本文選題：離散時間線性系統(tǒng)　切入點：有限時間穩(wěn)定　出處：《魯東大學(xué)》2017年碩士論文

【摘要】：有限時間穩(wěn)定是系統(tǒng)在受到初始擾動后,在所給定的時間區(qū)間內(nèi)系統(tǒng)的狀態(tài)不會超出規(guī)定的誤差范圍.其問題主要集中在穩(wěn)定性分析和控制器設(shè)計方面.模型預(yù)測控制(Model predictive control,MPC)能夠有效處理系統(tǒng)約束和參數(shù)不確定性等因素,能夠使系統(tǒng)有更好的性能,已經(jīng)成為應(yīng)用較為廣泛的現(xiàn)代控制策略.本文以離散時間線性系統(tǒng)為研究對象,對有限時間穩(wěn)定預(yù)測控制進(jìn)行了一些研究,總結(jié)如下:針對離散時間線性時不變(Linear Time Invariant,LTI)系統(tǒng)研究其有限時間MPC問題.當(dāng)系統(tǒng)狀態(tài)不可測時,構(gòu)造多Lyapunov函數(shù),在有限時域最小化性能指標(biāo)下,將求解有限時域的最小化轉(zhuǎn)化為具有LMI約束優(yōu)化問題.利用LMI方法,求解出有限時間穩(wěn)定輸出反饋預(yù)測控制器系數(shù)矩陣,進(jìn)而得到動態(tài)輸出反饋預(yù)測控制器.設(shè)計出具有有限時間穩(wěn)定性的預(yù)測控制算法.證明了優(yōu)化問題在所給定的條件下,系統(tǒng)是有限時間穩(wěn)定的.針對時不變、有限能量外部干擾的LTI系統(tǒng),研究了有限時間H_∞預(yù)測控制問題.給出了線性系統(tǒng)有限時間預(yù)測控制的定義,通過構(gòu)造Lyapunov-Krasovskii函數(shù)并結(jié)合矩陣不等式技術(shù),得到系統(tǒng)有限時間預(yù)測控制器有解的充分條件;進(jìn)一步,將問題轉(zhuǎn)化為具有線性矩陣不等式約束的優(yōu)化問題,并給出了相應(yīng)的求解算法.數(shù)值算例和仿真對比圖表明了設(shè)計方法的有效性.
[Abstract]:Finite time stability is that the state of the system does not exceed the prescribed error range in the given time interval after the system is initially disturbed.The problems mainly focus on stability analysis and controller design.Model predictive control (MPC), which can effectively deal with system constraints and parameter uncertainties, can make the system have better performance, and has become a widely used modern control strategy.In this paper, the finite time stability predictive control is studied for discrete time linear systems. The results are summarized as follows: the finite time Time problem is studied for discrete-time linear time invariant linear Time (LTI) systems.When the state of the system is unmeasurable, multiple Lyapunov functions are constructed, and the minimization of the finite time domain is transformed into an optimization problem with LMI constraints under the finite time domain minimization performance index.The coefficient matrix of the finite time stable output feedback predictive controller is solved by using the LMI method, and then the dynamic output feedback predictive controller is obtained.A predictive control algorithm with finite time stability is designed.It is proved that the optimization problem is finite time stable under the given conditions.For LTI systems with time-invariant and finite energy external disturbances, the finite time H _ 鈭，

本文編號：1716068