivity constrained linear quadratic controller. In Proceedings of the 22nd Mediterranean Conference on Control and Automation, IEEE, Palermo, Italy 2014.Google Scholar
- M. Yagoubi. Synthesis of multiple sensitivity constrained controllers for parametric uncertain LTI systems. In Proceedings of the 23rd Mediterranean Conference on Control and Automation, IEEE, Torremolinos, Spain, 2015.Google Scholar
- A. Ansari, T. Murphey. Minimal parametric sensitivity trajectories for nonlinear systems. In Proceedings of 2013 American Control Conference, IEEE, Washington, USA, 2013.Google Scholar
- M. Yagoubi, P. Chevrel. A solution to the insensitive H2 problem and its application to automotive control design. In Proceedings of the 15th Triennial World Congress, IFAC, Barcelona, Spain, 2002.Google Scholar
- M. Yagoubi, P. Chevrel. A convex method for the parametric insensitive H2 control problem. In Proceedings of the IFAC World Congress, IFAC, Czech Republic, 2005.Google Scholar
- J. Choi, R. Nagamune, R. Horowitz. Synthesis of multiple robust controllers for parametric uncertain LTI systems. In Proceedings of American Control Conference, IEEE, Minneapolis, USA, 2006.Google Scholar
- A. I. Lure. Some non-linear Problems in the Theory of Automatic Control: Nekotorye Nelineinye Zadachi Teorii Avtomaticheskogo Regulirovaniya, H. M. Stationery, 1957.Google Scholar
- F. van den Bergh, A. P. Engelbrecht. A new locally convergent particle swarm optimizer. In Proceedings of 2002 IEEE Conference on Systems, Man and cybernetics, IEEE, Hammamet, Tunisia, 2002.Google Scholar
- J. Löfberg. YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, IEEE, Taipei, China, 2004.Google Scholar
- F. Gay, P. De Larminat. Robust vehicle dynamics control under cornering stiffness uncertainties with insensitive H2 theory. In Proceedings of the 4th World Multiconference on Circuits, Systems, Communications, Computers, CSCC, Vouliagmeni, Greece, 2000.Google Scholar