Abstract
We consider a distributed NMPC scheme in which the individual systems are coupled via state constraints. In order to avoid violation of the constraints, the subsystems communicate their individual predictions to the other subsystems once in each sampling period. For this setting, Richards and How have proposed a sequential distributed MPC formulation with stabilizing terminal constraints. In this chapter we show how this scheme can be extended to MPC without stabilizing terminal constraints or costs.We show theoretically and by means of numerical simulations that under a suitable controllability condition stability and feasibility can be ensured even for rather short prediction horizons.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Altmüller, N., Grüne, L., Worthmann, K.: Performance of NMPC schemes without stabilizing terminal constraints. In: Diehl, M., et al. (eds.) Recent Advances in Optimization and Its Applications in Engineering, pp. 289–298. Springer, London (2010)
Altmüller, N., Griine, L., Worthmann, K.: Receding horizon optimal control for the wave equation. In: Proc. 49th IEEE Conf. Decision and Control (CDC 2010), Atlanta, GA, pp. 3427–3432 (2010)
Dashkovskiy, S., Rüffer, B.S., Wirth, F.R.: An ISS small gain theorem for general networks. Math. Control Signals Systems 19(2), 93–122 (2007)
Giselsson, P., Rantzer, A.: Distribited model predictive control with siboptimality and stability giarantees. In: Proc. 49th IEEE Conference on Decision and Control (CDC 2010), Atlanta, GA, pp. 7272–7277 (2010)
Grimm, G., Messina, M.J., Tuna, S.E., Teel, A.R.: Model predictive control: For want of a local control Lyapunov finction, all is not lost. IEEE Trans. Automatic Control, 546–558 (2005)
Grüne, L., Pannek, J.: Nonlinear Model Predictive Control. Theory and Algorithms. Springer, London (2011)
Grüne, L., Pannek, J., Seehafer, M., Worthmann, K.: Analysis of iinconstrained nonlinear MPC schemes with varying control horizon. SIAM J. Control Optimization 48, 4938–4962 (2010)
Grüne, L.: Analysis and design of iinconstrained nonlinear MPC schemes for finite and infinite dimensional systems. SIAM J. Control Optimization 48, 1206–1228 (2009)
Jadbabaie, A., Hauser, J.: On the stability of receding horizon control with a general terminal cost. IEEE Trans. Aromatic Control 50(5), 674–678 (2005)
Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: stability and optimality. Automatica 36, 789–814 (2000)
Primbs, J., Nevistić, V.: Feasibility and stability of constrained finite receding horizon control. Automatica 36(7), 965–971 (2000)
Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Pib- lishing, Madison (2009)
Richards, A., How, J.P.: Robust distributed model predictive control. Int. J. Control 80(9), 1517–1531 (2007)
Richards, A., How, J.P.: A decentralized algorithm for robist constrained model predictive control. In: Proc. American Control Conf. (ACC 2004), Boston, MA, pp. 4261–4266 (2004)
Scattolini, R.: Architectires for distribited and hierarchical model predictive control—A review. J. Process Control 19(5), 723–731 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer London
About this chapter
Cite this chapter
Grüne, L., Worthmann, K. (2012). A Distributed NMPC Scheme without Stabilizing Terminal Constraints. In: Johansson, R., Rantzer, A. (eds) Distributed Decision Making and Control. Lecture Notes in Control and Information Sciences, vol 417. Springer, London. https://doi.org/10.1007/978-1-4471-2265-4_12
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2265-4_12
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2264-7
Online ISBN: 978-1-4471-2265-4
eBook Packages: EngineeringEngineering (R0)