journal article·2021-08-14Open access

Continuous-Time Perfect Control Algorithm—A State Feedback Approach

Marek Krok, Wojciech P. Hunek, Paweł Majewski

Applied Sciences· Volume 11· Issue 16

Abstract

In this paper, a new approach to the continuous-time perfect control algorithm is given. Focusing on the output derivative, it is shown that the discussed control law can effectively be implemented in terms of state-feedback scenarios. Moreover, the application of nonunique matrix inverses is also taken into consideration during the perfect control design process. Simulation examples given within this work allow us to showcase the main properties obtained for continuous-time perfect control closed-loop plants.
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Research context

OpenAlex topics: Control and Stability of Dynamical Systems · Advanced Control Systems Design · Matrix Theory and Algorithms

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Affiliations

Department of Control Science and Engineering, Opole University of Technology, Prószkowska 76 Street, 45-758 Opole, Poland

References (32)

Show source-provided references
1. Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control10.1109/TAC.2019.2921835 ↗
2. Cao, F., Yang, T., Li, Y., and Tong, S. (2019, January 24–27). Adaptive Neural Inverse Optimal Control for a Class of Strict Feedback Stochastic Nonlinear Systems. Proceedings of the 2019 IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS), Dali, China.10.1109/DDCLS.2019.8908901 ↗
3. Ma, H., Chen, M., and Wu, Q. (2019, January 24–27). Disturbance Observer-Based Inverse Optimal Tracking Control of the Unmanned Aerial Helicopter. Proceedings of the 2019 IEEE 8th Data Driven Control and Learning Systems Conference (DDCLS), Dali, China.10.1109/DDCLS.2019.8908917 ↗
4. Asadzadeh, M.Z., Raninger, P., Prevedel, P., Ecker, W., and Mücke, M. (2019). Inverse model for the control of induction heat treatments. Materials, 12.10.3390/ma12172826 ↗
5. Inverse model control for a quad-rotor aircraft using TS-fuzzy support vector regression
6. Zhiteckii, L.S., and Solovchuk, K.Y. (June, January 29). Analysis of multivariable regulation systems using pseudo-inverse model-based controllers. Proceedings of the 2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON), Kyiv, Ukraine.10.1109/UKRCON.2017.8100377 ↗
7. Continuous-time inverse quadratic optimal control problem10.1016/j.automatica.2020.108977 ↗
8. Filip, I., Dragan, F., Szeidert, I., and Albu, A. (2020). Minimum-Variance Control System with Variable Control Penalty Factor. Appl. Sci., 10.10.3390/app10072274 ↗
9. A new approach to estimate the Minimum Variance Control law for Nonminimum phase Multivariable Systems10.1016/j.ifacol.2019.06.174 ↗
10. Dube, D.Y., and Patel, H.G. (2018). Discrete time minimum variance control of satellite system. International Conference on Mathematical Modelling and Scientific Computation, Springer.
11. Design and real-time implementation of a wireless autopilot using multivariable predictive generalized minimum variance control in the state-space10.1016/j.ast.2020.106053 ↗
12. Perfect Control for Continuous-Time LTI State-Space Systems: The Nonzero Reference Case Study10.1109/ACCESS.2021.3087223 ↗
13. Further results on Moore–Penrose inverses of tensors with application to tensor nearness problems10.1016/j.camwa.2018.11.001 ↗
14. Inverse and Moore-Penrose inverse of Toeplitz matrices with classical Horadam numbers10.7153/oam-2017-11-65 ↗
15. Zhang, W., Wu, Q.J., Yang, Y., and Akilan, T. (2020). Multimodel Feature Reinforcement Framework Using Moore-Penrose Inverse for Big Data Analysis. IEEE Trans. Neural Netw. Learn. Syst.10.1109/TNNLS.2020.3026621 ↗
16. Zhang, B., and Uhlmann, J. (2018). A Generalized Matrix Inverse with Applications to Robotic Systems. arXiv.
17. Kafetzis, I.S., and Karampetakis, N.P. On the algebraic structure of the Moore–Penrose inverse of a polynomial matrix. IMA J. Math. Control. Inf., 2021.10.1093/imamci/dnab001 ↗
18. Nayan Bhat, K., Karantha, M.P., and Eagambaram, N. (2020). Inverse complements of a matrix and applications. J. Algebra Appl., 2150144.10.1142/S0219498821501449 ↗
19. Krok, M., and Hunek, W.P. (2017). Pole-Free vs. Minimum-Norm Right Inverse in Design of Minimum-Energy Perfect Control for Nonsquare State-Space Systems. Biomedical Engineering and Neuroscience, Proceedings of the 3rd International Scientific Conference on Brain-Computer Interfaces, BCI 2018, Opole, Poland, 13–14 March 2017, Springer. Advances in Intelligent Systems and Computing.10.1007/978-3-319-75025-5_17 ↗
20. On pole-placement controllers for linear time-delay systems with commensurate point delays10.1155/MPE.2005.123 ↗
21. State feedback stabilization of linear systems with unknown input time delay10.1016/j.ifacol.2017.08.349 ↗
22. Antenna Azimuth Position Control System using PID Controller & State-Feedback Controller Approach10.11591/ijece.v8i3.pp1539-1550 ↗
23. Input-to-state stability and inverse optimality of predictor feedback for multi-input linear systems10.1016/j.automatica.2019.02.038 ↗
24. A comprehensive comparison of ODE solvers for biochemical problems10.1016/j.renene.2020.04.089 ↗
25. Torres-Del Carmen, F.d.J., Jaramillo-Gernández, R., Díaz-Sánchez, A., and Núñez-Altamirano, D.A. (2020). Comparison of numerical methods in code as solvers for simulation of robotic systems. J. Appl. Comput., 4–15.10.35429/JCA.2020.15.4.1.8 ↗
26. Hunek, W.P., and Krok, M. (2018, January 10–13). Towards a new minimum-energy criterion for nonsquare LTI state-space perfect control systems. Proceedings of the 5th International Conference on Control, Decision and Information Technologies, CoDIT 2018, Thessaloniki, Greece.10.1109/CoDIT.2018.8394774 ↗
27. Ben-Israel, A., and Greville, T.N.E. (2003). Generalized Inverses, Theory and Applications, Springer. [2nd ed.].
28. A study on a new criterion for minimum-energy perfect control in the state-space framework
29. An Application of New Polynomial Matrix σ-Inverse in Minimum-Energy Design of Robust Minimum Variance Control for Nonsquare LTI MIMO Systems10.1016/j.ifacol.2015.09.449 ↗
30. Hunek, W.P., and Krok, M. (2017, January 3–6). Pole-free perfect control for nonsquare LTI discrete-time systems with two state variables. Proceedings of the 2017 13th IEEE International Conference on Control Automation (ICCA), Ohrid, Macedonia.10.1109/ICCA.2017.8003082 ↗
31. Krok, M., and Hunek, W.P. (2018, January 27–30). Pole-Free Perfect Control: Theory vs. Simulation Examples. Proceedings of the 23rd International Conference on Methods & Models in Automation & Robotics (MMAR’18), Miȩdzyzdroje, Poland.10.1109/MMAR.2018.8486108 ↗
32. Hunek, W.P. (2011). Towards a General Theory of Control Zeros for LTI MIMO Systems, Opole University of Technology Press.