Common use of See Appendix Clause in Contracts

See Appendix. Note that in case the controller at a node i ∈ I11 or i ∈ I21 does not have access to the desired output y∗, one can set ui to a constant, namely a nominal value, and incor- porate the node i in the subdynamics of (11) corresponding to the nodes indexed by I12 or I22, respectively. In Theorem 2, the control input u has been designed such that output agreement on a prescribed vector y∗ is achieved for the network. Observe that the “steady-state” control signal u¯ = ξ¯ is primarily determined by the initialization of the system/controller. Next, under the constraint of output agreement (6), we aim to minimize the following quadratic cost function 0 = (J11 − R11)∇H11(x¯11) min = 1 Σ u¯T Q u¯ (16) − G11(B11 ⊗ I)∇He(η¯) u¯ 2 i∈Ic + G11u¯11 + G11δ11 (13b) 0 = (J12 − R12)∇H12(x¯12) − G12(B12 ⊗ I)∇He(η¯) + G12δ12 (13c) 0 = (J21 − R21)∇H21(x¯21) − G21(B21 ⊗ I)∇He(η¯) (13d) + G21u¯21 + G21δ21 0 = (J22 − R22)∇H22(x¯22) − G22(B22 ⊗ I)∇He(η¯) + G22δ22 (13e) where Qi ∈ Rm × Rm is a positive definite matrix for each i, and Ic = I11 ∪ I21. Note that the optimization above determines the steady-state distribution of the control effort