Research On Control Of Nonlinear System With Time-Varying Powers

Time varying order nonlinear systems are research hotspot in recent years,which is widely used in underactuated system,boiler turbine unit and so on.Inspired by these practical applications,by using backstepping design method,parameter separation technology,graph theory and It(?) lemma,the control problem of the nonlinear system with time-varying order is studied.The research includes three parts:The adaptive tracking control for stochastic systems with unknown time-varying power and parameter is studied.By using the parameter separation technique and adding a power integrator design method,an adaptive controller is designed to ensure all states are bounded in probability and the output tracking error can be regulated into a small neighborhood of the origin in probability.Finally,a simulation example is used to illustrate the effectiveness of the designed controllers.The distributed output tracking problem of multi-agent systems with unknown time-varying powers is studied.For one leader case,by using the algebra graph and adding a power integrator,the distributed tracking controller is designed to achieve the tracking errors can be adjusted to be arbitrarily small and all the signals of the system are bounded.Then we extend this result to the case of multiple leaders and solve the containment tracking problem,the distributed containment controller can guarantee the followers outputs of the systems will eventually converge to a limit point.Finally,two simulation examples are used to illustrate the effectiveness of the designed schemes.The decentralized stabilization of large-scale stochastic nonlinear systems with unknown time-varying powers is studied.The decentralized state feedback controller is first designed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable(GAS)in probability.Then redesign a new optimal controller with infinite gain margin to solve the inverse optimal stabilization(IOS)problem.The optimal controller is not only optimal with respect to a meaningful cost functional but also globally asymptotically stabilizes the system.Finally,a simulation example is used to illustrate the effectiveness of the designed controllers.