On the control of lossy networks with hold strategy

The discipline of linear control in centralized systems has been extensively studied and optimal results can already be found in the literature. However, in recent years, new variants of control systems have appeared, among them control communication networks with various degrees of reliability. Two approaches have been defined to cope with missing control values in such non-ideal networks: output zero and hold. The optimal control law over output zero lossy networks has already been presented in the literature. In this paper, we present the optimal control law on generalized output schemes. Hence, the control law of derived from such generalized output scheme has more internal structure, being equal to optimal controller of each one of its sub-cases, including the zero and the hold approaches. Furthermore, it is presented the optimal output strategy to which the optimal control under it produces the smallest cost. Two proofs are provided for the proposed control law, one based on the collection/gathering terms and another based on a recursive differential expansion. The novel control law is tested via simulation and the obtained results are in perfect agreement with the presented theory.