脉冲微分系统的迭代学习控制问题研究
发布时间：2019-01-12 09:54
【摘要】：脉冲微分系统作为刻画突变现象的一类数学模型,在工业、经济等领域得到了诸多应用。迭代学习控制技术作为跟踪问题的一类解决方案,在设备制造、机器运行等工业领域得到了广泛应用。为解决某些带有瞬时突变的运动轨线的有限时间跟踪问题,本文研究了脉冲微分系统的迭代学习控制问题。主要内容如下：首先,将跟踪连续运动轨线的经典方法和结果,延拓到跟踪不连续运动轨线,针对一类非线性脉冲微分系统,设计带有初态学习的开环、闭环P型学习律,综合利用脉冲Gronwall不等式,Holder不等式等方法,在L2范数意义下,给出初态偏移情形下的收敛性充分条件。通过数值算例,验证了理论结果的有效性。其次,考虑到D型控制器具有前瞻、预测的特性,针对一类非线性脉冲微分系统,设计带有初态学习的开环、闭环PD型学习律,在λ范数意义下,给出初态偏移情形下的收敛性的充分条件。通过数值算例,验证了理论结果的有效性。最后,为了让控制器具有更灵活的控制手段,针对一类非线性脉冲微分系统,设计带有初态学习的开环、闭环PDDα型学习律,利用分数阶分部积分公式,给出λ范数意义下,带有初态偏移情形下的收敛性充分条件。通过数值算例,验证了理论结果的有效性。通过在仿生机器鱼速度控制的应用,验证了PDDα型学习律在迭代速度和收敛精度方面,明显优于P型学习律和PD型学习律。
[Abstract]:As a kind of mathematical model, impulsive differential system (PDS) has been applied in many fields such as industry, economy and so on. As a kind of solution to tracking problem, iterative learning control technology has been widely used in equipment manufacturing, machine operation and other industrial fields. In order to solve the finite time tracking problem of some trajectory with instantaneous abrupt changes, the iterative learning control problem for impulsive differential systems is studied in this paper. The main contents are as follows: firstly, the classical methods and results of tracking continuous motion trajectory are extended to track discontinuous motion trajectory. For a class of nonlinear impulsive differential systems, an open-loop, closed-loop P-type learning law with initial learning is designed. By means of impulsive Gronwall inequality, Holder inequality and so on, the sufficient conditions of convergence in the case of initial state migration are given in the sense of L 2 norm. The validity of the theoretical results is verified by numerical examples. Secondly, considering the prospective and predictive characteristics of D-type controllers, an open-loop, closed-loop PD learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, Sufficient conditions for convergence in the case of initial state migration are given. The validity of the theoretical results is verified by numerical examples. Finally, for a class of nonlinear impulsive differential systems, an open-loop, closed-loop PDD 伪 learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, the fractional partial integral formula is used to design the open loop and closed loop PDD 伪 learning law for a class of nonlinear impulsive differential systems. Sufficient conditions for convergence with initial state migration. The validity of the theoretical results is verified by numerical examples. It is proved that PDD 伪 learning law is superior to P type learning law and PD type learning law in iterative speed and convergence accuracy through the application of speed control in bionic robot fish.
【学位授予单位】：贵州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175;O231
，
本文编号：2407646
[Abstract]:As a kind of mathematical model, impulsive differential system (PDS) has been applied in many fields such as industry, economy and so on. As a kind of solution to tracking problem, iterative learning control technology has been widely used in equipment manufacturing, machine operation and other industrial fields. In order to solve the finite time tracking problem of some trajectory with instantaneous abrupt changes, the iterative learning control problem for impulsive differential systems is studied in this paper. The main contents are as follows: firstly, the classical methods and results of tracking continuous motion trajectory are extended to track discontinuous motion trajectory. For a class of nonlinear impulsive differential systems, an open-loop, closed-loop P-type learning law with initial learning is designed. By means of impulsive Gronwall inequality, Holder inequality and so on, the sufficient conditions of convergence in the case of initial state migration are given in the sense of L 2 norm. The validity of the theoretical results is verified by numerical examples. Secondly, considering the prospective and predictive characteristics of D-type controllers, an open-loop, closed-loop PD learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, Sufficient conditions for convergence in the case of initial state migration are given. The validity of the theoretical results is verified by numerical examples. Finally, for a class of nonlinear impulsive differential systems, an open-loop, closed-loop PDD 伪 learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, the fractional partial integral formula is used to design the open loop and closed loop PDD 伪 learning law for a class of nonlinear impulsive differential systems. Sufficient conditions for convergence with initial state migration. The validity of the theoretical results is verified by numerical examples. It is proved that PDD 伪 learning law is superior to P type learning law and PD type learning law in iterative speed and convergence accuracy through the application of speed control in bionic robot fish.
【学位授予单位】：贵州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175;O231
，
本文编号：2407646
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