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Item type:Item, Optimal fuzzy controller design: Local concept approach(2000-04-01) ;Wu, SJ ;Lin, CT ;電控工程研究所Institute of Electrical and Control EngineeringIn this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory, The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes, Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.Item type:Item, Optimal fuzzy controller design in continuous fuzzy system: Global concept approach(2000-12-01) ;Wu, SJ ;Lin, CT ;電控工程研究所Institute of Electrical and Control EngineeringIn this paper, we propose a systematic and theoretically sound way to design a global optimal fuzzy controller to control and stabilize a continuous fuzzy system with free- or fixed-end point under finite or infinite horizon (time), A linear-like global system representation of continuous fuzzy system is first proposed by viewing a continuous fuzzy system in global concept and unifying the individual matrices into synthetical matrices. Based on this, the optimal control law which can achieve global minimum effect is developed theoretically. The nonlinear segmental two-point boundary-value problem (TPBVP) is derived for the finite-horizon problem and a forward Riccati-like differential equation (DE) for the infinite-horizon problem. To further simplify the computation, a segmental Riccati-like DE is derived in solving the finite- or infinite-horizon issues. Moreover, in the case of time-invariant fuzzy systems, we show that the optimal controller can be obtained by Just solving algebraic Riccati-like equations. Grounding on this, several fascinating characteristics of the resultant closed-loop fuzzy system can be elicited easily. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. An example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.Item type:Item, Discrete-time optimal fuzzy controller design: Global concept approach(2002-02-01) ;Wu, SJ ;Lin, CT ;電控工程研究所Institute of Electrical and Control EngineeringIn this paper, we propose a systematic and theoretically sound way to design a global optimal discrete-time fuzzy controller to control and stabilize a nonlinear discrete-time fuzzy system with finite or infinite horizon (time). A linear-like global system representation of discrete-time fuzzy system is first proposed by viewing a discrete-time fuzzy system in global concept and unifying the individual matrices into synthetical matrices. Then, based on this kind of system representation, the discrete-time optimal fuzzy control law which can achieve global minimum effect is developed theoretically. A nonlinear two-point-boundary-value-problem (TPBVP) is derived as the necessary and sufficient condition for the nonlinear quadratic optimal control problem. To simplify the computation, a multistage decomposition of optimization scheme is proposed and then a segmental recursive Riccati-like equation is derived. Moreover, in the case of time-invariant fuzzy systems, we show that the optimal controller can be obtained by just solving discrete-time algebraic Riccati-like equations. Grounding on this, several fascinating characteristics of the resultant closed-loop fuzzy system can be elicited easily. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system can not only be guarantee to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. An example is given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.Item type:Item, Global optimal fuzzy tracker design based on local concept approach(2002-04-01) ;Wu, SJ ;Lin, CT ;電控工程研究所Institute of Electrical and Control EngineeringIn this paper, we propose a global optimal fuzzy tracking controller, implemented by fuzzily blending the individual local fuzzy tracking laws, for continuous and discrete-time fuzzy systems with the aim of solving, respectively, the continuous and discrete-time quadratic tracking problems with moving or model-following targets under finite or infinite horizon (time). The differential or recursive Riccati equations, and more, the differential or difference equations in tracing the variation of the target are derived. Moreover, in the case of time-invariant fuzzy tracking systems, we show that the optimal tracking controller can be obtained by just solving algebraic Riccati equations and algebraic matrix equations. Grounding on this, several fascinating characteristics of the resultant closed-loop continuous or discrete time-invariant fuzzy tracking systems can be elicited easily. The stability of both closed-loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers. The optimal closed-loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Moreover, the resulting closed-loop fuzzy tracking systems possess infinite gain margin; that is, their stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties.