Second-order continuous characteristic model based adaptive control for a class of linear systems

A novel second-order continuous characteristic model for a class of linear systems is proposed, which is different from the traditional discrete characteristic model. The proposed continuous characteristic model has convenient structure denoted by a second-order time-varying differential equation and is equivalent to its original plant in output for the same input. Then the continuous characteristic model is applied to a class of linear plants whose parameters are unknown bounded with bounded derivatives and output is affected by unknown bounded disturbances. As the characteristic parameters of the continuous characteristic model are usually fast time-varying, therefore, the robust adaptive dynamic surface control technique is combined with the continuous characteristic model. The design procedure of proposed adaptive control scheme is simple and the control law is easy to be implemented. With the continuous characteristic model, the state observer is not necessary and the plant system order and structure can be unknown. Finally, it has been proved that all the closed-loop signals are semi-globally uniformly ultimately bounded with the proposed adaptive control scheme. Simulation results have demonstrated that proposed adaptive control scheme has perfect performances.