Abstract
The distributed RHC is of great efficiency to deal with large-scale systems, but relies heavily on communication networks which may not be reliable. In this chapter, we study the distributed RHC problem for a class of continuous-time decoupled nonlinear systems subject to communication delays. By using the robustness constraint and designing the waiting mechanism, a delay-involved distributed RHC scheme is proposed. Furthermore, the iterative feasibility and stability properties are analyzed. It is shown that, if the communication delays are bounded by an upper bound, and the cooperation weights and the sampling period are designed appropriately, the overall system state converges to the equilibrium point. The theoretical results are verified by a simulation study.
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Notes
- 1.
In this example, there are two subsystems. One is the subsystem i with three neighbors \(i_1\), \(i_2\) and \(i_3\), and the other is the subsystem j with one neighbor \(j_1\). At time \(t_k\), the overall system is synchronized and the optimal control inputs are applied for the subsystem i and j, and the assumed state information begins being transmitted from their neighbors to the subsystems i and j. The system states are measured at time instant \(t_k+\delta \). For the subsystem i, the time delays from its neighbors to itself are \(\tau _k^{ii_1}\), \(\tau _k^{ii_2}\) and \(\tau _k^{ii_3}\), respectively. Since \(\tau _k^{ii_1}<\tau _k^{ii_2}<\tau _k^{ii_3}\), it has \(\tau _k^i = \tau _k^{ii_3}\) and all the neighbors’ information has been received at time \(\tilde{t}_{k+1}^i = t_k + \delta + \tau _k^i\). For the subsystem j, the time delay from its neighbor to itself is \(\tau _k^{jj_1}\). So \(\tilde{t}_{k+1}^{j} = t_k +\delta + \tau _k^{j} = t_k +\delta + \tau _k^{jj_1}\). Since \(\tau _k^j>\tau _k^i\), the synchronized time of the subsystem i and j will be at \(t_{k+1} = t_k + \delta + \tau _{k}^{jj_1}\), and the subsystems i and j will generate and apply the new control signals at the time \(t_{k+1}\).
References
Chen, H., Allgöwer, F.: A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica 34(10), 1205–1217 (1998)
Dunbar, W.B.: Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans. Autom. Control 52(7), 1249–1263 (2007)
Dunbar, W.B., Murray, R.M.: Distributed receding horizon control for multi-vehicle formation stabilization. Automatica 42(4), 549–558 (2006)
Franco, E., Magni, L., Parisini, T., Polycarpou, M.M., Raimondo, D.M.: Cooperative constrained control of distributed agents with nonlinear dynamics and delayed information exchange: A stabilizing receding-horizon approach. IEEE Trans. Autom. Control 53(1), 324–338 (2008)
Keviczky, T., Borrelli, F., Balas, G.J.: Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica 42(12), 2105–2115 (2006)
Khalil, H.K.: Nonlinear Systems, 3 edn. Prentice Hall (2002)
Li, H., Shi, Y.: Distributed model predictive control of constrained nonlinear systems with communication delays. Syst. Control Lett. 62(10), 819–826 (2013)
Li, H., Shi, Y.: Robust distributed model predictive control of constrained continuous-time nonlinear systems: a robustness constraint approach. IEEE Trans. Autom. Control 59(6), 1673–1678 (2014)
Michalska, H., Mayne, D.Q.: Robust receding horizon control of constrained nonlinear systems. IEEE Trans. Autom. Control 38(11), 1623–1633 (1993)
Raimondo, D.M., Magni, L., Scattolini, R.: Decentralized MPC of nonlinear systems: an input-to-state stability approach. Int. J. Robust Nonlinear Control 17(17), 1651–1667 (2007)
Richards, A., How, J.P.: Robust distributed model predictive control. Int. J. Control 80(9), 1517–1531 (2007)
Venkat, A.N., Hiskens, I.A., Rawlings, J.B., Wright, S.J.: Distributed MPC strategies with application to power system automatic generation control. IEEE Trans. Control Syst. Technol. 16(6), 1192–1206 (2008)
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Li, H., Shi, Y. (2017). Distributed RHC of Nonlinear Systems with Communication Delays. In: Robust Receding Horizon Control for Networked and Distributed Nonlinear Systems. Studies in Systems, Decision and Control, vol 83. Springer, Cham. https://doi.org/10.1007/978-3-319-48290-3_6
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DOI: https://doi.org/10.1007/978-3-319-48290-3_6
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