Distributed coordination in multi-agent control systems through model predictive control.

摘要

This dissertation presents a new framework to achieve distributed coordination in multi-agent control systems. The control agents coordinate their actions without the help of a central coordinator.; A distributed coordination framework based on model predictive control (MPC) is proposed as the main result. Each agent uses an MPC strategy, viewing influences from neighbor subsystems as disturbances in its local model. Control agents exchange predictions of future state trajectories in local subsystems and incorporate this information into their local MPC problems.; First, we consider a scheme where each control agent predicts and broadcasts a single state trajectory. A contractive constraint, called the stability constraint, is included in the local MPC formulation. It is proved that the system in a controllable companion form is asymptotically stable if the interactions between subsystems are sufficiently weak.; In the second scheme, each control agent computes and exchanges sets of future reachable states. A robust distributed MPC formulation is proposed for the control agents. Min-max optimization is used to minimize the worst-case performance. Semi-infinite constraints, i.e. robustness constraints, are imposed to guarantee constraint satisfaction under all possible circumstances. Parameterized feedback control laws are introduced in the MPC optimization to obtain less conservative solutions and predictions. The agents impose their own predicted reachable sets as constraints in subsequent MPC iterations to guarantee their subsystems satisfy the bounds broadcast to the other agents. Bounded stability for general systems and exponential stability for LTI systems are proved.; As another major result, a three-step numerical method based on conservative approximations to semi-infinite constraints using linear matrix inequality (LMI) techniques is proposed to solve the robust MPC optimization problem in each agent. The method applies to problems with quadratic costs, linear and quadratic constraints, and linear dynamics with bounded parametric uncertainty and bounded disturbances. It is shown that the solutions of the optimizations with LMI constraints provide feasible solutions to the original robust MPC. If the optimization with LMI constraints is feasible at the initial control step (the first application of the MPC optimization), it is feasible at all control steps and the controlled system will be closed-loop stable. (Abstract shortened by UMI.)