Control of a nonlinear system utilizing analytical target cascading
Abstract
The present article introduces an approach that uses the analytical target cascading (ATC) method for managing nonlinear optimal control problems. Using this ATC approach, a decomposed nonlinear optimal control problem is obtained. This decomposed nonlinear control problem is then used to solve a synchronous machine optimal control problem. The numerical behavior of this decomposed synchronous machine optimal control problem is then examined and the solution time properties are also investigated. We demonstrated ATC as a valuable tool to solving nonlinear optimal control problems.
References
Alexander, M.J., Allison, J.T. & Papalambros, P.Y. 2011. Reduced representations of vector-valued coupling variables in decomposition-based design optimization. Structural and Multidisciplinary Optimization 44(3): 379-391.
Allison, J., Walsh, D., Kokkolaras, M., Papalambros, P.Y. & Cartmell, M. 2006. Analytical target cascading in aircraft design. Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada.
Bayrak, A.E., Kang, N. & Papalambros, P.Y. 2016. Decomposition-based design optimization of hybrid electric powertrain architectures: simultaneous configuration and sizing design. Journal of Mechanical Design 138(7): 071405.
Chan, K.Y. 2011. Sequential linearization in analytical target cascading for optimization of complex multilevel systems. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225(2): 451-462.
Choudhary, R., Malkawi, A. & Papalambros, P.Y. 2005. Analytic target cascading in simulation-based building design. Automation in Construction 14: 551-568.
Dormohammadi, S. & Rais-rohani, M. 2013. Exponential penalty function formulation for multilevel optimization using the analytical target cascading framework. Structural and Multidisciplinary Optimization 47(4): 599-612.
Fawzy, A. 1981. Hierarchical optimization of nonlinear dynamical systems with nonquadratic objective functions. IEEE Transactions on Systems, Man, and Cybernetics 11(3): 232-236.
Guarneri, P., Gobbi, M. & Papalambros, P.Y. 2011. Efficient multi-level design optimization using analytical target cascading and sequential quadratic programming. Structural and Multidisciplinary Optimization 44(3): 351-362.
Han, J. & Papalambros, P.Y. 2010. A sequential linear programming coordination algorithm for analytical target cascading. Journal of Mechanical Design 132(2): 021003.
Hassan, M., Hurteau, R., Singh, M.G. & Titli, A. 1978. A three level costate prediction method for continuous dynamical systems. Automatica 14(2): 177-181.
Hassan, M. & Singh, M.G. 1976. The optimization of non-linear systems using a new two level method. Automatica 12(4): 359-363.
Jamshidi, M. 1997. Large-scale systems: modeling, control and fuzzy logic. Prentice Hall, New Jersey, USA.
Kang, N., Kokkolaras, M., Papalambros, P.Y., Yoo, S., Na, W., Park, J. & Featherman, D. 2014. Optimal design of commercial vehicle systems using analytical target cascading. Structural and Multidisciplinary Optimization 50(6): 1103-1114.
Kim, H.M., Chen, W. & Wiecek, M.M. 2006. Lagrangian coordination for enhancing the convergence of analytical target cascading. AIAA Journal 44(10): 2197-2207.
Kim, H.M., Rideout, D.G., Papalambros, P.Y. & Stein, J.L. 2003. Analytical target cascading in automotive vehicle design. Journal of Mechanical Design 125(3): 481-489.
Lassiter, J.B., Wiecek, M.M. & Andrighetti, K.R. 2005. Lagrangian coordination and analytical target cascading: solving ATC-decomposed problems with lagrangian duality. Optimization and Engineering 6(3): 361-381.
Li, X., Liu, C., Li, W. & Shang, H. 2013. Application of collaborative optimization to optimal control problems. AIAA Journal 51(3): 745-750.
Li, Y., Lu, Z. & Michalek, J.J. 2008. Diagonal quadratic approximation for parallelization of analytical target cascading. Journal of Mechanical Design 130(5): 051402.
Masmoudi, N.K., Rekik, C., Djemel, M. & Derbel, N. 2009. Decomposition and hierarchical control for discrete large scale system using neural networks. 2009 International Conference on Advances in Computational Tools for Engineering Applications. Zouk Mosbeh, Lebanon.
Michalek, J.J. & Papalambros, P.Y. 2005. An efficient weighting update method to achieve acceptable consistency deviation in analytical target cascading. Journal of Mechanical Design 127(2): 206-214.
Moussouni, F., Kreuawan, S., Brisset, S., Gillon, F., Brochet, P. & Nicod, L. 2009. Multi-level design optimization using target cascading an improvement of convergence. The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 28(5): 1162-1178.
Mukhopadhyay, B.K. & Malik, O.P. 1972. Optimal control of synchronous-machine excitation by quasilinearisation techniques. Proceedings of the Institution of Electrical Engineers 119(1): 91-98.
Papalambros, P.Y., Wilde, D.J. 2000. Principles of optimal design: modeling and computation. Cambridge University Press, Cambridge, UK.
Picasso, B., DeVito, D., Scattolini, R. & Colaneri, P. 2010. An MBC approach to the design of two-layer hierarchical control systems. Automatica 46(5): 823-831.
Sadati, N. & Babazadeh, A. 2006. Optimal control of robot manipulators with a new two-level gradient-based approach. Electrical Engineering 88(5): 383-393.
Sadati, N., & Berenji, H. 2016. Coordination of large-scale systems using fuzzy optimal control strategies and neural networks. 2016 IEEE International Conference on Fuzzy Systems, Vancouver, Canada.
Sadati, N., & Ramezani, M.H. 2008. Hierarchical optimal control of nonlinear systems: an application to a benchmark cstr problem. 3rd IEEE Conference on Industrial Electronics and Applications, Singapore, Singapore.
Sadati, N. & Ramezani, M.H. 2010. Novel interaction prediction approach to hierarchical control of large-scale systems. IET Control Theory Appl. 4(2): 228-243.
Singh, M.G. & Hassan, M. 1977. A two level prediction algorithm for non-linear systems. Automatica 13(1): 95-96.
Tang, J., Luh, P.B. & Chang, T. 1991. Mixed coordination method for long-horizon optimal control problems. International Journal of Control 53(6): 1395-1412.
Tang, Y., Landers, R.G. & Balakrishnan, S.N. 2006. Hierarchical optimal force-position-contour control of machining processes. Control Engineering Practice 14(8): 909-922.
Tosserams, S., Etman, L.F., Papalambros, P.Y. & Rooda, J.E. 2006. An augmented lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers. Structural and Multidisciplinary Optimization 31(3): 176-189.
Wang, W., Blouin, V.Y., Gardenghi, M.K., Fadel, G.M., Wiecek, M.M & Sloop, B.C. 2013. Cutting plane methods for analytical target cascading with augmented lagrangian coordination. Journal of Mechanical Design 135(10): 104502.
