Distributed Lyapunov-based Model Predictive Control

Ralph Hermans, Mircea Lazar and Andrej Jokic

We provide an almost decentralized solution to the problem of stabilizing a network of discrete-time nonlinear systems with coupled dynamics that are subject to local state/input constraints. By “almost decentralized” we mean that each local controller is allowed to use the states of neighboring systems for feedback, whereas it is not permitted to employ iterations between the systems in the network to compute the control action. The controller synthesis method used in this work is Lyapunov-based model predictive control. The closed-loop stability conditions are decentralized via a set of structured control Lyapunov functions (CLFs) for which the maximum over all the functions in the set is a CLF for the global network of systems. However, this does not necessarily imply that each function is a CLF for its corresponding subsystem. Additionally, a solution is provided for relaxing the temporal monotonicity of the network-wide CLF. For infinity-norm based structured CLFs and input-affine dynamics, we show that the decentralized MPC algorithm can be implemented by solving a single linear program in each network node. Two application examples are provided to illustrate the effectiveness of the developed theory and to show that the proposed method can perform as well as more complex distributed, iteration-based MPC algorithms.