A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model
Abstract
:1. Introduction
2. Heterogeneous Multiple Model of Nonlinear System
3. Hybrid-Model-Based Optimal Control
4. A Partitioned Operating Space Algorithm
Algorithm 1. Boundary Calculation | |
1: | Initialize The parameters of the system, , etc. |
2: | Discretize the state space X into finite difference grid by discrete step and obtain and . |
3: | Numerical solution of value function in ith model, , and give an initial guess of. |
4: | For interior point , update using Equation (18). For boundary point , update using Equation (19). |
5: | Calculate the convergence error, where is the obtained value function in previous iteration. Compare with convergence constant ; if then jump to Step IV, else go to Step II. |
6: | Collect the optimal state point in setof boundary condition by: |
7: | Optimal boundary in state space is fitted by least square method by: |
8: | Output: |
5. Multiple Model Predictive Controller
6. Case Study
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Subramanian, A.S.R.; Adams, T.A. Modeling and simulation of energy systems: A review. Processes 2018, 6, 238. [Google Scholar] [CrossRef] [Green Version]
- Zendehboudi, S.; Rezaei, N.; Lohi, A. Applications of hybrid models in chemical, petroleum, and energy systems: A systematic review. Appl. Energy 2018, 228, 2539–2566. [Google Scholar] [CrossRef]
- Murray-Smith, R.; Johansen, T.A. The operating regime approach to nonlinear modelling and control. In Multiple Model Approaches to Modelling and Control, 1st ed.; Murray-Smith, R., Johansen, T.A., Eds.; Taylor & Francis: London, UK, 1997; Volume 3, pp. 60–78. [Google Scholar]
- Takagi, T.; Sugeno, M. Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 1985, 15, 116–132. [Google Scholar] [CrossRef]
- Xu, J.; Huang, X.L.; Wang, S.N. Adaptive hinging hyperplanes and its applications in dynamic system identification. Automatica 2009, 45, 2325–2332. [Google Scholar] [CrossRef]
- Ferrari-Trecate, G.; Muselli, M.; Liberati, D.; Morari, M. A clustering technique for the identification of piecewise affine systems. Automatica 2003, 39, 205–217. [Google Scholar] [CrossRef]
- Walczak, B.; Massart, D.L. Local modelling with radial basis function networks. Chem. Intell. Lab. Syst. 2000, 50, 179–198. [Google Scholar] [CrossRef]
- Bachnas, A.A.; Tóth, R.; Ludlage, J.H.A.; Mesbah, A. A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study. J. Process Control 2014, 24, 272–285. [Google Scholar] [CrossRef] [Green Version]
- Miranian, A.; Rouzbehi, K. Nonlinear power system load identification using local model networks. IEEE Trans. Power Syst. 2013, 28, 2872–2881. [Google Scholar] [CrossRef]
- Adeniran, A.A.; El Ferik, S. Modeling and identification of nonlinear systems: A review of the multimodel approach—Part 2. IEEE Trans. Syst. Man Cybern. Syst. 2017, 47, 1160–1168. [Google Scholar] [CrossRef]
- Adeniran, A.A.; El Ferik, S. Modeling and identification of nonlinear systems: A review of the multimodel approach—Part 1. IEEE Trans. Syst. Man Cybern. Syst. 2016, 47, 1149–1159. [Google Scholar] [CrossRef]
- Feng, G. A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy Syst. 2006, 14, 676–697. [Google Scholar] [CrossRef] [Green Version]
- Li, X.R.; Bar-Shalom, Y. A recursive multiple model approach to noise identification. IEEE Tran. Aerosp. Electron. Syst. 1994, 30, 671–684. [Google Scholar] [CrossRef]
- Nakada, H.; Takaba, K.; Katayama, T. Identification of piecewise affine systems based on statistical clustering technique. Automatica 2005, 41, 905–913. [Google Scholar] [CrossRef]
- Du, J.; Johansen, T.A. Integrated multimodel control of nonlinear systems based on gap metric and stability margin. Ind. Eng. Chem. Res. 2014, 53, 10206–10215. [Google Scholar] [CrossRef]
- Böling, J.M.; Seborg, D.E.; Hespanha, J.P. Multi-model adaptive control of a simulated pH neutralization process. Control Eng. Pract. 2007, 15, 663–672. [Google Scholar] [CrossRef]
- Song, C.; Wu, B.; Li, P. A hybrid model-based optimal control method for nonlinear systems using simultaneous dynamic optimization strategies. J. Process Control 2012, 22, 852–860. [Google Scholar] [CrossRef]
- Xu, D.; Jiang, B.; Shi, P. Nonlinear actuator fault estimation observer: An inverse system approach via a T–S fuzzy model. Int. J. Appl. Math. Comput. Sci. 2012, 22, 183–196. [Google Scholar] [CrossRef] [Green Version]
- Narendra, K.S.; Wang, Y.; Mukhopadhay, S. Fast Reinforcement Learning using multiple models. In Proceedings of the IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12–14 December 2016; pp. 7183–7188. [Google Scholar]
- Angelov, P.P.; Gu, X.; Príncipe, J.C. Autonomous Learning Multimodel Systems from Data Streams. IEEE Trans. Fuzzy Syst. 2017, 26, 2213–2224. [Google Scholar] [CrossRef] [Green Version]
