scholarly journals A numerical framework for optimal control of switched input affine nonlinear systems subject to path constraint

2014 ◽  
Vol 95 ◽  
pp. 63-77 ◽  
Author(s):  
Pierre Riedinger ◽  
Irinel-Constantin Morărescu
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Affine Nonlinear Systems ◽  
Path Constraint

Extended Finite Time Inverse Optimal Control of Nonlinear Systems

2011 ◽  
Vol 403-408 ◽  
pp. 1499-1502
Author(s):  
Xin Jun Ren ◽  
Yan Jun Shen
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Control Law ◽  
Inverse Optimal Control ◽  
Closed Loop System ◽  
Affine Nonlinear Systems ◽  
Definition Of ◽  
The Cost

In this paper, we use the definition of control Lyapunov functions to study finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a finite time universal control formula is presented, which can ensure the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. We design a finite time inverse optimal control law, which minimizes the cost functional. A numerical example verifies the validity of the proposed method.

scholarly journals On the optimal control of affine nonlinear systems

2005 ◽  
Vol 2005 (4) ◽  
pp. 465-475 ◽  
Author(s):  
M. Popescu ◽  
A. Dumitrache
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Closed Form Solution ◽  
Bilinear System ◽  
Open Loop ◽  
Form Solution ◽  
Loop Control ◽  
Nilpotent Operators ◽  
Affine Nonlinear Systems

The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input bilinear system for such systems. For the multi-input system, usually an analytic closed-form solution for the optimal controlui∗(t)is not possible and it is necessary to use numerical integration for the set ofmnonlinear coupled second-order differential equations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-loop control depending on the initial value of the statex0.

Sign in / Sign up

Export Citation Format

Share Document