A robust and accurate disturbance damping control design for nonlinear dynamical systems

Abstract

Summary The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is converted into a nonlinear quadratic regulator (NQR) problem for an undisturbed augmented system. Then, an iterative technique is designed to solve this NQR problem effectively. The proposed iterative method is also extended through the use of a nonlinear model predictive control in an offline framework. In this case and in the presence of unknown disturbances, the Lyapunov stability of the closed‐loop system is guaranteed. Numerical simulations and comparative results verify the effectiveness of the proposed approach.

Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

“…For integer order and fractional order nonlinear systems, the stabilization conditions of the sliding mode control are derived in the form of linear matrix inequalities (Jafari and Mobayen, 2019; Mobayen and Baleanu, 2017). For a class of nonlinear dynamical systems, a robust disturbance damping controller has been designed in Jajarmi et al (2019). Also, different studies have been conducted about the robust stability analysis of LTI fractional order systems.…”

Numerical investigation of distributed‐order fractional optimal control problems via Bernstein wavelets

“…The optimal control problem represents a set of differential equations describing the paths of the control variables that minimize a criterion function of the state and control variables 1 . The fractional optimal control problem (FOCP) is an optimal control problem in which the criterion function or the differential equations governing the dynamics of the system or both contains at least one fractional order derivative term.…”

Improved Decentralized Fractional PD Control of Structure Vibrations

“…Building structures occasionally suffer from unpredictable earthquakes, strong winds, or other natural hazards that may cause severe damage and threaten human lives. Thus, effective control methods are needed to protect against structural vibration in buildings [1,2]. During the past few decades, a variety of control techniques, including linear quadratic regulator (LQR) [3], sliding-mode [4], neural network [5], fuzzy [6], neural terminal sliding-mode [7], disturbance rejection [8], and proportional-derivative (PD) [9,10] algorithms were analyzed.…”