Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Eucl...Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.展开更多
Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
The problem of robust H∞ guaranteed cost satisfactory fault-tolerant control with quadratic D stabilizability against actuator failures is investigated for a class of discrete-time systems with value-bounded uncertai...The problem of robust H∞ guaranteed cost satisfactory fault-tolerant control with quadratic D stabilizability against actuator failures is investigated for a class of discrete-time systems with value-bounded uncertainties existing in both the state and control input matrices.Based on a more practical and general model of actuator continuous gain failures,taking the transient property,robust behaviour on H∞ performance and quadratic cost performance requirements into consideration,sufficient conditions for the existence of satisfactory fault-tolerant controller are given and the effective design steps with constraints of multiple performance indices are provided.Meanwhile,the consistency of the regional pole index,H∞ norm-bound constraint and cost performance indices is set up for fault-tolerant control.A simulation example shows the effectiveness of the proposed method.展开更多
基金Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of ScienceProject(69904003) supported by the National Natural Science Foundation of ChinaProject(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China
文摘Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
基金supported by the National Natural Science Foundation of China (6057408260804027)
文摘The problem of robust H∞ guaranteed cost satisfactory fault-tolerant control with quadratic D stabilizability against actuator failures is investigated for a class of discrete-time systems with value-bounded uncertainties existing in both the state and control input matrices.Based on a more practical and general model of actuator continuous gain failures,taking the transient property,robust behaviour on H∞ performance and quadratic cost performance requirements into consideration,sufficient conditions for the existence of satisfactory fault-tolerant controller are given and the effective design steps with constraints of multiple performance indices are provided.Meanwhile,the consistency of the regional pole index,H∞ norm-bound constraint and cost performance indices is set up for fault-tolerant control.A simulation example shows the effectiveness of the proposed method.
