Control of Complex Nonlinear Dynamic Rational Systems

Abstract

Nonlinear rational systems/models, also known as total nonlinear dynamic systems/models, in an expression of a ratio of two polynomials, have roots in describing general engineering plants and chemical reaction processes. The major challenge issue in the control of such a system is the control input embedded in its denominator polynomials. With extensive searching, it could not find any systematic approach in designing this class of control systems directly from its model structure. This study expands the U-model-based approach to establish a platform for the first layer of feedback control and the second layer of adaptive control of the nonlinear rational systems, which, in principle, separates control system design (without involving a plant model) and controller output determination (with solving inversion of the plant U-model). This procedure makes it possible to achieve closed-loop control of nonlinear systems with linear performance (transient response and steady-state accuracy). For the conditions using the approach, this study presents the associated stability and convergence analyses. Simulation studies are performed to show off the characteristics of the developed procedure in numerical tests and to give the general guidelines for applications.

Weight Least Squares Algorithm for Rational Models with Outliers

“…(4) Form y(t) by equation (26). (5) Form ϕ(t) according to equation (25). (6) Compute P(t) by equation (27).…”

“…Processes in industry usually suffer from outliers in measurement data [23][24][25], which make the identification of the process a challenging problem.…”

Modeling of Coupling Mechanism between Ballast Bed and Track Structure of High-Speed Railway

“…For U-model research, by Zhu et al [12], the first and second feedback adaptive control platforms of the nonlinear system are established based on U-model. At the same time, a U-neural network (U-NN) structure is proposed to facilitate the design and control of all dynamic systems modeled by linear/nonlinear polynomials/state space equations [13]. In addition, Geng et al [14] proposed a predictive control scheme based on U-model, which solves the problem of input delay in nonlinear systems.…”

Homeomorphism Mapping Based Neural Networks for Finite Time Constraint Control of a Class of Nonaffine Pure-Feedback Nonlinear Systems

“…Among these works, the core is NNs which are used as online approximation functions for the unknown nonlinearities, due to their inherent approximation capabilities [4,5]. Almost all the neural adaptive control designs and stability analyses are Lyapunov uniformly ultimately bounded (UUB) results [5]; based on the Krasovskii-LaSalle invariance principle, it is challenging to establish a generalized powerful framework for neural control [6][7][8], even though it has been used to get sufficient conditions for smooth stabilization for closed-loop systems [9][10][11].…”