From the perspective of large system, a directed complex dynamic network (DCDN) is regarded as being made up of the nodes subsystem (NS) and the links subsystem (LS), which are coupled to each other. Different from previous studies, which propose the dynamic model of LS with the matrix differential equations, this paper describes the dynamic behaviour of LS with the outgoing links vector at every node, by which the dynamic model of LS can be represented as the vector differential equation to form the outgoing links subsystem (OLS). Due to the fact that vectors have more flexible mathematical properties than matrices, this paper proposes the more convenient mathematic method to investigate the double tracking control problem of NS and OLS. Under the condition that the states of NS are available and the states of OLS are unavailable, the asymptotical state observer of OLS is designed, by which the tracking controllers of NS and OLS are synthesised to ensure achieving the double tracking goals. Finally, an example simulation for supporting the theoretical results is also provided.

Most of the literature on robust parameter design concerns simple response systems; however, many engineering systems can be described as signal–response systems, in which the relationship between the signal factor and response is linear or nonlinear. In this article, a robust parameter design method is proposed to optimize nonlinear signal–response systems. To make the signal–response relationship insensitive to noise factors, the variation model and response model are developed using kriging models. In the variation model, the mean and standard deviation of the variation in response over the range of the signal factor are fitted and then synthesized as the robustness criterion, which is minimized to optimize the settings of control factors. The response model is used to obtain the fitting model of the signal–response relationship at the optimal setting of control factors. The applicability and efficiency of the proposed method are demonstrated using an engineering case.

This paper provides a way to optimise the steady-state tracking performance of the adaptive control system in the presence of unknown external disturbances. A-priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. Especially, the updatable non-empty admissible model set, which is consistent to the a-priori knowledge of the plant parameter and the online measurements, is computed. Treating the overall system performance as the criteria, the nominal model is optimally chosen within the admissible model set. The optimal nominal model is subsequently used to synthesise the optimal closed-loop controller that minimises the steady-state absolute value of the tracking error. Combining the above two aspects, an optimal adaptive control scheme is proposed. Because of the consistency of the identification criteria and control object, the adaptive control scheme proposed in this paper can achieve the overall optimal steady-state tracking performance, and the effect of the interplay between the identification and control of the adaptive system can be handled effectively. In addition, the computable optimal performance is also provided.

This article presents a robust adaptive control scheme for a discrete-time plant that is subjected to both coprime factor perturbations and unknown exogenous disturbances. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of the perturbations and disturbances, and an a priori computable upper bound on the size of the nonparametric dynamical uncertainty, for which stability is ensured, is provided. Moreover, one can guarantee a priori bound on the asymptotic performance of the overall adaptive system which is arbitrarily close to that of the corresponding nonadaptive control system. In addition, it is shown that the ℓ₁ optimal robust controller design is continuous as a map from the plant to the optimal closed-loop solution. Furthermore, if the set of plants is compact, then the ℓ₁ optimal robust controller design is uniformly continuous on the set of plants. These properties are necessary for analysing the interplay between identification and control in the overall adaptive system.