• 제어로봇시스템학회논문지
• /
• 제15권1호
• /
• pp.67-71
• /
• 2009

This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

• 대한수학회지
• /
• 제32권3호
• /
• pp.519-529
• /
• 1995

Let M be a compact smooth manifold of dimension n and let E be a flat (complet) vector bundle over M of rank r.

• 제어로봇시스템학회논문지
• /
• 제13권11호
• /
• pp.1048-1052
• /
• 2007

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2005년도 학술대회 논문집 정보 및 제어부문
• /
• pp.523-525
• /
• 2005

This paper deals with a linear matrix inequality (LMI) approach to the design of a static output feedback controller that simultaneously stabilizes a finite collection of linear time-invariant plants. Simultaneous stabilization by static ouput feedback is represented in terms of LMIs with a rank condition. An iterative penalty method is proposed to solve the rank-constrained LMI problem. Numerical experiments show the effectiveness of the proposed algorithm.

• 대한수학회지
• /
• 제45권4호
• /
• pp.1043-1056
• /
• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.

• 대한수학회지
• /
• 제45권2호
• /
• pp.301-312
• /
• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
• /
• pp.729-731
• /
• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제53권11호
• /
• pp.747-752
• /
• 2004

This paper presents an iterative linear matrix inequality (LMI) approach to the design of a static output feedback (SOF) stabilization controller. A linear penalty function is incorporated into the objective function for the non-convex rank constraint so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. Hence, the overall procedure results in solving a series of semidefinite programs (SDPs). With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Extensive numerical experiments are Deformed to illustrate the proposed algorithm.

• 대한전기학회논문지:전력기술부문A
• /
• 제53권12호
• /
• pp.655-660
• /
• 2004

This paper deals with the design of a fixed-structure $H_\infty$ power system stabilizer (PSS) by using an iterative linear matrix inequality (LMI) method. The fixed-structure $H_\infty$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the practical applicability of the proposed algorithm.

• 제어로봇시스템학회논문지
• /
• 제11권4호
• /
• pp.279-283
• /
• 2005

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.