Research On Cooperative Distributed Model Predictive Control

Model predictive control(MPC)can handle state and control constraints and has been receiving increasing attention in the past decades.Centralized MPC is currently the mainstream research,however,its application to a large-scale system is difficult due to limited communication and heavy computation burden,etc.Such a large-scale system can be considered as a combination of several less complicated subsystems with state and control coupling,and then controlling each subsystem based on cooperative distributed model predictive control(DMPC)method to achieve optimal performance for the entire large-scale system.Cooperative DMPC is of less computation burden and improved optimization performance.Consequently,this framework has both theoretical significance and engineering value.In this thesis,several cooperative DMPC methods are designed for linear constrained system,linear constrained system with unknown bounded disturbance,as well as piecewise affine constrained system,respectively.Terminal weighted functions and terminal inequality constraints guaranteeing stability of closed-loop systems are investigated.Optimization problems and stability of the cooperative DMPC methods are analyzed.Based on these results,a cooperative DMPC method is applied to an electric vehicle with inwheel motors for yaw stability control.A cooperative explicit DMPC method is proposed for a class of linear constrained system with control coupling.A terminal weighted matrix and a terminal invariant set are designed for the entire system to guarantee stability of the closed-loop system.System states and controls from other subsystems are considered as external parameters of the current sub-optimization problem.An explicit piecewise affine control law can be obtained by solving these sub-optimization problems with a multi-parameter quadratic programming algorithm.The proposed cooperative explicit DMPC method has less computation limitation and performs similarly to MPC that are on-line solved.A cooperative DMPC method,being able to steer state to a robust control invariant set,is developed for linear constrained system with unknown bounded disturbance.Worst-case control actions can be obtained by solving min-max optimization problem.Due to the unsolvability of the min-max optimization problem,two algorithms are designed.One is converting the min-max optimization problem to linear matrix inequalities(LMI)by S-procedure process,and another is converting the optimization to quadratic programming by introducing extra decision variants.Because of external disturbance,the entire closed-loop system under the proposed cooperative DMPC is input-to-state practically stable.A nonlinear MPC requires to solve non-convex optimization,which is difficult to be globally optimized.A cooperative DMPC is proposed for piecewise affine(PWA)constrained system,which is an approximation of the nonlinear system.A switching terminal invariant set and a terminal cost function of the entire system are added for stability guarantee.The optimization problem of each subsystem is converted into mixed-integer quadratic programming(MIQP)for obtaining control actions.Although the cooperative DMPC is suboptimal,non-convex nonlinear optimization is not required,and therefore higher computation efficiency can be achieved.For exploring the feasibility of the methods presented in this thesis,a cooperative DMPC for yaw stability control of an electric vehicle with in-wheel motor is established based on the distributed structure of yaw stability control system of electric vehicle with in-wheel motors.Firstly,a large-scale linear constrained yaw stability model with state coupling which contains vehicle and wheels dynamic is developed,where steering angle is considered as an external input.In addition,the vehicle body and four wheels are considered as five coupled distributed sub-systems,respectively.The cooperative DMPC method is designed to generate each wheel torque to track an expected yaw velocity.Several simulation cases exhibit that the proposed cooperative DMPC can track the desired yaw velocity efficiently with constraint guarantee.