Neural Observer With Lyapunov Stability Guarantee for Uncertain Nonlinear Systems.

In this article, we propose a novel nonlinear observer based on neural networks (NNs), called neural observers, for observation tasks of linear time-invariant (LTI) systems and uncertain nonlinear systems. In particular, the neural observer designed for uncertain systems is inspired by the active disturbance rejection control, which can measure the uncertainty in real time. The stability analysis (e.g., exponential convergence rate) of LTI and uncertain nonlinear systems (involving neural observers) are presented and guaranteed, where it is shown that the observation problems can be solved only using the linear matrix inequalities (LMIs). Also, it is revealed that the observability and controllability of the system matrices are required to demonstrate the existence of solutions for LMIs. Finally, the effectiveness of neural observers is verified in three simulation cases, including the X-29A aircraft model, the nonlinear pendulum, and the four-wheel steering vehicle.

Computational bilinear optimal control for a class of one-dimensional MHD flow systems.

In this paper, we consider a bilinear optimal control problem arising in a one-dimensional (1-D) MHD flow modeled by an array of coupled partial differential equations (PDEs). The external control input (external induction of magnetic field) in the model takes the multiplicative effect on both state variables (i.e., momentum and magnetic components). Our aim is to drive the flow velocity to within close proximity of a desired target flow velocity at the pre-indicated terminal time. We first use the Galerkin method combined with a set of basis quadratic B-spline functions to obtain a semi-discrete approximation problem. Next, the convergence of the semi-discrete approximation problem is proved. Then the control parameterization method combined with the time-scaling transformation technique is utilized to obtain an approximate optimal parameter selection problem, in which the exact gradients of the cost function with respect to the decision parameters are computed based on our analytical equations. The approximate problem are then solved by using the gradient-based optimization techniques such as the sequential quadratic programming (SQP). Finally, the numerical results validate the effectiveness of our method.