## 1 Introduction
For cooperative schemes, in Reference [13], the authors introduced DMPC with bounded disturbances where the bound of the disturbance is time varying. For both decentralised and distributed versions, feasibility was shown. Several cooperative control schemes were utilised to show these properties: the authors of Reference [5] used terminal costs to speed up the convergence rate while assuming bounded interactions among the subsystems. In Reference [14], a cooperative control was applied where the subsystems optimise sequentially with predetermined terminal regions and cost functions to achieve feasibility and convergence. The authors of Reference [15] added a global stability constraint to show convergence, which is locally impaired by each subsystem. In Reference [16], the authors address linear networked systems in cooperative control regarding the consensus via static couplings, which are imposed on the input of each subsystem from the output of other systems. For gradient-based DMPC schemes based on dual decomposition, an upper bound on the system dynamics is used to improve the convergence rate [17]. The results were extended in Reference [18] to general DMPC problems, and convergence is shown via a stopping criterion which computes lower and upper bounds when a sufficient control is found to keep the system in the desired state. Considering noncooperative schemes, a global objective was completely decomposed in Reference [19] and applied on network traffic control,. Moreover, the control values of all affected neighbours were considered in a proposed communication protocol to obtain a fixed decision order for execution. In Reference [20], an iterative exchange of information in each time instant was not needed, as reference trajectories are provided for each subsystem while convergence is ensured via terminal constraints. The authors of Reference [21] utilised the scheme of Reference [11] to show feasibility and convergence without using terminal costs or constraints. Therefore, asymptotic controllability of the distributed system was assumed to derive stability properties. Instead of using a fixed optimisation order, in Reference [22], a dynamic deordering rule was presented to iteratively change the order dynamically on an abstract criterion. Convergence was shown based on a relaxed Lyapunov condition. A leader-follower system with flexible leader was considered in Reference [23] with an arbitrary chosen convex hull. The sequential order of the execution of optimisation is fixed, while small perturbations were incorporated. Regarding slow dynamics, in Reference [24] a quantisation scheme was applied for the communication among subsystems which allow slow variation of the quantisation interval. Here, the quantisation parameters are exchanged among the subsystems to establish terminal regions which ensured that, from a warm start initial condition, the equilibrium was reached within finite time. Other approaches to stabilise nonlinear systems used Lyapunov-based controllers to keep the system stable with tight state and input constraints, while relaxations on the states were possible via a switched control [25]. On the distributed level, in Reference [26], the Lyapunov controllers were executed in either a sequential or iterative manner while stability was ensured by a cost decrease constraint. In Reference [27], the authors relaxed the Lyapunov scheme via a time delay to allow for a temporary increase of costs. The authors in Reference [28] applied a Lyapunov controller with a global bounded state feedback controller for a tracking problem of a non-holonomic robot.