Performance Assessment And Optimization Of Decentralized Control Systems

Large-scale complex systems are common occurrences in modern industry systems (e.g. chemical and petrochemical processes) which are composed of distributed interconnected subsystems that are tightly integrated through material, energy and information flows. While the centralized control framework is shown to provide the best performance theoretically, its high computational and organizational burden and fragile fault tolerance often make its implementation impractical. In the industrial applications, decentralized control framework is widely adapted because of its flexibility and operability. However, it may lead to deteriorated performance or even lost of closed-loop stability since the reduced complexity in decentralized control comes at the cost of totally neglecting the interconnections between the subsystems. To select an appropriate control framework, as well as evaluate the performance of the current control system, control performance assessment needs to be carried out. In recent years, much efforts have been made into the research of control performance assessment in the academic field. Most of the existing results foucus on the performance assessment of univariate systems or centralized systems. Control performance of decentralized control systems, however, has received much less attention. in this work, an efficient approach for performance assessment of decentralized control systems based on a general quadratic (LQG-type) performance index which can take both control actions and system states into account is proposed. The main contributions of this work are listed as follows:(1) First, a strategy to solve the decentralized linear quadratic regulator(LQR) problem is proposed under the case that state-feedback is available. In this work, the decentralized LQR problem is formulated as an optimization problem subject to constraints in the form of linear matrix inequalities (LMIs) which explicitly take the block-diagonal structural constraint on decentralized control systems into account. An iterative procedure in which two simplified problem of the original problem are solved iteratively is proposed. The iterative approach is proved to converge to a local minimum. The proposed iterative approach can efficiently handle the block-diagonal structure constraint in LMIs and significantly reduces the conservativeness of the existing methods of solving decentralized LQR problem.(2) Subsequently, the approach is extended to the case in which only output feedback is available. In this case, separation principle is used to divide the overall problem into two independent problems:a decentralized state feedback control problem and a decentralized observer design problem. The decentralized observer is designed based on LMI in which the the block-diagonal structural constraint is dealt in a similar manner as in decentralized LQR. The resulting observer is a decentralized Kalman filter. Based on the obtained optimal decentralized controllers and observers, the decentralized LQG problem can be solved.(3) The decentralized LQG benchmark is then applied to the economic performance of decentralized control systems. The performance assessment optimization problem is also based on LMI which could handle variance constraint directly so that it is more flexible compared with the conventional approach of solving algebraic Riccati equation. A stochastic optimization is established to assess the economic performance of dencentralized MPC. The assessment result reveals the potential achievable performance of dentralized or centralized MPC and can therefore provide valueble guidance for controller parameter tuning and controller structure selection.