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
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.