On the equivalence of maximum principle open-loop controllers and Carath�odory feedback controllers for time-delay systems

1974 ◽  
Vol 14 (2) ◽  
pp. 163-178 ◽  
Author(s):  
H. N. Koivo
Keyword(s):  
Time Delay ◽  
Maximum Principle ◽  
Open Loop ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Feedback Controllers ◽  
Open Loop Controllers

Eigenvalue Assignment for Control of Time-Delay Systems Via the Generalized Runge–Kutta Method

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
JinBo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Time Delay ◽  
Optimization Techniques ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Kutta Method ◽  
Feedback Controllers ◽  
Runge Kutta Method ◽  
Linear Delay ◽  
Runge Kutta ◽  
Eigenvalue Assignment

This paper presents an eigenvalue assignment method for the time-delay systems with feedback controllers. A new form of Runge–Kutta algorithm, generalized from the classical fourth-order Runge–Kutta method, is utilized to stabilize the linear delay differential equation (DDE) with a single delay. Pole placement of the DDEs is achieved by assigning the eigenvalue with maximal modulus of the Floquet transition matrix obtained via the generalized Runge–Kutta method (GRKM). The stabilization of the DDEs with feedback controllers is studied from the viewpoint of optimization, i.e., the DDEs are controlled through optimizing the feedback gain matrices with proper optimization techniques. Several numerical cases are provided to illustrate the feasibility of the proposed method for control of linear time-invariant delayed systems as well as periodic-coefficient ones. The proposed method is verified with high computational accuracy and efficiency through comparing with other methods such as the Lambert W function and the semidiscretization method (SDM).

Sign in / Sign up

Export Citation Format

Share Document