Suboptimal control of nonlinear continuous-time locally positive systems using input-state linearization and SDRE approach

• Autorzy: Bernat J. , Kołota J. , Stępień S. , Superczyńska P.

Identyfikatory

DOI

10.24425/119054

• Języki publikacji: EN

Abstrakty

EN

The infinite time suboptimal control problem for continuous-time nonlinear positive systems is formulated and solved. A solution to the problem using input-state linearization and state-dependent Riccati equation method (SDRE) is established, a procedure for solving the problem is proposed and illustrated with a numerical example.

Słowa kluczowe

EN

positive nonlinear systems; feedback control; Riccati equation

PL

sprzężenie zwrotne; układy nieliniowe; równanie Riccatiego

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 1
• Strony: 17--21
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Bernat J.

• Poznan University of Technology, Faculty of Computing, Institute of Automation and Robotics, Piotrowo 3a, 61-138 Poznan

autor

Kołota J.

• Poznan University of Technology, Faculty of Computing, Institute of Automation and Robotics, Piotrowo 3a, 61-138 Poznan

autor

Stępień S.

• Poznan University of Technology, Faculty of Computing, Institute of Automation and Robotics, Piotrowo 3a, 61-138 Poznan

autor

Superczyńska P.

• Poznan University of Technology, Faculty of Computing, Institute of Automation and Robotics, Piotrowo 3a, 61-138 Poznan

Bibliografia

• [1] E.D. Sontag, “Molecular systems biology and control”, European J. of Control 11, 396‒435 (2005).
• [2] W.M. Haddad and V.S. Chellaboina, “Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems”, Nonlinear Analysis: Real World Applications 6(1), 35–65 (2005).
• [3] R. Shorten, F. Wirth, and D. Leith, “A positive systems model of tcp-like congestion control: Asymptotic results”, IEEE/ACM Transactions on Networking 14(3), 616–629 (2006).
• [4] J. von Neumann, “A model of general economic equilibrium”, The Review of Economic Studies 13(1), 1–9 (1945).
• [5] I. Chang, S.Y. Park, and K.H. Choi, “Nonlinear attitude control of a tether-connected multi-satellite in three-dimensional space”, IEEE Trans. Aeros. Electron. Syst. 46(4), 1950–1968, (2010).
• [6] H.T. Banks, B.M. Lewis, and H.T. Tran, “Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach”, Comput. Optim. Appl. 37, 177–218, (2007).
• [7] T. Do, S. Kwak, H. Choi, and J. Jung, “Suboptimal control scheme design for interior permanent-magnet synchronous motors: an SDRE-based approach”, IEEE Trans on Power Electron. 29(6), 3020‒3030, (2014).
• [8] T.D. Do, H.H. Choi, and J.W. Jung, “SDRE-based near optimal control system design for PM synchronous motor”, IEEE Trans. Ind. Electron. 59(11), 4063–4074 (2012).
• [9] B.D.O. Anderson and J.B. Moore, Optimal Control Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, 1990.
• [10] A. Isidori, Nonlinear Control Systems. Springer, New York, 1995.
• [11] T. Kaczorek, “Minimum energy control of positive continuous- time linear systems with bounded inputs”, Int. J. Appl. Math. Comput. Sci. 23(4), 725–730, (2013).
• [12] J.S. Shamma and M. Athens, “Analysis of gain scheduled control for nonlinear plants”, IEEE Trans. Autom. Control 35(8), 898–907, (1990).
• [13] J.R. Cloutier, C.N. D’Souza, and C.P. Mracek, “Nonlinear regulation and nonlinear h∞ control via the state-dependent Riccati equation technique: part 1”, Proceedings of the First International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, (1996).
• [14] A. Wernli and G. Cook, “Suboptimal control for the nonlinear quadratic regulator problem”, Automatica 11, 75–84, (1975).
• [15] W.L. Garrard, “Design of non-linear automatic flight control system”, Automatica 13(5), 497–505, (1977).

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).