Adaptive Actuator Failure Compensation Control of Uncertain Nonlinear PDE–ODE Cascaded Systems
针对一类反应扩散方程描述的PDE-ODE级联系统，研究了存在未知非线性和执行器故障时的镇定问题，通过反步法变换和补偿函数设计了一种容错控制策略，并证明了系统稳定性与状态渐近收敛。
In this article, the stabilization problem is addressed for a class of reaction–diffusion equation described by a cascaded partial differential equation (PDE)–ordinary differential equation (ODE) system. Because of the inherent unknown nonlinearity and actuator failure existing in the considered system, it is fundamentally different from the systems studied in most related studies. To simplify the stability analysis, the original PDE–ODE cascaded system is redescribed as a new target system by leveraging finite- and infinite-dimensional backstepping techniques. In the newly transformed system, the compensation term in the form of the smoothing function is used to eliminate the influence caused by actuator faults. Then, a novel fault-tolerant control strategy is further developed, which can not only eliminate the influence of uncertainty, but also overcome the difficulties of actuator faults. The system stability and the asymptotic convergence of all states in the original system are proved by applying the Lyapunov function theory. The simulation example shows that the presented control method ensures the realization of the control objectives.