Optimization And L₁ Gain Analysis Of Linear Switched Positive Systems

A switched positive system is a kind of special switched systems,which has been widely used in industrial production application.The optimization and L₁ gain problems of switched positive system have been a hot research topic in the field of control science and engineering,which has important guiding significance for a series of engineering technical problems such as production process automation,automatic scheduling,robot control and computer control.However,in the study of the practical application of switched positive systems,there are still some problems that need to be solved by researchers.For example,how to optimize the control of a switched positive system to reduce the production cost and improve the stability of the system.In industrial production practice,many subsystems interact with each other,so it is worth to study the optimization and L₁ gain analysis of the switched interconnection positive system composed of these interacting subsystems.This thesis addresses the above problems.The main contents are as follows:The optimization problem of linear switched positive systems under dwell time switching and state dependent switching signals with dwell time is studied.Considering that switching speed of physical systems is limited in practice and in the study of the optimal control problem of linear switched systems,copositive Lyapunov function is constructed to study the stability of the system and design conditions to ensure the performance indexes reach the requirements under the dwell time constraint,and the system dwell time limit is reduced through the optimization algorithm.Then,the stability of the switched positive system under the state dependent switching signal with the dwell time constraint is analyzed,and an appropriate performance index function is constructed to analyze the optimal control of the switched positive system.At the same time,the upper bound of the optimized performance index is given.The optimization of linear switched interconnected positive systems based on state dependence and time dependence is further studied.A copositive Lyapunov function is constructed based on the interconnectedness and positivity of the system.First,the stability of the system under the state dependent switching signal with the dwell time constraint is studied.Then,the appropriate cost function is selected to analyze the performance of the system,and the performance upper bound of the system is given.Secondly,considering that most of the actual systems operate in the case of periodic sampling,this part studies the optimization problem of the system in the case of discrete sampling time,and calculates and evaluates the performance of the system by designing the state with dwell time constraint in the case of discrete sampling time and relying on the switching signal.Finally,the L₁ gain problem of linear switched interconnected positive systems is studied.The complexity of the stability analysis of interconnected large systems increases exponentially with the increase of the order and number of subsystems.Due to the particularity of the large system structure,considering that the interconnection term of a class of systems satisfies the linear growth condition,the L₁ performance of the system is studied by designing the copositive Lyapunov function,and the simulation are used to prove the effectiveness of the results.