Implementation Strategy Of Nonlinear Model Predictive Control Based On Koopman Operator

Model predictive control,also named as receding horizon control,solves an optimization problem at each sampling time,and deals with system constraints simultaneously.Nonlinear model predictive control usually needs to solve non-convex optimization problems,which in general leads to heavy computational burden.The fast realization strategy of nonlinear model predictive control is important for its potential user.Due to Koopman operator theory,high-dimensional global linearization model of a nonlinear system can be obtained through its input-output data,which can theoretically retain its complete nonlinear characteristics.The classical Koopman operator theory only discusses infinite dimension autonomous systems,which cannot be directly used in practical control systems.This thesis generalizes the Koopman operator theory to nonlinear systems under control,and establishes a high-dimensional linear model of nonlinear system by extended dynamic mode decomposition.The vector of state lifting function is manually selected,which maps a nonlinear system to a high-dimensional space.Finally,model predictive controller is designed based on the high-dimensional linear model,thereby reducing the online computational burden.In extended dynamic mode decomposition,the selection of state lifting function is subjective.Based on extended dynamic mode decomposition,this thesis replaces manual selection of state lifting function by trained deep neural network,and obtains a highdimensional linear model of nonlinear systems based on Koopman operator theory.Finally,the linear model is used to design model predictive controller.At each sampling time,the deep neural network is used to obtain the system state of lift nonlinear systems before solving the involved optimization problem,i.e.,the initial value of states of the prediction model is estimated.That is,the neural network structure does not involve in the process of iterations while optimization problem is solved online.In this thesis,a linear model of nonlinear systems(obtained offline,not online)is used as the prediction model of model predictive control,which avoids to solve nonconvex optimization problems online,and reduces the computational burden accordingly.This method is a data-driven strategy indeed,and the nonlinear model given in this thesis is only used for collecting training data.It is emphasized that mechanical model is not needed any more,while it is possible to actually collect system data.