Fractional-Order Optimal Control of Fractional-Order Linear Vibration Systems with Time Delay

2018 ◽  
Vol 7 (3) ◽  
pp. 72-93
Author(s):  
Saeed Balochian ◽  
Nahid Rajaee
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Linear Structure ◽  
Control Input ◽  
Linear Vibration ◽  
Order Linear ◽  
Input Control ◽  
Delayed System

Vibration control of fractional-order linear systems in the presence of time delays has been dealt in this article. Considering a delayed n-degree-of freedom linear structure that is modeled by fractional order equations, a fractional-order optimal control is provided to minimize both control input and output of delayed system via quadratic objective function. To do this, first the fractional order model of system that is subject to time delay is rewritten into a non-delay form through a particular transformation. Then, a fractional order optimal controller is provided using the classical optimal control theory to find an optimal input control. A delayed viscose system is then presented as a practical worked-out example. Numerical simulation results are given to confirm the efficiency of the proposed control method.

scholarly journals T-S Fuzzy Control of Uncertain Fractional-Order Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yilin Hao ◽  
Xiulan Zhang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Control Method ◽  
Fuzzy Model ◽  
Linear Structure ◽  
Adaptive Method ◽  
Delay Systems ◽  
Robust Controller ◽  
External Disturbances ◽  
Fuzzy Adaptive

In this article, the adaptive control of uncertain fractional-order time-delay systems (FOTDSs) with external disturbances is discussed. A Takagi-Sugenu (T-S) fuzzy model with if-then rules is adopted to characterize the dynamic equation of the FOTDS. Besides, a fuzzy adaptive method is proposed to stabilize the model. By utilizing the Lyapunov functions, a robust controller is constructed to stabilize the FOTDS. Due to the uncertainty of system parameters, some fractional-order adaptation laws are designed to update these parameters. At the same time, some if-then rules with linear structure based on the fuzzy T-S adaption concept are established. The designed method not only guarantees that the state of closed-loop system asymptotically converges to origin but also keeps the signal in the FOTDS bounded. Finally, the applicability of the control method is proved by simulation examples.

Optimal Tracking Control for Discrete-time Systems with Time-delay Based on the Preview Control Method

2019 ◽  
Vol 7 (5) ◽  
pp. 452-461
Author(s):  
Haishan Xu ◽  
Fucheng Liao
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Discrete Time ◽  
Tracking Control ◽  
Control Method ◽  
Reference Signal ◽  
Control Law ◽  
Preview Control ◽  
Optimal Tracking ◽  
Delayed System

Abstract In this paper, the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method. First, a transformation is introduced. Thus, the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal. Then, by applying the preview control theory, an augmented system for the non-delayed system is derived, and a controller with preview function is designed, assuming that the reference signal is previewable. Finally, the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Comparative studies for the fractional optimal control in transmission dynamics of West Nile virus

2017 ◽  
Vol 10 (07) ◽  
pp. 1750095 ◽  
Author(s):  
N. H. Sweilam ◽  
O. M. Saad ◽  
D. G. Mohamed
Keyword(s):  
Optimal Control ◽  
West Nile Virus ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Order ◽  
Comparative Studies ◽  
Control Method ◽  
Euler Method ◽  
West Nile ◽  
Iterative Optimal Control

In this paper, optimal control for a novel West Nile virus (WNV) model of fractional order derivative is presented. The proposed model is governed by a system of fractional differential equations (FDEs), where the fractional derivative is defined in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Two numerical methods are used to study the fractional-order optimal control problem. The methods are, the iterative optimal control method (OCM) and the generalized Euler method (GEM). Positivity, boundedness and convergence of the IOCM are studied. Comparative studies between the proposed methods are implemented, it is found that the IOCM is better than the GEM.

scholarly journals Distributed Optimal Control for a Class of Switched Nonlinear Systems with the State Time Delay

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yuxing Duan ◽  
Baili Su
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Control Method ◽  
The State ◽  
Switched Nonlinear Systems ◽  
Distributed Optimal Control ◽  
Switching Sequence ◽  
State Time ◽  
Optimal Control Method

This paper is focused on a kind of distributed optimal control design for a class of switched nonlinear systems with the state time delay which have a prescribed switching sequence. Firstly, we design a bounded controller to make the system stable for each mode of the nominal system. Then, a distributed optimal controller which can satisfy input constraint is designed based on the bounded stabilization controller. A sufficient condition to guarantee ultimate boundedness of the system is given based on appropriate assumption. The significance of this paper is that distributed optimal control method is applied to switched nonlinear systems with the state time delay. Finally, a simulation example is given to verify the effectiveness of the proposed method.

scholarly journals Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Junhai Luo ◽  
Guanjun Li ◽  
Heng Liu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Control ◽  
Control Input ◽  
Saturated Control ◽  
Laplace Transform Technique

In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 <α≤ 1 and 1 <α< 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method.

An optimal control method for linear systems with time delay

2003 ◽  
Vol 81 (15) ◽  
pp. 1539-1546 ◽  
Author(s):  
Guo-Ping Cai ◽  
Jin-Zhi Huang ◽  
Simon X Yang
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Linear Systems ◽  
Control Method ◽  
Optimal Control Method
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