Decentralized MPC under arbitrary packet loss Sample Clauses

Decentralized MPC under arbitrary packet loss. In the previous section we assumed that the communication model among neighboring MPC con- trollers was faultless, so that each MPC agent could successfully receive the information about the states of its corresponding submodel. However, one of the main issues in networked control systems is the unreliability of communication channels, which may result in data packet dropout. In this sec- tion we derive a sufficient condition for ensuring convergence of the DMPC closed-loop in the case packets containing measurements are lost for an arbitrary but upper-bounded number N of consec- utive time steps. The results shown here are based on formulation (126) and rely on the open-loop asymptotic stability Assumptions 2 and 3. The issue is still non-trivial, as if a set of measures for subsystem i is lost, this would affect not only the trajectory of subsystem i because of the improper control action ui, but, due to the dynamical coupling, also the trajectories of subsystems j ∈ J, where J = {j | i ∈ Ixj ∪ Iuj}, and thus the closed-loop stability of the overall system may be endangered. By relying on open-loop stability, setting u(t) = 0 is a natural choice for backup input moves when no state measurements are available because of a communication blackout. The next theorem proves asymptotic closed-loop stability of decentralized MPC under packet loss. The proof of the theorem generalizes and unifies the results of [100, 101]. Theorem 8. Let N be a positive integer such that no more than N consecutive steps of channel transmission blackout can occur. Assume u(t) = 0 is applied when no packet is received. Let Assumptions 2, 3 hold and i = 1, . . . , M define Pi as in (127), ∆ui(t), ∆xi(t), ∆Ai, ∆Bi as in (129), ∆Y i(x(t)) as in (130), i ∆Si(x) , [2(AiWrx + Biu∗i(x))rWr + ∆Y i(x)r](Aj—1)rWiPiWrAj—1∆Y i(x) (132) and let ξi(x) , AiWirx + Biu∗0i(x). If the condition (i) Σ x′WiWi′QWiWi′x + ξi(x)′(Pi — Wi′(Aj−1)′WiPiWi′Aj−1Wi)ξi(x) — ∆Si(x) ≥ 0, 6x ∈ Rn, 6j = 1, ..., N (133a) (ii) Σ x′WiWi′QWiWi′x + ξi(x)′(Pi — Wi′(Aj−1)′WiPiWi′Aj−1Wi)ξi(x) — ∆Si(x) + u0∗i(x)′Zi′RZiu0∗i(x) — αx′x ≥ 0, 6x ∈ Rn, 6j = 1, ..., N (133b) is satisfied for some scalar α > 0, then the decentralized MPC scheme defined in (126)–(128) in closed loop with (118) is globally asymptotically stable under packet loss.