This paper presents a new formulation and synthesis approach for stabilizing cooperative distributed model predictive control (MPC) for networks of linear systems, which are coupled in their dynamics. The controller is defined by a network-wide constrained optimal control problem, which is solved online by distributed optimization. The main challenge is the definition of a global MPC problem, which both defines a stabilizing control law and is amenable to distributed optimization, i.e., can be split into a number of appropriately coupled subproblems. For such a combination of stability and structure, we propose the use of a separable terminal cost function, combined with novel time-varying local terminal sets. For synthesis, we introduce a method that allows for constructing these components in a completely distributed way, without central coordination. The paper covers the nominal case in detail and discusses the extension of the methodology to reference tracking. Closed-loop functionality of the controller is illustrated by a numerical example, which highlights the effectiveness of the proposed controller and its time-varying local terminal sets.

Abstract-This work presents an approach for both distributed synthesis and control for a network of discrete-time constrained linear systems without central coordinator. Every system in the network is dynamically coupled to a number of neighboring systems and it is assumed that communication among neighbors is possible. A model predictive controller based on distributed optimization is introduced, by which every system in the network can compute feasible and stabilizing control inputs online. Stability of the closed-loop network of systems is guaranteed by introducing local terminal cost functions and sets, which together satisfy invariance conditions in a distributed way. This includes in particular that the local terminal sets are not static but evolve over time. It is shown that synthesis of both quadratic terminal cost functions and corresponding terminal sets can be done by distributed optimization. Finally, closed-loop performance of the proposed controller is demonstrated on a coupled array of inverted pendulums.

Abstract-This paper presents a systematic computational study on the performance of distributed optimization in model predictive control (MPC). We consider networks of dynamically coupled systems, which are subject to input and state constraints. The resulting MPC problem is structured according to the system's dynamics, which makes the problem suitable for distributed optimization. The influence of fundamental aspects of distributed dynamic systems on the performance of two particular distributed optimization methods is systematically analyzed. The methods considered are dual decomposition based on fast gradient updates (DDFG) and the alternating direction method of multipliers (ADMM), while the aspects analyzed are coupling strength, stability, initial state, coupling topology and network size. The methods are found to be sensitive to coupling strength and stability, but relatively insensitive to initial state and topology. Moreover, they scale well with the number of subsystems in the network.

SUMMARYThis paper focuses on cooperative distributed model predictive control (MPC) of wind farms, where the farms respond to active power control commands issued by the transmission system operator. A distributed MPC scheme is proposed, which aims at satisfying the requirements imposed by the grid code while minimizing the farm-wide mechanical structure fatigue. The distributed MPC control law is defined by a global finite-horizon optimal control problem, which is solved at every time step by distributed optimization. The computational approach is completely distributed, that is, every turbine evaluates its own globally optimal input by considering local measurements and communicating to neighboring turbines only. Two MPC versions are compared, in the first of which the farm-wide power output constraint is implemented as a hard constraint, whereas in the second, it is implemented as a soft constraint. As for distributed optimization methods, the alternating direction method of multipliers as well as a dual decomposition scheme based on fast gradient updates are compared. The performance of the proposed distributed MPC controller, as well as the performance of the distributed optimization methods used for its operation, are compared in the simulation on four exemplary scenarios. The results of the simulations imply that the use of cooperative distributed MPC in wind farms is viable both from a performance and from a computational viewpoint.

In this work, synthesis and closed-loop operation of robust distributed model predictive control (MPC) for linear systems using distributed optimization is discussed. Previous work has shown that a nominal MPC controller for this setup can be synthesized and operated in a purely distributed manner. This paper extends this concept to linear systems subject to additive bounded disturbance. It is shown how well-established robust MPC approaches can be applied to distributed systems. The main focus of the paper is on a thorough discussion of computational issues arising from distributed synthesis and closed-loop operation of existing robust MPC controllers. In particular, techniques for distributed synthesis of structured robust positive invariant sets and distributed constraint tightening are proposed. The paper is concluded by a numerical example which illustrates the functionality and performance of the proposed techniques.