TY - JOUR
T1 - Design of optimal controller for interval plant from signal energy point of view via evolutionary approaches
AU - Hsu, Chen Chien
AU - Yu, Chih Yung
N1 - Funding Information:
Manuscript received June 12, 2003; revised November 16, 2003. This work was supported in part by the National Science Council, Taiwan, R.O.C., under Grant NSC 91-2213-E-129-002. This paper was recommended by Associate Editor H. Takagi.
PY - 2004/6
Y1 - 2004/6
N2 - Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.
AB - Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach.
KW - Genetic algorithms
KW - Integral of squared error (ISE)
KW - Interval plants
KW - Minimax optimization
KW - Robust controllers
KW - Signal energy
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U2 - 10.1109/TSMCB.2004.826396
DO - 10.1109/TSMCB.2004.826396
M3 - Letter
C2 - 15484931
AN - SCOPUS:2942607419
SN - 1083-4419
VL - 34
SP - 1609
EP - 1617
JO - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
JF - IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IS - 3
ER -