Abstract
In this chapter, we present an algorithm based on the model predictive control approach. Such an algorithm allows assigning on-line the optimal values of the control inputs and the scheduling inputs of resource-constrained systems. By focusing on its practical implementation aspects, such as its computational requirements, we propose a more efficient heuristic, called OPP. Next, by using a pre-computed off-line schedule, OPP is able to assign on-line the values of the control inputs and the scheduling inputs based on the plant available state information. The computational requirements of this heuristic are considerably reduced compared to those of the “standard” model predictive control approach. Furthermore, we prove that if some mild conditions are satisfied, then OPP guarantees the stability of the system as well as some performance improvements compared to its basic off-line schedule. We also show that the use of the periodic optimal control in the design of the control gains that will be used by OPP leads to a significant simplification of its implementations, which boils down to the comparison of T quadratic cost functions, T being the period of the basic off-line schedule. The OPP scheduling algorithm was finally applied to two distributed control systems: the active suspension controller of car and the quadrotor attitude control.
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
References
S. Al-Areqi, D. Görges, S. Liu, Robust control and scheduling codesign for networked embedded control systems, in 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, December 2011
M. Andersson, D. Henriksson, A. Cervin, TrueTime 1.3—reference manual. Department of Automatic Control, Lund Institute of Technology, Sweden, June 2005
C. Aubrun, D. Simon, Y.Q. Song (eds.), Co-design Approaches for Dependable Networked Control Systems (Wiley, New York, 2010)
A. Bemporad, M. Morari, Control of systems integrating logic, dynamics, and constraints. Automatica 35(3), 407–427 (1999)
M.-M. Ben Gaid, A. Çela, S. Diallo, R. Kocik, R. Hamouche, A. Reama, Performance evaluation of the distributed implementation of a car suspension system, in Proceedings of the IFAC Workshop on Programmable Devices and Embedded Systems, Brno, Czech Republic, February 2006
M.-M. Ben Gaid, A. Çela, Y. Hamam, Optimal integrated control and scheduling of networked control systems with communication constraints: application to a car suspension system. IEEE Trans. Control Syst. Technol. 14(4), 776–787 (2006)
M.-M. Ben Gaid, A. Çela, R. Kocik, Distributed control of a car suspension system, in Proceedings of the 5th EUROSIM Congress on Modeling and Simulation, Paris, France, September 2004
F. Borrelli, M. Baotić, A. Bemporad, M. Morari, Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41(10), 1709–1721 (2005)
M.S. Branicky, S.M. Phillips, W. Zhang, Scheduling and feedback co-design for networked control systems, in 41st IEEE Conference on Decision and Control, Las Vegas, NV, USA, December 2002
A. Cervin, D. Henriksson, B. Lincoln, J. Eker, K.-E. Årzén, How does control timing affect performance? IEEE Control Syst. Mag. 23(3), 16–30 (2003)
R.M. Chalasani, Ride performance potential of active suspension systems—Part II: comprehensive analysis based on a full-car model, in Proceedings of the Symposium on Simulation and Control of Ground Vehicles and Transportation Systems, ASME AMD, Anaheim, CA, USA, December 1986
G.C. Goodwin, H. Haimovich, D.E. Quevedo, J.S. Welsh, A moving horizon approach to networked control systems design. IEEE Transactions on Automatic Control 49(9), 1427–1445 (2004)
D. Görges, M. Izák, S. Liu, Optimal control and scheduling of switched systems. IEEE Transactions on Automatic Control 56(1), 135–140 (2011)
T.A. Johansen, A. Grancharova, Approximate explicit model predictive control implemented via orthogonal search tree partitioning, in 15th IFAC World Congress, Barcelona, Spain, July 2002
R. Kocik, M.-M. Ben Gaid, R. Hamouche, Software implementation simulation to improve control laws design, in Proceedings of the First European Congress: Sensors & Actuators for Advanced Automotive Applications, Paris, France, December 2005
S. Longo, G. Herrmann, P. Barber, Optimization approaches for controller and schedule codesign in networked control, in 6th IFAC Symposium on Robust Control Design, Haifa, Israel, June 2009
P. Martí, J.M. Fuertes, G. Fohler, K. Ramamritham, Improving quality-of-control using flexible timing constraint: metric and scheduling issues, in Proceedings of the 23rd IEEE Real-Time Systems Symposium, Austin, Texas, USA, December 2002
P. Martí, J.M. Fuertes, K. Ramamritham, G. Fohler, Jitter compensation for real-time control systems, in Proceedings of the 22nd IEEE Real-Time Systems Symposium, London, England, December 2001
D. Nešić, A.R. Teel, Input-output stability properties of networked control systems. IEEE Trans. Autom. Control 49(10), 1650–1667 (2004)
L. Palopoli, A. Bicchi, A. Sangiovanni-Vincentelli, Numerically efficient control of systems with communication constraints, in Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, USA, December 2002
U. Rettig, O. von Stryk, Numerical optimal control strategies for semi-active suspension with electrorheological fluid dampers, in Fast Solution of Discretized Optimization Problems (Springer, Berlin, 2001), pp. 221–241
G.C. Walsh, O. Beldiman, L.G. Bushnell, Error encoding algorithms for networked control systems. Automatica 38(2), 261–267 (2002)
G.C. Walsh, H. Ye, Scheduling of networked control systems. IEEE Control Syst. Mag. 21(1), 57–65 (2001)
G.C. Walsh, H. Ye, L.G. Bushnell, Asymptotic behavior of nonlinear networked control systems. IEEE Trans. Autom. Control 46(7), 1093–1097 (2001)
Y. Ye, A fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem. Math. Oper. Res. 18(2), 334–345 (1993)
J.K. Yook, D.M. Tilbury, N.R. Soparkar, Trading computation for bandwidth: reducing communication in distributed control systems using state estimators. IEEE Trans. Control Syst. Technol. 10(4), 503–518 (2002)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Çela, A., Ben Gaid, M., Li, XG., Niculescu, SI. (2014). Optimal Integrated Control and On-line Scheduling of Resource-Constrained Systems. In: Optimal Design of Distributed Control and Embedded Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-02729-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-02729-6_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02728-9
Online ISBN: 978-3-319-02729-6
eBook Packages: EngineeringEngineering (R0)