【摘要】：近年來,隨著計(jì)算機(jī)技術(shù)的高速發(fā)展,非線性離散系統(tǒng)的研究變得尤為重要,而輸入狀態(tài)穩(wěn)定作為魯棒控制研究的一個(gè)重要分支,對于分析帶有外部擾動(dòng)輸入的非線性系統(tǒng)具有較好的效果,因此輸入狀態(tài)穩(wěn)定性已經(jīng)成為一種較為普遍的非線性系統(tǒng)的分析方法。輸入狀態(tài)穩(wěn)定分析已經(jīng)涉及眾多理論研究領(lǐng)域并具有較強(qiáng)的工程背景,例如機(jī)器人控制系統(tǒng)、某些工程系統(tǒng)、生物系統(tǒng)、智能高速公路系統(tǒng)等。本文主要研究了幾類非線性系統(tǒng)在一定條件下的輸入狀態(tài)穩(wěn)定性以及一類非線性系統(tǒng)的輸入狀態(tài)鎮(zhèn)定問題。(1)針對一類離散時(shí)間非線性級聯(lián)系統(tǒng),運(yùn)用Lyapunov函數(shù)方法分析了由兩個(gè)積分輸入狀態(tài)穩(wěn)定(Integral input-to-state stability,iISS)的子系統(tǒng)組成的級聯(lián)系統(tǒng)仍然是ilSS的,給出該級聯(lián)系統(tǒng)達(dá)到iISS的充分條件,并將結(jié)果應(yīng)用于線性級聯(lián)的情況下,通過數(shù)值仿真證明了推導(dǎo)結(jié)果的正確性。(2)針對一類離散時(shí)間切換非線性系統(tǒng)的輸入狀態(tài)穩(wěn)定性研究問題,首先研究了非切換情況下,系統(tǒng)的全局漸近穩(wěn)定(Global asymptotic stability,GAS)和輸入狀態(tài)穩(wěn)定(Input-to-state stability,ISS),然后通過多Lyapunov函數(shù)方法并結(jié)合比較定理將結(jié)果推廣到離散切換非線性系統(tǒng)上,給出了切換系統(tǒng)GAS和ISS的充分條件。運(yùn)用切換信號的平均停留時(shí)間方法研究了切換系統(tǒng)的ISS。最后,通過數(shù)值實(shí)例證明了研究結(jié)果的正確性。(3)針對一類帶有外部擾動(dòng)的離散時(shí)間非線性嚴(yán)反饋系統(tǒng),利用Backstepping設(shè)計(jì)方法,設(shè)計(jì)了帶有外部擾動(dòng)的離散時(shí)間嚴(yán)反饋控制系統(tǒng)的輸入狀態(tài)鎮(zhèn)定控制器,并利用Lyapunov函數(shù)理論對閉環(huán)系統(tǒng)進(jìn)行了 ISS分析,最后通過數(shù)值仿真驗(yàn)證了所研究控制算法的正確性。
[Abstract]:In recent years, with the rapid development of computer technology, the study of nonlinear discrete systems becomes more and more important, and input state stability is an important branch of robust control. The analysis of nonlinear systems with external disturbances has a good effect, so the stability of input states has become a general analysis method for nonlinear systems. Input state stability analysis has been involved in many theoretical fields and has a strong engineering background, such as robot control systems, some engineering systems, biological systems, intelligent highway systems and so on. In this paper, the input state stability of some nonlinear systems under certain conditions and the input state stabilization of a class of nonlinear systems are studied. (1) for a class of discrete-time nonlinear cascaded systems, In this paper, the Lyapunov function method is used to analyze that the cascade system composed of two Integral input-to-state input state stability subsystems is still ilSS. The sufficient conditions for the cascade system to reach iISS are given, and the results are applied to the linear cascade. Numerical simulations show that the derivation is correct. (2) for a class of discrete-time switched nonlinear systems, the input state stability is studied. The globally asymptotically stable (Global asymptotic stability gas) and the input state stability of the system are given. Then the results are extended to discrete-time switched nonlinear systems by the method of multiple Lyapunov functions and the comparison theorem. The sufficient conditions of GAS and ISS for switched systems are given. The ISSs of switched systems are studied by means of the average residence time (RTD) method of switched signals. Finally, a numerical example is given to prove the correctness of the research results. (3) for a class of discrete-time nonlinear strict feedback systems with external disturbances, the Backstepping design method is used. The input state stabilization controller of discrete-time strict feedback control system with external disturbance is designed. The ISS analysis of the closed-loop system is carried out by using Lyapunov function theory. Finally, the correctness of the proposed control algorithm is verified by numerical simulation.
【學(xué)位授予單位】：濟(jì)南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TP13

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本文編號：2176591