1. Adaptive output regulation of nonlinear systems with unknown high-frequency gains
- Author
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Chen, Jingyu, Wang, Zhongdong, and Ding, Zhengtao
- Subjects
629.8 - Abstract
Disturbance rejection and output regulation problem is an important topic in control design since disturbances are inevitable in practical systems. This thesis is concerned with this problem for a class of single-input-single-output (SISO) nonlinear systems and multi-agent nonlinear systems, especially when the high-frequency gains are unknown. Output regulation aims to design a control law to achieve asymptotic tracking in the presence of a class of disturbances while maintaining the stability of the closed-loop system. "Multi-agent systems (MASs)" is referred as a group of agents which are connected together by a communication network. In many applications, the subsystems or agents are required to reach an agreement, which is regarded as "consensus control". The main contribution of this thesis is to provide feasible methods to deal with the output regulation of SISO system and consensus output regulation for multiagent systems. The adaptive output regulation for SISO nonlinear output feedback system with unknown exosystem and unknown high frequency gain is first investigated. By transforming the system with rho relative degree to 1, the augmented system is obtained. Then, using the invariant manifold theory, an adaptive internal model is proposed to tackle the unknown feedforward input. In terms of the unknown high-frequency gain, a type of Nussbaum gain is presented, the control law is then obtained by adopting this gain and the adaptive internal model. To establish the closed-loop stability, the Lyapunov function is invoked, and this control scheme is finally validated by simulation example. The adaptive consensus output regulation of multi-agent nonlinear systems with unknown control directions is then investigated. A new type Nussbaum gain with a potentially faster rate is proposed such that the boundedness of the system parameters can be established by an argument of contradiction even if the Nussbaum gain parameter for only one of the subsystems goes unbounded. The adaptive laws and control inputs with the information available from the subsystems and their neighbourhood are proposed, and therefore the adaptive laws and inputs are viewed as decentralized. The proposed control can deal with the subsystems with different dynamics as long as the subsystems with the same relative degree. An example is finally included to demonstrate the proposed control design. The consensus tracking problem for multi-agent nonlinear systems with unknown high-frequency gains is finally investigated for the subsystems connected over directed graph. An integral-Lyapunov function is proposed to tackle the asymmetry of the Laplacian matrices, then the new Nussbaum gain and the adaptive internal model are combined to design the controller. It can be shown that the control scheme and the adaptive laws are fully distributed, and the simulation result illustrates that the proposed control scheme guarantee the convergence of errors to zero asymptotically and the boundedness of the state variables.
- Published
- 2020