by João M. Lemos and José M. Igreja.

This chapter describes D-SIORHC, a distributed MPC algorithm with stability constraints based on a game approach. This controller is designed for chained linear systems, in which each local subsystem interacts only with their neighbors. At the beginning of each sampling interval, each local controller agent computes the value of the corresponding manipulated variable in an iterative process where, in each iteration, it optimizes a quadratic cost by assuming that the neighbor controllers will use for their manipulated variables the value which they have computed in the previous iteration. Therefore, in a game theory framework, if this coordination procedure converges, a Nash equilibrium is reached. The use of linear plant models and the absence of inequality operational constraints allows to compute the manipulated variables in an explicit way, in each iteration of the coordination procedure, thereby reducing the computational load. This approach differs from other distributed MPC algorithms based on linear models in the inclusion of stability constraints in the local controllers that leads to a different control law. The controller usage is illustrated through its application to a water delivery canal.