- Ru, J.; Li, X.R. Variable-structure multiple-model approach to fault detection, identification, and estimation. IEEE Trans. Control Syst. Technol. 2008, 16, 1029–1038. [Google Scholar] [CrossRef]
- Orjuela, R.; Marx, B.; Ragot, J.; Maquin, D. Nonlinear system identification using heterogeneous multiple models. Int. J. Appl. Math. Comput. Sci. 2013, 23, 1–13. [Google Scholar] [CrossRef] [Green Version]
- Filev, D. Fuzzy modeling of complex systems. Int. J. Approx. Reason. 1991, 5, 281–290. [Google Scholar] [CrossRef] [Green Version]
- Gawthrop, P.J. Continuous-time local state local model networks. In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, Vancouver, BC, Canada, 22–25 October 1995; Volume 1, pp. 852–857. [Google Scholar]
- Venkat, A.N.; Vijaysai, P.; Gudi, R.D. Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space. J. Process Control 2003, 13, 473–488. [Google Scholar] [CrossRef]
- Gregorcic, G.; Lightbody, G. Nonlinear system identification: From multiple-model networks to Gaussian processes. Eng. Appl. Artif. Intell. 2008, 21, 1035–1055. [Google Scholar] [CrossRef]
- Kanev, S.; Verhaegen, M. Multiple model weight estimation for models with no common state. In Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Beijing, China, 30 August–1 September 2006; pp. 637–642. [Google Scholar]
- Uppal, F.J.; Patton, R.J.; Witczak, M. A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem. Control Eng. Pract. 2006, 14, 699–717. [Google Scholar] [CrossRef]
- Orjuela, R.; Marx, B.; Ragot, J.; Maquin, D. On the simultaneous state and unknown inputs estimation of complex systems via a multiple model strategy. IET Control Theory Appl. 2009, 3, 877–890. [Google Scholar] [CrossRef] [Green Version]
- Gao, Y.; Liu, Y.; Li, X.R.; Jilkov, V.P. Multiple-model estimation with heterogeneous state representation. In Proceedings of the 2015 18th International Conference on Information Fusion (Fusion), Washington, DC, USA, 6–9 July 2015; pp. 1840–1847. [Google Scholar]
- Ben Atia, S.; Messaoud, A.; Ben Abdennour, R. An online identification algorithm of unknown time-varying delay and internal multimodel control for discrete non-linear systems. Mat. Comput. Modell. Dyn. Syst. 2018, 24, 26–43. [Google Scholar] [CrossRef]
- Du, J.J.; Song, C.Y.; Li, P. Multimodel control of nonlinear systems: An integrated design procedure based on gap metric and H∞ loop shaping. Ind. Eng. Chem. Res. 2012, 51, 3722–3731. [Google Scholar] [CrossRef]
- Nikolaou, M.; Misra, P. Linear control of nonlinear processes: Recent developments and future directions. Comput. Chem. Eng. 2003, 27, 1043–1059. [Google Scholar] [CrossRef]
- Du, J.J.; Johansen, T.A. Control-relevant nonlinearity measure and integrated multi-model control. J. Process Control 2017, 57, 127–139. [Google Scholar] [CrossRef]
- Song, C.Y.; Wu, B.; Zhao, J.; Li, P. An integrated state space partition and optimal control method of multi-model for nonlinear systems based on hybrid systems. J. Process Control 2015, 25, 59–69. [Google Scholar] [CrossRef]
- Song, C.Y.; Wu, B.; Zhao, J. An integrated output space partition and optimal control method of multiple-model for nonlinear systems. Comput. Chem. Eng. 2018, 113, 32–43. [Google Scholar] [CrossRef]
- Song, C.Y.; Li, P. Near optimal control for a class of stochastic hybrid systems. Automatica 2010, 46, 1553–1557. [Google Scholar] [CrossRef]
- Kushner, H.J.; Dupuis, P.G. Numerical Methods for Stochastic Control Problems in Continuous Time, 2nd ed.; Springer: Berlin, NY, USA, 2002; pp. 1240–1351. [Google Scholar]
- Mayne, D.Q. Model predictive control: Recent developments and future promise. Automatica 2014, 50, 2967–2986. [Google Scholar] [CrossRef]
- Bemporad, A.; Morari, M. Control of systems integrating logic, dynamics, and constraints. Automatica 1999, 35, 407–427. [Google Scholar] [CrossRef]
- Du, J.J.; Song, C.; Li, P. Application of gap metric to model bank determination in multilinear model approach. J. Process Control 2009, 19, 231–240. [Google Scholar] [CrossRef]
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Wu, B.; Liu, X.; Yue, Y. A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model. Processes 2020, 8, 215. https://doi.org/10.3390/pr8020215
Wu B, Liu X, Yue Y. A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model. Processes. 2020; 8(2):215. https://doi.org/10.3390/pr8020215
Chicago/Turabian StyleWu, Bing, Ximei Liu, and Yaobin Yue. 2020. "A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model" Processes 8, no. 2: 215. https://doi.org/10.3390/pr8020215
APA StyleWu, B., Liu, X., & Yue, Y. (2020). A Control-Performance-Based Partitioning Operating Space Approach in a Heterogeneous Multiple Model. Processes, 8(2), 215. https://doi.org/10.3390/pr8020215