Moncrief-O’Donnell Chair, UTA Research Institute (UTARI)The University of Texas at Arlington, USA

and

F.L. Lewis, NAI

Talk available online at http://www.UTA.edu/UTARI/acs

Summary of Optimal Control DesignSupported by :China Qian Ren Program, NEUChina Education Ministry Project 111 (No.B08015)NSF, ONR

Qian Ren Consulting Professor, State Key Laboratory of SyntheticalAutomation for Process Industries

Northeastern University, Shenyang, China

Static Optimization

min ( , )u

L x u

Subject to constraint ( , ) 0f x u

Solution. Define Hamiltonian function

( , , ) ( , ) ( . )TH x u L x u f x u

Adjoin constraints to the performance index using Lagrange multiplier

Discrete-time Nonlinear Optimal Control

Steady-State Discrete-Time LQR

SOLUTION

BuAxx u Kx

02

1 dtRuuQxxJ TT

Steady-State Continuous-Time LQR

System

Select input

To minimize the Performance Index

01 PBPBRQPAPA TT