不确定系统的耗散性和无源性问题研究
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摘要
耗散性和无源性理论由于在系统控制和工程实践中的广泛应用，近年来已成为控制界的研究热点。本论文针对当前耗散性和无源性理论的研究现状，重点研究非线性系统和线性时滞系统的鲁棒耗散性、无源性综合问题，并在耗散性理论框架下研究几乎扰动解耦和非线性H_∞控制问题，提出一些新的解决问题的方法，研究内容如下：
一、研究一类带有凸性不确定参数的非线性系统的自适应反馈无源化问题。利用反演法并结合速度-梯度技巧，设计出使系统从新输入到构造输出无源的自适应控制律。
二、研究一类带有界范数不确定性的仿射非线性系统的鲁棒无源性综合问题。首先，基于非线性矩阵不等式方法得到系统是鲁棒无源的充分条件；然后在此基础上，设计出状态反馈控制器实现闭环系统的鲁棒无源控制。
三、研究一类带输入-输出馈通项，且控制项系数包含不确定性的仿射非线性系统的鲁棒耗散性综合问题。基于HJI不等式方法给出系统是鲁棒耗散的充分条件；在此基础上，设计出相应的状态反馈控制器，实现闭环系统的鲁棒耗散控制。
四、研究一类单输入非仿射非线性系统的逆最优控制问题，设计出参数化的状态反馈逆最优控制器；进而讨论当系统为耗散系统时的逆最优控制问题，基于耗散性理论，获得系统的最优值函数和最优控制律，并揭示出非线性耗散系统在线性输出反馈意义下稳定性与最优性之间的等价关系。
五、研究一类非最小相位且带有参数不确定性的高阶级连非线性系统的满足稳定性的鲁棒几乎扰动解耦问题。基于输入到状态稳定性理论，在一定的增长条件下，应用李雅普诺夫第二方法，并结合加一个幂积分器的技巧，显式地构造出光滑的状态反馈控制器，使对所有允许的参数不确定性闭环系统是输入到状态稳定的，且从扰动输入到输出的L_2-增益不超过某给定的任意小的值。
六、研究一类可部分反馈线性化且具扰动下三角结构的非线性参数不确定系统的鲁棒H_∞控制问题。所研究系统的伪零动态是渐进稳定的，且不确定参数是非线性的。在输入到状态稳定性理论框架下，运用李雅普诺夫第二方法构造出状态反馈控制器使得所研究的问题有解。
七、研究状态和控制输入都带有时变时滞的不确定线性系统的基于观测器的
Dissipativity and passivity theories have been the focuses in control community, due to their wide applications in systems control and engineering problems. In the light of these recent studies in the fields, this dissertation provides a systematic study in robust dissipativity and passivity synthesis problems of nonlinear systems and linear time-delayed systems. Meanwhile, in the framework of dissipativity theory, almost disturbance decoupling with internal stability problem and nonlinear H_∞ control problem are also addressed. Some new design techniques are proposed and several new results are obtained. The major contents in this dissertation are as follows:
1、 The problem of adaptive feedback passification of a class of nonlinear systems with uncertain parameters is studied. Combining backstepping methodology with speed-gradient technique, the adaptive controller and the corresponding parameter update law are obtained, which render the closed-loop systems passive from new input to output.
2、 The robust passivity synthesis problem is concerned for a class of affine nonlinear systems with bounded-norm uncertainties. Firstly, based on the nonlinear matrix inequality (NLMI) approach, the sufficient conditions under which the unforced uncertain systems are robustly passive are derived; and then, again applying NLMI approach, the solvable conditions for the problem at hand are proposed, and the parameterized state feedback controllers are explicitly expressed.
3、 The robustly dissipative synthesis problem is discussed for a class of affine nonlinear uncertain systems with input-output feedthrough. Uncertainties appear in the vector field which multiplies the control. Firstly, based on Hamilton-Jacobi-Issacs (HJI) inequality approach, the sufficient condition under which the unforced systems are robustly dissipative is proposed; based on the former result, the solvable condition for the robustly dissipative control problem is obtained, and the corresponding state feedback controller is explicitly designed.
