An Optimal Control Problem For A Novel LPV System

This paper studies a class of new optimal control problems for linear parametervarying(LPV)systems.The LPV system was obtained from the data provided by the Aircraft Engine Integrated Control Research Center of Dalian University of Technology through a system identification method.On the one hand,the system can describe the dynamic characteristics of the aero-engine transition state.On the other hand,it is essentially different from most existing dynamic models.In this paper,a general linear variable parameter system is extracted.In the system,the parameters are not only be measured in real time but also dependent on the state variables and observed variables of the next sampling time.The system can get the feedback of the system in time and further influence the control variables,and this makes the system have time-varying characteristics.The numerical solution of the optimal control problem for this type of system is studied in depth.First,we present the description of the problem,some auxiliary fractional systems,the gradient formulas and use traditional nonlinear optimization techniques to solve an example.Then,given that traditional computation of complicated questions is rather difficult,particle swarm algorithm illustrated by a numerical example is presented.In the context of engine,in addition to dynamical system,the optimal control problem is limited by temperature and pressure.For example,the temperature of the turbine must be guaranteed within the upper bound limit,which can be described by LPV system.Further,the optimal control problem of LPV system with constrains is more practical and useful.The problem with constrains have to handle two system(dynamical system and constrained system)sharing the same scheduling signal.So,the algorithm based on particle swarm has been proposed.To illustrative this method a numerical example is presented.