本文選題：非線性系統(tǒng)　切入點：狀態(tài)測量漂移　出處：《東南大學》2016年博士論文　論文類型：學位論文

【摘要】：實際系統(tǒng)中存在測量漂移、參數不確定性、時滯及隨機干擾等因素,不可避免地對系統(tǒng)的控制性能產生影響。因此,對不確定非線性系統(tǒng)反饋控制問題的研究具有重要的理論和實際意義。本文基于齊次系統(tǒng)理論、Lyapunov穩(wěn)定性理論和隨機系統(tǒng)理論,利用增加冪積分方法、齊次壓制方法和動態(tài)增益技術,針對一類不確定廣義齊次非線性系統(tǒng),研究其狀態(tài)反饋、輸出反饋以及自適應反饋控制問題。主要工作包括以下幾個方面：第一,在確定型系統(tǒng)中,針對系統(tǒng)狀態(tài)測量函數的指數中含有未知漂移量的情況,研究其魯棒控制器設計問題。利用單調遞減齊次度的概念和改進的增加冪積分方法,通過構造含有未知參數的Lyapunov函數,得到了一個具有單調遞減齊次度的反饋控制器。通過求解一個優(yōu)化問題,給出了未知指數漂移量的約束條件,同時保證了所設計的魯棒控制器能夠鎮(zhèn)定該系統(tǒng)。第二,在隨機型系統(tǒng)中,研究系統(tǒng)受到時滯、未知參數等不確定因素影響時反饋控制器的設計方法。(1)針對系統(tǒng)非線性函數中存在時滯且增長率未知的情況,研究其通用型輸出反饋控制器的設計問題�；谕ㄓ每刂频乃枷朐O計了一個動態(tài)輸出反饋控制器,其增益隨著系統(tǒng)輸出和它的估計值之間的誤差在線實時更新。最后,利用Lyapunov-Krasovskii泛函和隨機Barbalat引理,證明了閉環(huán)系統(tǒng)的所有信號依概率強有界,且系統(tǒng)狀態(tài)幾乎必然收斂至原點。(2)針對系統(tǒng)輸出增益和非線性函數增長率均未知的情況,構造一個全維齊次觀測器來估計未知的系統(tǒng)狀態(tài)。將增加冪積分方法與自適應控制相結合,設計了一個自適應輸出反饋控制器。根據推廣的隨機Lyapunov穩(wěn)定性定理,證明了系統(tǒng)狀態(tài)幾乎必然被調節(jié)至原點,進一步放寬了隨機非線性系統(tǒng)需滿足局部Lipschitz條件的限制。(3)針對系統(tǒng)的漂移項和擴散項滿足下三角齊次增長條件的情況,研究其依概率有限時間反饋控制問題�；邶R次壓制方法,設計了非光滑觀測器和輸出反饋控制器。進一步研究具有非線性參數化的系統(tǒng)。利用參數分離原則將未知非線性參數從非線性函數中分離出來,同時將增加冪積分方法與自適應技術相結合,構造了一種自適應狀態(tài)反饋控制器。根據隨機有限時間Lyapunov穩(wěn)定性定理,證明了所提出的反饋控制器使得系統(tǒng)狀態(tài)在有限時間內幾乎必然收斂至原點。(4)針對系統(tǒng)中存在高階次冪和時變時滯的情況,考慮其全局輸出反饋鎮(zhèn)定問題,進一步放寬了對系統(tǒng)高階次冪和系統(tǒng)非線性函數的限制條件。通過選取恰當的Lyapunov-Krasovskii泛函,構造了齊次觀測器和控制器。結合齊次壓制方法證明了整個閉環(huán)系統(tǒng)依概率全局漸近穩(wěn)定。最后,數值仿真驗證了所提控制算法的有效性。
[Abstract]:There are some factors such as measurement drift, parameter uncertainty, time delay and random disturbance in the real system, which inevitably affect the control performance of the system. It is of great theoretical and practical significance to study the feedback control problem of uncertain nonlinear systems. Based on the Lyapunov stability theory and stochastic system theory of homogeneous systems, the method of adding power integral is used in this paper. For a class of uncertain generalized homogeneous nonlinear systems, the state feedback, output feedback and adaptive feedback control problems are studied by homogeneous suppression method and dynamic gain technique. The main work includes the following aspects: first, In the deterministic system, the robust controller design problem is studied for the condition that the exponent of the system state measurement function contains unknown drift quantity. The concept of monotone decreasing homogeneity degree and the improved method of increasing power integral are used. By constructing the Lyapunov function with unknown parameters, a feedback controller with monotone decreasing homogeneous degree is obtained. By solving an optimization problem, the constraint conditions of the unknown exponential drift are given. At the same time, the designed robust controller is guaranteed to stabilize the system. Secondly, in the stochastic system, the system is time-delay. The design method of feedback controller under the influence of uncertain factors such as unknown parameters. (1) aiming at the case where there is time delay and the growth rate is unknown in the nonlinear function of the system, A dynamic output feedback controller is designed based on the idea of universal control. The gain of the controller is updated in real time with the error between the system output and its estimated value. By using the Lyapunov-Krasovskii functional and stochastic Barbalat Lemma, it is proved that all the signals of the closed-loop system are strongly bounded by probability, and the state of the system almost necessarily converges to the origin. A full dimensional homogeneous observer is constructed to estimate the unknown state of the system. An adaptive output feedback controller is designed by combining the method of increasing power integral with adaptive control. According to the generalized stochastic Lyapunov stability theorem, a new adaptive output feedback controller is proposed. It is proved that the state of the system is almost necessarily adjusted to the origin, and the restriction of local Lipschitz condition for stochastic nonlinear systems is further relaxed. For the condition that the drift term and diffusion term of the system satisfy the lower triangular homogeneous growth condition, Based on the homogeneous suppression method, the feedback control problem based on probability finite time is studied. A non-smooth observer and an output feedback controller are designed to further study the nonlinear parameterized system. The unknown nonlinear parameters are separated from the nonlinear function by the principle of parameter separation. At the same time, an adaptive state feedback controller is constructed by combining the method of adding power integral with adaptive technique. According to the stochastic finite time Lyapunov stability theorem, It is proved that the proposed feedback controller makes the state of the system almost bound to converge to the origin in a finite time) in view of the existence of higher order power and time-varying delays in the system, the global output feedback stabilization problem is considered. The restrictions on the nonlinear function of the higher order power sum of the system are further relaxed. By selecting the appropriate Lyapunov-Krasovskii functional, The homogeneous observer and controller are constructed, and the global asymptotic stability of the closed-loop system is proved by the homogeneous suppression method. Finally, the effectiveness of the proposed control algorithm is verified by numerical simulation.
【學位授予單位】：東南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TP13

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