Abstract
This paper presents a novel method for designing robust MPC schemes that are self-optimizing in terms of disturbance attenuation. The method employs convex control Lyapunov functions and disturbance bounds to optimize robustness of the closed-loop system on-line, at each sampling instant - a unique feature in MPC. Moreover, the proposed MPC algorithm is computationally efficient for nonlinear systems that are affine in the control input and it allows for a decentralized implementation.
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References
Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optimality. Automatica 36(6), 789–814 (2000)
Lazar, M., Heemels, W.P.M.H., Bemporad, A., Weiland, S.: Discrete-time non-smooth NMPC: Stability and robustness. In: Assessment and Future Directions of NMPC. LNCIS, vol. 358, pp. 93–103. Springer, Heidelberg (2007)
Magni, L., Scattolini, R.: Robustness and robust design of MPC for nonlinear discrete-time systems. In: Assessment and Future Directions of NMPC. LNCIS, vol. 358, pp. 239–254. Springer, Heidelberg (2007)
Mayne, D.Q., Kerrigan, E.C.: Tube-based robust nonlinear model predictive control. In: 7th IFAC Symposium on Nonlinear Control Systems, Pretoria, pp. 110–115 (2007)
Raković, S.V.: Set theoretic methods in model predictive control. In: Proc. of the 3rd Int. Workshop on Assessment and Future Directions of NMPC, Pavia, Italy (2008)
Sontag, E.D.: Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control AC-34, 435–443 (1989)
Sontag, E.D.: Stability and stabilization: Discontinuities and the effect of disturbances. In: Clarke, F.H., Stern, R.J. (eds.) Nonlinear Analysis, Differential Equations, and Control, pp. 551–598. Kluwer, Dordrecht (1999)
Jiang, Z.-P., Wang, Y.: Input-to-state stability for discrete-time nonlinear systems. Automatica 37, 857–869 (2001)
Kokotović, P., Arcak, M.: Constructive nonlinear control: A historical perspective. Automatica 37(5), 637–662 (2001)
Lazar, M.: Model predictive control of hybrid systems: Stability and robustness, PhD Thesis, Eindhoven University of Technology, The Netherlands (2006)
Lazar, M., Muñoz de la Peña, D., Heemels, W.P.M.H., Alamo, T.: On input-to-state stability of min-max MPC. Systems & Control Letters 57, 39–48 (2008)
Wayne, S.U.: Mathematical Dept., Coffee Room. Every convex function is locally Lipschitz, The American Mathematical Monthly 79(10), 1121–1124 (1972)
Bertsekas, D.P.: Nonlinear programming, 2nd edn. Athena Scientific (1999)
Lazar, M., Heemels, W.P.M.H., Weiland, S., Bemporad, A.: Stabilizing model predictive control of hybrid systems. IEEE Transactions on Automatic Control 51(11), 1813–1818 (2006)
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Lazar, M., Heemels, W.P.M.H., Jokic, A. (2009). Self-optimizing Robust Nonlinear Model Predictive Control. In: Magni, L., Raimondo, D.M., Allgöwer, F. (eds) Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01094-1_2
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DOI: https://doi.org/10.1007/978-3-642-01094-1_2
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