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Performance Limitations Analysis And Optimality Design Of MPC Systems

Posted on:2016-08-12Degree:DoctorType:Dissertation
Country:ChinaCandidate:X CaiFull Text:PDF
GTID:1108330503993717Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
In comparison with traditional control methods, the most eminent features of predictive control are the rolling optimization mechanism and the ability to handle constraints, which makes predictive control the most universal method in industrial applications. At present, there exists abundant theoretical literatures in analysis of predictive control systems, most of which focus on stability, optimality and robustness,etc. However, little attention is paid to exploit the essential properties of predictive control including the unique mechanism of rolling optimization, the ability to handle constraints and the intrinsic nature of adaptiveness, nor relevant quantitative analysis on corresponding performance of closed-loop systems.Performance limitation is a class of methods that analyze quantitatively the relationship between performance and essential properties of system, which is developed in feedback control. This dissertation introduces the essential thought of performance limitation into predictive control. Based on the well-known scientific fact that “predictive control essentially solves a standard finite horizon optimal control problem, the only difference is the implementation of rolling optimization”, this dissertation tries to investigate, analytically or quantitatively, performance limitations of predictive control systems. By exploring the internal similarities and differences between predictive control and optimal control, the essential features of rolling optimization mechanism and its relevant impact on performance of dynamic closed-loop systems are discussed preliminarily. In the case that input saturation exists, the adaptiveness of rolling optimization is analyzed and corresponding performance enhancement is studied. Model predictive control design methods based on the performance limitation analysis are also discussed. The main contents are as follows1) For linear unconstrained model predictive control systems, based on the formulation of finite horizon optimal control and receding horizon optimization, performance limitations of linear unconstrained predictive control systems is analyzed by exploiting novel convergent properties of Riccati difference equation. The finite time performance of optimal controllers and predictive controllers is compared and both upper and lower bounds of the ratio are explicitly obtained. The results are finally extended into investigation of infinite time performance of predictive control systems, which provides guidance to controller design including consideration of optimality.2) For a class of predictive control systems with zero terminal constraints, performance limitations is investigated by exploring novel properties of algebraic Riccati equation under minimum energy control problem and relationship between Kleinman controller and minimum energy controller. Upper bound of the ratio between performance of zero terminal constraint predictive controller and minimum energy controller is obtained. Finally, controller design based on the optimality requirements is discussed.3) For predictive control system with input saturation, performance limitations are addressed by use of geometric theory of quadratic programming. By comparing the total cost of input saturated predictive control systems with input saturated system, the upper and lower bounds of the ratio are expressed analytically. The results illustrate from viewpoint of performance the ability and advantage of MPC in specific constrained environment.4) For nonlinear constrained predictive control systems, based on the unified formu-lation using dynamic programming method, performance limits is investigated by developing novel convergent properties of value iteration. Quantitative relationships between infinite time performance of predictive control systems and finite(or infinite) horizon optimal cost are revealed.
Keywords/Search Tags:predictive control, optimal control, performance limitations, dynamic programming
PDF Full Text Request
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