• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2001년도 하계학술대회 논문집 D
• /
• pp.1996-1998
• /
• 2001

This paper presents the closed-loop composite control for weakly coupled bilinear systems with a quadratic performance criterion. The Riccati equation for weakly coupled bilinear system is decomposed into three reduced Riccati equations by the weak coupling theory, and we obtain optimal solutions of each reduced Riccati equation using successive Galerkin approximation(SGA). We design the composite control law that consists of optimal solutions of each reduced Riccati equation. The proposed algorithm reduces the disadvantages of SGA method.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
• /
• pp.68-72
• /
• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.

• 대한수학회논문집
• /
• 제10권1호
• /
• pp.163-173
• /
• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
• /
• pp.461-466
• /
• 1989

This paper describes some properties of a discrete algebraic Riccati equation and its application to $H^{\infty}$ control design. The conditions, under which an input weighting matrix can be found for a negative output weighting matrix in order that a solution P for a discrete algebraic equation may exist, are suggested in case of a stable A. This result is applied to a $H^{\infty}$ controller design for the special case of nonsingular B. It is based on a state feedback control law whose objective is to reduce the effect of input disterbances below a prespecified level. This law requires the solution of a modified algebraic Riccati equation, which provides an method for the $H^{\infty}$ optimization control problem approximately.ly.

• Kyungpook Mathematical Journal
• /
• 제62권4호
• /
• pp.729-736
• /
• 2022

To help solving intractable nonlinear evolution equations (NLEEs) of waves in the field of fluid dynamics we develop an algorithm to find new high order solutions of the class of Abel, Bernoulli, Chini and Riccati equations of the form y' = ayⁿ + by + c, n > 1, with constant coefficients a, b, c. The role of this class of equations in NLEEs is explained in the introduction below. The basic algorithm to compute the coefficients of the power series solutions of the class, emerged long ago and is further developed in this paper. Practical application for hitherto unknown solutions is exemplified.

• International Journal of Control, Automation, and Systems
• /
• 제6권5호
• /
• pp.776-784
• /
• 2008

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabilizing solution of the CARE exists. Finally, numerical examples are given to demonstrate the effectiveness of the present schemes.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.95-99
• /
• 1993

In this paper, we discuss H$_{\infty}$ robust performance problem for uncertain system described in a descriptor form. We show that the method based on Riccati equation can be extended to solve this problem. First, such a sufficient condition is given that the system described in a descriptor form is quadratic stable and H$_{\infty}$ norm of a specified transfer function is less than a given level. Using this result, a state feedback law which ensures H$_{\infty}$ robust performance of closed loop system is derived based on a positive definite solution of a Riccati equation. This result shows that a solution of the problem can be also obtained by solving H$_{\infty}$ standard problem for an extended plant. Finally, a design example and simulation results will be given.ven.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
• /
• pp.20-23
• /
• 1994

It is well known that the Boyd's theorem states the relation between the imaginary eigenvalues of discriminant H of Riccati equation (A, R, Q) and the singular value of transfer function, but it is only available for R .geq. 0 and Q .geq. 0. In this paper, we extend Boyd's theorem for two case, that is, R is symmetric, Q is sign definite, and R is sign definite, Q is symmetric. We give under the condition that there is a real symmetric solution of Riccati equation the relation between H has imaginary eigenvalue and the maximum eigenvalue of transfer functoin. Finally, we give a necessary and sufficient condition to determine whether H has imaginary eigenvalue under some conditions.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
• /
• pp.81-84
• /
• 1996

We propose the robust nonlinear controller design methodology, the $H_{\infty}$ constrained quasi - linear quadratic Gaussian control (QLQG/ $H_{\infty}$), for the statistically-linearized multivariable system with hard nonlinearties such as Coulomb friction, deadzone, etc. The $H_{\infty}$ performance constraint is involved in the optimization process by replacing the covariance Lyapunov equation with the Riccati equation whose solution leads to an upper bound of the QLQG performance. Because of the system's nonlinearity, however, one equation among three Riccati equations contain the nonlinear correction terms that are very difficult to solve numerically. To treat this problem, we use simple algebraic techniques. With some analytic transformation for Riccati equations, the nonlinear correction terms can be so eliminated that the set of a linear controller to the different operating points are designed. Synthesizing these via inverse random input describing function (IRIDF) technique, the final nonlinear controller can be designed.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
• /
• pp.27-27
• /
• 2000

The nonlinear observers are proposed for a nonlinear system. To improve the characteristics such as a stability, a convergence, and an H$\sub$$\infty$/ filter performance criterion, we utilize and H$\sub$$\infty$/ filter Riccati equation or a modified H$\sub$$\infty$/ filter Riccati equation with a freedom parameter. Using the Lyapunov, the characteristics of the observer are analyzed. Then the in-flight alignment for a strapdown inertial navigation system(SDINS) is designed using the observer proposed. Simulation results show that the observer with the modified H$\sub$$\infty$/ fitter Riccati equation effectively improve the performance of the in-flight alignment.