QUADRATIC POLYNOMIAL SOLUTIONS OF THE HAMILTON-JACOBI INEQUALITY IN RELIABLE CONTROL DESIGN

Authors
Citation
Dc. Liaw et Yw. Liang, QUADRATIC POLYNOMIAL SOLUTIONS OF THE HAMILTON-JACOBI INEQUALITY IN RELIABLE CONTROL DESIGN, IEICE transactions on fundamentals of electronics, communications and computer science, E81A(9), 1998, pp. 1860-1866
Citations number
12
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Engineering, Eletrical & Electronic","Computer Science Hardware & Architecture","Computer Science Information Systems
ISSN journal
0916-8508
Volume
E81A
Issue
9
Year of publication
1998
Pages
1860 - 1866
Database
ISI
SICI code
0916-8508(1998)E81A:9<1860:QPSOTH>2.0.ZU;2-Q
Abstract
In the design of nonlinear reliable controllers, one major issue is to solve for the solutions of the Hamilton-Jacobi inequality. In general , it is hard to obtain a closed form solutions due to the nonlinear na ture of the inequality. In this paper, we seek for the existence condi tions of quadratic type positive semidefinite solutions of Hamilton-Ja cobi inequality. This is achieved by taking Taylor's series expansion of system dynamics and investigating the negative definiteness of the associated Hamilton up to fourth order. An algorithm is proposed to se ek for possible solutions. The candidate of solution is firstly determ ined from the associated algebraic Riccati inequality. The solution is then obtained from the candidate which makes the the truncated fourth order polynomial of the inequality to be locally negative definite. E xistence conditions of the solution are explicitly attained for the ca ses of which system linearization possesses one uncontrollable zero ei genvalue and a pair of pure imaginary uncontrollable eigenvalues. An e xample is given to demonstrate the application to reliable control des ign problem.