On Adaptive Output Feedback Control Of Nonlinear Systems With Prescribed Performance

In recent years, the transient performance of systems has received more and more attentions in the field of control. Along with the concept of prescribed performance proposed, both the steady state and the transient performance were discussed. The prescribed performance means that the tracking error should converge to predefined arbitrarily small residual set. Meanwhile, the convergence rate, maximum overshoot and undershoot should be preserved to satisfy the conditions which were set before. In this paper, using neural networks to approximate the unknown nonlinear functions, several adaptive output feedback control schemes are proposed for several classes of nonlinear systems with prescribed performance by combing dynamic surface control technique, K-filters and MT-filters. The main contents of this paper are as follows:Firstly, an adaptive output feedback dynamic surface control is proposed for a class of nonlinear systems with prescribed performance and unmodeled dynamics. Radial basis function neural networks are used to approximate the unknown nonlinear functions. K-filters are employed to estimate the unmeasured states. In order to dominate the unmodeled dynamics, an available dynamic signal is introduced. By introducing a performance function and an output error transformation, the original system is transformed into an equivalent one. In order to avoid the explosion of complexity in traditional backstepping design, dynamic surface control is introduced. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error satisfies the prescribed performance. At last, the simulation results illustrate the effectiveness of the proposed approach.Secondly, adaptive output feedback control schemes using construction method and using Nussbaum function are proposed respectively for a class of nonlinear systems with prescribed performance and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. MT-filters and the state observer are employed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. The original system is transformed into an equivalent one by introducing a performance function and an output error transformation. According to the new error signal and partial states of observers, adaptive dynamic surface control and parameter adaptive laws are proposed. The dynamic surface control is introduced to avoid the explosion of complexity in traditional backstepping design. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error satisfies the prescribed performance. Both the numerical simulation example results and the applied simulation example results are provided to illustrate the effectiveness of the proposed approach.Thirdly, the centralized and decentralized adaptive output feedback control schemes are presented for a class of uncertain interconnected nonlinear systems with unknown dead-zone and prescribed performance. Radial basis function neural networks are used to approximate the unknown nonlinear functions. By introducing a performance function and an output error transformation, the original system is transformed into an equivalent one and the problem of prescribed performance is transformed into the problem of stability analysis. In order to estimate the unmeasured states of each subsystems, the decentralized observers are constructed based on MT-filters. The dynamic surface control is introduced to avoid the explosion of complexity in traditional backstepping design. Two kinds of control laws and adaptive laws are desiged for the the centralized control and decentralized control of the system. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error satisfies the prescribed performance. At last, simulation results illustrate the effectiveness of the proposed approach.