Necessary conditions for optimality for control problems with time delays appearing in both state and control variables

1977 ◽  
Vol 23 (3) ◽  
pp. 413-428 ◽  
Author(s):  
K. L. Teo ◽  
E. J. Moore
Keyword(s):  
Time Delays ◽  
Necessary Conditions ◽  
Control Problems ◽  
Control Variables ◽  
Necessary Conditions For Optimality ◽  
And Control

scholarly journals A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

2011 ◽  
Vol 1 ◽  
pp. 387-394 ◽  
Author(s):  
Zhen Yu Han ◽  
Shu Rong Li
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
State Variables ◽  
Linear Quadratic ◽  
Control Variables ◽  
Linear Quadratic Optimal Control ◽  
Haar Functions ◽  
And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

Tracking Controller for Linear Systems With Time Delays in Both State and Control Variables

1993 ◽  
Vol 115 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Dong H. Chyung
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
System Response ◽  
Control Variables ◽  
Linear Time Invariant ◽  
Tracking Controller ◽  
Invariant Control ◽  
Necessary And Sufficient ◽  
And Control ◽  
Reference Input

Linear time invariant control systems with time delays in both state and control variables are studied. The problem is to design a controller so that the system response will follow a given reference input with zero steady-state error. The reference input is assumed to be a polynomial function of time. The controller is based on feeding forward the reference input and its delayed values. A method is derived for determining the feed-forward gain matrices. Necessary and sufficient condition for the existence of proposed tracking controller is also obtained. An example is given to illustrate the proposed method.

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