• Dinita Rahmalia Universitas Islam Darul Ulum Lamongan
Keywords: Optimal Control, Linear Quadratic Regulator, Ant Colony Optimization


Inverted pendulum consists of cart and pendulum attached in it. The force is given to the system consists of angle position, angle velocity, cart position, and cart velocity. The objective function of inverted pendulum is minimizing pendulum angle and cart position following trajectories so that pendulum is stable. The model of optimal control used in this research is applying Linear Quadratic Regulator (LQR). In LQR, the value of objective function is determined by weight matrices and weight matrices are generally approached by trial and error. Ant Colony Optimization  (ACO) is optimization method based on behavior of ants in searching path from home towards to food source. The simulation results show that ACO method can find optimal weight matrices minimizing performance index as objective function.


[1] Hassani, K., Lee, W.S., “Optimal Tuning of Linear Quadratic Regulators Using Quantum Particle Swarm Optimization,” Proceedings of the Int. Conference of Control, Dynamic System, and Robotics, (Canada), pp. 59(1-8), 2014.

[2] Karthick, S., Jerome, J., “APSO Based Weighting Matrices Selection of LQR Applied to Tracking Control of SIMO System,” Proceedings of 3rd International Conference on Advanced Computing, Networking and Informatics, Smart Innovation, Systems and Technologies, (India), pp. 11-20, 2016.

[3] Rahmalia, D., Herlambang, T., “Application Ant Colony Optimization on Weight Selection of Optimal Control SEIR Epidemic Model,” Proceeding The 7th Annual Basic Science International Conference, (Malang), pp. 196–199, 2017.

[4] Herlambang, T., Rahmalia, D., Yulianto, T., “Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) for Optimizing PID Parameters on Autonomous Underwater Vehicle (AUV) Control System,” Journal of Physics : Conference Series, (Jember), 2019.

[5] Lewis, F.L., Vrabie, D.L., Syrmos, V.L., Optimal Control. New Jersey: John Wiley and Sons, 2012.

[6] Naidu, D.S., Optimal Control System. Florida: CRC Press, 2003.

[7] Ogata, K., Modern Control Engineering. New Jersey: Prentice Hall, 2002.

[8] Rao, S.S., Engineering Optimization Theory and Practice. New Jersey: John Wiley and Sons, 2009.

[9] Dorigo, M., Stutzle, T., Ant Colony Optimization. London: The MIT Press, 2004

[10] Rahmalia, D., “Estimation of Exponential Smoothing Parameter on Pesticide Characteristic Forecast Using Ant Colony Optimization (ACO),” Eksakta: Jurnal Ilmu-Ilmu MIPA, UII Yogyakarta, vol. 18, no. 1, pp. 56–63, 2018.

[11] Rahmalia, D., Herlambang, T., “Weight Optimization of Optimal Control Influenza Model Using Artificial Bee Colony,” International Journal of Computing Science and Applied Mathematics, ITS Surabaya, vol. 4, no. 1, pp. 27-31, 2018.