Observer-Based Quadratic Guaranteed Cost Control for Linear Uncertain Systems with Control Gain Variation
This study proposes a method for designing observer-based quadratic guaranteed cost controllers for linear uncertain systems with control gain variations. In the proposed approach, an observer is designed, and then a feedback controller that ensures the upper bound on the given quadratic cost function is derived. This study shows that sufficient conditions for the existence of the observer-based quadratic guaranteed cost controller are given in terms of linear matrix inequalities. A sub-optimal quadratic guaranteed cost control strategy is also discussed. Finally, the effectiveness of the proposed controller is illustrated by a numerical example. The result shows that the proposed controller is more effective than conventional methods even if system uncertainties and control gain variations exist.
H. Oya, et al., “Observer-Based Robust Control Giving Consideration to Transient Behavior for Linear Systems with Structured Uncertainties,” International Journal of Control, vol. 75, no. 15, pp. 1231-1240, October 2002.
H. Oya, et al., “Adaptive Robust Control Scheme for Linear Systems with Structure Uncertainties,” IEICE Transactions on Fundamentals of Electronics, Communications, and Computer Sciences, vol. E87-A, no. 8, pp. 2168-2173, August 2004.
H. Oya, et al., “Robust Control Giving Consideration to Time Response for a Linear Systems with Uncertainties,” Transactions of the Institute of Systems, Control, and Information Engineers, vol. 15, no. 8, pp. 404-412, August 2002.
S. S. Chang, et al., “Adaptive Guaranteed Cost Control of Systems with Uncertain Parameters,” IEEE Transactions on Automatic Control, vol. 17, no. 4, pp. 474-483, August 1972.
S. O. R. Moheimani, et al., “Optimal Quadratic Guaranteed Cost Control of a Class of Uncertain Time-Delay Systems,” IEE Proceedings—Control Theory and Applications, vol. 144, no. 2, pp. 183-188, March 1997.
I. R. Petersen, et al., “Optimal Guaranteed Cost Control and Filtering for Uncertain Linear Systems,” IEE Transactions on Automatic Control, vol. 39, no. 9, pp.1971-1977, September 1994.
L. Yu, et al., “An LMI Approach to Guaranteed Cost Control of Linear Uncertain Time Delay Systems,” Automatica, vol. 35, no. 6, pp. 1155-1159, June 1999.
S. H. Park, et al., “H∞ Control with Performance Bound for a Class of Uncertain Linear Systems,” Automatica, vol. 30, no. 12, pp. 2009-2012, April 1994.
R. Petersen, “A Riccati Equation Approach to the Design of Stabilizing Controllers and Observers for a Class of Uncertain Linear Systems,” IEEE Transactions on Automatic Control, vol. 30, no. 9, pp. 904-907, September 1985.
H. Oya, et al., “Observer-Based Guaranteed Cost Control for Polytopic Uncertain Systems,” The Japan Society of Mechanical Engineers, vol. 71, no. 710, pp. 89-98, October 2005.
S. Nagai, et al., “A Point Memory Observer with Adjustable Parameters for a Class of Uncertain Linear Systems with State Delay,” Proceedings of Engineering and Technology Innovation, vol. 11, pp. 38-45, January 2019.
L. H. Keel, et al., “Robust, Fragile, or Optimal?” IEEE Transactions on Automatic Control, vol. 42, no. 8, pp. 1098-1105, August 1997.
G. H. Yang, et al., “H∞ Control for Linear Systems with Additive Controller Gain Variations,” International Journal of Control, vol. 73, no. 16, pp. 1500-1506, February 2000.
D. Famularo, et al., “Robust Non-Fragile LQ Controllers: The Static State Feedback Case,” Proceedings of the 1998 American Control Conference, vol. 2, pp. 1109-1113, June 1998.
H. Oya, et al., “Guaranteed Cost Control for Uncertain Linear Continuous-Time Systems under Control Gain Perturbations,” The Japan Society of Mechanical Engineers, vol. 72, no. 713, pp. 72-101, January 2006.
K. Miyakoshi, et al., “Synthesis of Formation Control Systems for Multi-Agent Systems under Control Gain Perturbations,” Advances in Technology Innovation, vol. 5, no. 2, pp. 112-125, April 2020.
D. Rosinová, et al., “Output Feedback Stabilization of Linear Uncertain Discrete Systems with Guaranteed Cost,” 15th Triennial World Congress, vol. 35, no. 1, pp. 211-215, July 2002.
M. Noton, Modern Control Engineering, New York: Pergamon Press, 1972.
S. Nagai, et al., “Synthesis of Decentralized Variable Gain Robust Controllers with Guaranteed L2 Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems,” Journal of Control Science and Engineering, vol. 2015, Article no. 342867, 2015.
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