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Necessary conditions for Pareto optimality in multiobjective programming with subdifferentiable set functions are established in Theorem 12 of H. C. Lai and L. J. Ž . Lin J. Math. Anal. Appl. 132, 1988, 558]571 . In this paper, we establish some sufficient conditions under which a feasible solution of such a problem will be Pareto optimal provided that a… (More)

- Hiroaki Mukaidani, Hua Xu, Koichi Mizukami
- IEEE Trans. Automat. Contr.
- 2001

- Hua Xu, Koichi Mizukami
- Automatica
- 1997

- Hiroaki Mukaidani, Hua Xu, Koichi Mizukami
- Int. J. Systems Science
- 1999

- Hiroaki Mukaidani, Hua Xu, Koichi Mizukami
- Int. J. Systems Science
- 2000

In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system. The construction of the controller involves solving the full-order algebraic Riccati equation with small parameter ε. Under control-oriented assumptions, we first provide the sufficient conditions such that… (More)

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross–coupled algebraic Riccati equations with a small positive parameter ε. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov… (More)

- Hiroaki Mukaidani, Hua Xu, Koichi Mizukami
- Automatica
- 2002

In this paper, we show that the Kleinman algorithm can be used well to solve the algebraic Riccati equation (ARE) of singularly perturbed systems, where the quadratic term of the ARE may be inde1nite. The quadratic convergence property of the Kleinman algorithm is proved by using the Newton–Kantorovich theorem when the initial condition is chosen… (More)

- Hua Xu, Hiroaki Mukaidani, Koichi Mizukami
- Int. J. Systems Science
- 1997

In this paper, Pareto optimal strategy for general multiparameter singularly perturbed systems is investigated. The main contribution is to propose a new computational method for obtaining the high–order Pareto near–optimal strategy. Newton’s method and two fixed point algorithms are combined. As a result, the new iterative algorithm achieves the quadratic… (More)