4、 The inverse optimal stabilization problem of a class of single-input non-affine nonlinear systems with nonlinear-nonquadratic performance index is firstly addressed, and the parameterized inverse optimal controllers are designed. Secondly, when the systems are dissipative, the inverse optimal control problem is discussed in the
一、研究一类带有凸性不确定参数的非线性系统的自适应反馈无源化问题。利用反演法并结合速度-梯度技巧，设计出使系统从新输入到构造输出无源的自适应控制律。
二、研究一类带有界范数不确定性的仿射非线性系统的鲁棒无源性综合问题。首先，基于非线性矩阵不等式方法得到系统是鲁棒无源的充分条件；然后在此基础上，设计出状态反馈控制器实现闭环系统的鲁棒无源控制。
三、研究一类带输入-输出馈通项，且控制项系数包含不确定性的仿射非线性系统的鲁棒耗散性综合问题。基于HJI不等式方法给出系统是鲁棒耗散的充分条件；在此基础上，设计出相应的状态反馈控制器，实现闭环系统的鲁棒耗散控制。
四、研究一类单输入非仿射非线性系统的逆最优控制问题，设计出参数化的状态反馈逆最优控制器；进而讨论当系统为耗散系统时的逆最优控制问题，基于耗散性理论，获得系统的最优值函数和最优控制律，并揭示出非线性耗散系统在线性输出反馈意义下稳定性与最优性之间的等价关系。
五、研究一类非最小相位且带有参数不确定性的高阶级连非线性系统的满足稳定性的鲁棒几乎扰动解耦问题。基于输入到状态稳定性理论，在一定的增长条件下，应用李雅普诺夫第二方法，并结合加一个幂积分器的技巧，显式地构造出光滑的状态反馈控制器，使对所有允许的参数不确定性闭环系统是输入到状态稳定的，且从扰动输入到输出的L_2-增益不超过某给定的任意小的值。
六、研究一类可部分反馈线性化且具扰动下三角结构的非线性参数不确定系统的鲁棒H_∞控制问题。所研究系统的伪零动态是渐进稳定的，且不确定参数是非线性的。在输入到状态稳定性理论框架下，运用李雅普诺夫第二方法构造出状态反馈控制器使得所研究的问题有解。
七、研究状态和控制输入都带有时变时滞的不确定线性系统的基于观测器的
Dissipativity and passivity theories have been the focuses in control community, due to their wide applications in systems control and engineering problems. In the light of these recent studies in the fields, this dissertation provides a systematic study in robust dissipativity and passivity synthesis problems of nonlinear systems and linear time-delayed systems. Meanwhile, in the framework of dissipativity theory, almost disturbance decoupling with internal stability problem and nonlinear H_∞ control problem are also addressed. Some new design techniques are proposed and several new results are obtained. The major contents in this dissertation are as follows:
1、 The problem of adaptive feedback passification of a class of nonlinear systems with uncertain parameters is studied. Combining backstepping methodology with speed-gradient technique, the adaptive controller and the corresponding parameter update law are obtained, which render the closed-loop systems passive from new input to output.
2、 The robust passivity synthesis problem is concerned for a class of affine nonlinear systems with bounded-norm uncertainties. Firstly, based on the nonlinear matrix inequality (NLMI) approach, the sufficient conditions under which the unforced uncertain systems are robustly passive are derived; and then, again applying NLMI approach, the solvable conditions for the problem at hand are proposed, and the parameterized state feedback controllers are explicitly expressed.
3、 The robustly dissipative synthesis problem is discussed for a class of affine nonlinear uncertain systems with input-output feedthrough. Uncertainties appear in the vector field which multiplies the control. Firstly, based on Hamilton-Jacobi-Issacs (HJI) inequality approach, the sufficient condition under which the unforced systems are robustly dissipative is proposed; based on the former result, the solvable condition for the robustly dissipative control problem is obtained, and the corresponding state feedback controller is explicitly designed.
4、 The inverse optimal stabilization problem of a class of single-input non-affine nonlinear systems with nonlinear-nonquadratic performance index is firstly addressed, and the parameterized inverse optimal controllers are designed. Secondly, when the systems are dissipative, the inverse optimal control problem is discussed in the
引文
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