## Decentralized receding horizon control for large scale dynamically decoupled systems.(English)Zbl 1104.93038

Summary: We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.

### MSC:

 93C55 Discrete-time control/observation systems 93B40 Computational methods in systems theory (MSC2010) 93A15 Large-scale systems
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### References:

 [1] Borrelli, F. (2003). Constrained optimal control of linear and hybrid systems. Lecture notes in control and information sciences (Vol. 290). Berlin: Springer. · Zbl 1030.49036 [2] Borrelli, F.; Baotic, M.; Bemporad, A.; Morari, M., Dynamic programming for constrained optimal control of discrete-time hybrid systems, Automatica, 41, 1, 1709-1721, (2005) · Zbl 1125.49310 [3] Borrelli, F., & Keviczky, T. (2005). Distributed LQR design for dynamically decoupled systems. Technical Report 2005-01, University of Minnesota, Minneapolis, MN. 〈http://sciweb.lib.umn.edu/ej/Repository.phtml#ind〉. · Zbl 1367.93238 [4] Borrelli, F., Keviczky, T., & Balas, G. J. (2004). Collision-free UAV formation flight using decentralized optimization and invariant sets. In Proceedings of the 43rd IEEE conference on decision and control. [5] Borrelli, F., Keviczky, T., Balas, G. J., Stewart, G., Fregene, K., & Godbole, D. (2005). Hybrid decentralized control of large scale systems. In Hybrid systems: Computation and control. Lecture notes in computer science (Vol. 3414, pp. 168-183). Berlin: Springer. · Zbl 1078.93532 [6] Camponogara, E.; Jia, D.; Krogh, B.H.; Talukdar, S., Distributed model predictive control, IEEE control systems magazine, 22, 1, 44-52, (2002) [7] Chen, H.; Allgöwer, F., A quasi-infinite horizon nonlinear model predictive scheme with guaranteed stability, Automatica, 14, 10, 1205-1217, (1998) · Zbl 0947.93013 [8] D’Andrea, R.; Dullerud, G.E., Distributed control design for spatially interconnected systems, IEEE transactions on automatic control, 48, 9, 1478-1495, (2003) · Zbl 1364.93206 [9] Dunbar, W.B.; Murray, R.M., Distributed receding horizon control for multi-vehicle formation stabilization, Automatica, 42, 4, 549-558, (2006) · Zbl 1103.93031 [10] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514 [11] Jia, D., & Krogh, B. H. (2002). Min-max feedback model predictive control for distributed control with communication. In Proceedings of the American control conference. [12] Keerthi, S.S.; Gilbert, E.G., Optimal infinite-horizon feedback control laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations, Journal of optimization theory and applications, 57, 265-293, (1988) · Zbl 0622.93044 [13] Keviczky, T. (2005). Decentralized receding horizon control of large scale dynamically decoupled systems. Ph.D. Thesis, Control Science and Dynamical Systems Center, University of Minnesota, Minneapolis. · Zbl 1104.93038 [14] Keviczky, T., Borrelli, F., & Balas, G. J. (2004). A study on decentralized receding horizon control for decoupled systems. In Proceedings of the American control conference. · Zbl 1104.93038 [15] Keviczky, T., Borrelli, F., & Balas, G. J. (2006). Decentralized receding horizon control for large scale dynamically decoupled systems. Technical Report 2006-01, University of Minnesota, Minneapolis, MN. Online: 〈http://sciweb.lib.umn.edu/ej/Repository.phtml#ind〉. · Zbl 1104.93038 [16] Keviczky, T., Vanek, B., Borrelli, F., & Balas, G. J. (2006). Hybrid decentralized receding horizon control of vehicle formations. In Proceedings of the American control conference, Minneapolis, MN. [17] Magni, L.; De Nicolao, G.; Scattolini, R.; Allgöwer, F., Robust nonlinear model predictive control for nonlinear discrete-time systems, International journal of robust and nonlinear control, 13, 3-4, 229-246, (2003) · Zbl 1049.93030 [18] 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) · Zbl 0949.93003 [19] Online: $$\langle$$http://www.aem.umn.edu/ keviczky/Simulations.html〉. [20] Richards, A., & How, J. (2004a). A decentralized algorithm for robust constrained model predictive control. In Proceedings of the American control conference. [21] Richards, A., & How, J. (2004b). Decentralized model predictive control of cooperating UAVs. In Proceedings of the 43rd IEEE conference on decision and control. [22] Rotkowitz, M., & Lall, S. (2002). Decentralized control information structures preserved under feedback. In Proceedings of the 41st IEEE conference on decision and control. · Zbl 1365.93020 [23] Sandell, N.R.; Varaiya, P.; Athans, M.; Safonov, M., Survey of decentralized control methods for large scale systems, IEEE transactions on automatic control, AC-23, 2, 195-215, (1978) [24] Schouwenaars, T., How, J., & Feron, E. (2004). Receding horizon path planning with implicit safety guarantees. In Proceedings of the American control conference. [25] Vadigepalli, R.; Doyle III, F.J., A distributed state estimation and control algorithm for plantwide processes, IEEE transactions on control systems technology, 11, 1, 119-127, (2003) [26] Wang, S.; Davison, E.J., On the stabilization of decentralized control systems, IEEE transactions on automatic control, 18, 5, 473-478, (1973) · Zbl 0273.93047
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