A Distributed Model Predictive Control For Multi-agent Multi-rate Systems

"In this thesis, a new method is proposed to control multi-agent multi-rate systems with linear dynamics that are coupled via inputs and states. These systems are multi-rate in the sense that either output measurements or input updates are not available at certain sampling. Such systems can arise when the number of sensors is less than the number of variables to be controlled or when measurements of outputs cannot be completed simultaneously because of applicational limitations. The multi-rate nature gives rise to lack of information which will cause uncertainty in the system's performance. The proposal is to control such systems with a distributed model predictive control approach based on Nash game theory. In most existing predictive control structures, implementations are done through partitioning the overall system into a number of smaller dimension subsystems. Each subsystem is controlled by a so-called agent which solves its own local optimization problem. It is known that such a completely decentralized control strategy may result in unacceptable control performance especially when the agents interact strongly. Completely centralized control of large-scale systems is also viewed by most researchers as infeasible and unrealistic in practice. The proposed method here to control multi-agent multi-rate systems is a distributed MFC approach based on Nash game theory in which multiple control agents each determine actions for their own parts of the system. Via communication, the agents can in a cooperative way take one another’s actions into account. To compensate for the information loss due to the multi-rate nature of the systems under study, a distributed Kalman Filter is proposed to provide the optimal estimation of the missing information. In the proposed framework, linear predictive control with guaranteed closed-loop stability and performance properties is presented for three different cases. In the first case, a linear dynamic system with interacting inputs is considered and in the second case a linear dynamic system with coiii)led states is employed. In both cases, the conditions in which agents are either synchronous or asynchronous are studied. Measurements and process noises as well as disturbances are considered in the proposed modelling framework. Finally, the convergence and closed-loop stability for the proposed algorithm is established along with performance and computational cost investigations. Applications from chemical engineering and electrical engineering are examined and the benefits of employing the proposed distributed predictive control with distributed Kalman filter paradigm are demonstrated. By applying the proposed distributed MFC and distributed KF, the performance of the multi-rate model with interacting inputs improved by 38.20% for the asynchronous scenario and also the performance of the multi-rate model with interacting states improved by 74.41% for the synchronous scenario. The reason for this significant improvement is due to the proposed distributed state estimator which compensates for lost information faster than existing (decentralized) scheme. For example results show that by sharing information within the distributed Kalman filter the overall algorithm can converge almost 50% faster with its consequent effect on performance."