| 中文摘要 | 非线性系统的最优控制一直是控制领域研究的热点和难点之一. 而传统的基于数学模型的最优控制在面对模型不确定的复杂动态系统时常难达到预期的性能指标, 因此, 采用基于数据的控制理论来解决复杂被控系统的在线预测、优化和控制, 已成为智能控制领域的研究热点之一. 而融合神经网络、评价设计以及经典动态规划的自适应动态规划方法为解决非线性控制问题尤其是基于数据的控制问题时提供了一个新的切入点. 为此, 本文在横向项目“甲醇生产过程平行控制系统的人工系统研发” 的基础上以及国家自然科学基金项目“基于数据的智能电网电能供需自适应优化匹配与调控(61273140)” 和“基于数据的非线性控制系统分析与设计(61034002)” 等的资助下, 针对一类带有未知死区约束控制的非线性离散仿射系统, 基于自适应动态规划思想和自适应最优控制原理以及神经网络智能控制方法研究了该类系统的基于数据的最优控制问题. 本文的主要工作和贡献主要体现在以下三个方面: 1. 研究带有未知死区约束的离散时间仿射非线性系统的最优控制问题. 现有的最优控制律设计大多是基于线性系统或基于饱和约束, 而实际生活中死区约束控制输入严重影响了被控系统的动态性能, 现有的基于死区约束控制律的设计, 大都只关注稳定以及平滑的控制律设计. 因此研究基于死区约束的非线性自适应最优控制具有重要的意义. 而在研究非线性自适应最优控制问题时, 最终需要求解离散时间哈密顿一雅克比一贝尔曼方程(DTHJB). 所以我们首先将带有死区约束的自适应最优控制问题转化为求解DTHJB方程的解的问题, 而该方程的解析解是很难获得的. 我们引入迭代自适应动态规划(ADP)算法间接逼近DTHJB方程的最优解. 而现有的迭代ADP算法中的HDP技术具有结构简单、容易实现等优点, 因此我们首先利用HDP 技术研究了带有未知死区的非线性系统自适应最优控制问题, 在文中我们同时证明了DTHJB方程解的存在性以及唯一性, 并证明了该解就是非线性最优控制问题的最优代价函数, 而其相应的控制律就是最优控制律. 2. 首次应用全局二次启发式规划(Globalized Dual Heuristic Programming,GDHP)算法研究带有未知死区约束的非线性自适应最优控制. 虽然启发式动态规划(Heuristic Dynamic Programming, HDP) 技术具有结构简单、容易实现等优点, 但是精度较低, 误差较大. 而二次启发式规划(Dual Heuristic Programming, DHP)技术能够减少计算误差, 但实现结构比较复杂, 而且不能直接输出我们最需要的代价函数. 采用GDHP 技术可以同时克服上述两种方法的缺点又能融合这两种方法的优点. 因此, 本部分着重利用GDHP 技术研究基于未知死区控制约束的非线性自适应最优控制, 给出了基于死区约束控制的迭代GDHP算法, 同时使用三层误差反向传播(Back Propagation,BP)神经网络构建了模型网络、评价网络以及执行网络, 模型网络的构建使得基于数据驱动的控制成为可能, 最后通过仿真实例验证了该算法的可行性. 3. 首次利用径向基函数(Radial Basis Function, RBF)神经网络研究基于贪婪HDP迭代技术的自适应最优控制问题. 提出针对带有死区约束的非线性最优控制问题的贪婪HD... |
| 英文摘要 | The optimal control problem of nonlinear systems has been a hotspot and one of the most difficult tasks in control field. For the traditional control methods based on mathematic models may hardly achieve the expected performance index due to the model uncertainty. Therefore, the data-based optimal control theory or method to manage on-line prediction, optimization and control for the complex controlled systems is becoming a research focus in the domain of intelligent control. While adaptive dynamic programming(ADP) methods, as an integration of neural networks, adaptive critic designs and the classical dynamic programming, provide a new perspective for the study of the nonlinear optimal control problems especially the data-based control. Thus, based on the development of a parallel control system which is used to obtain the interaction between the actual system and the artificial system in the methanol production process, the project has been supported by National Natural Science Foundation of China (61273140) and (61034002). In this project, based on the ADP method, adaptive optimal control and neural networks intelligent control, we studied the optimal control problem for a class of discrete-time affine nonlinear systems with unknown dead-zone control constraints. The main contributions of this dissertation are summarized as follows: 1. The optimal control problems for a class of discrete-time affine nonlinear system with unknown dead-zone control are studied . The existing research relies instead on dead-zone control constraints which can seriously hinder performance of the controlled system in reality, based on linear systems or actuator saturations. Meanwhile the current study of the design of control law based on dead-zone constraints only focus on the stability or the design of smooth control input. Therefore, it is of great importance to study the adaptive optimal control problem of nonlinear systems with dead-zone constraints. The optimal control problems of nonlinear systems are often reduced to the nonlinear DTHJB equation which is difficult to get an accurate solution. So we first change the problem to the DTHJB equation, then by introducing ADP technique, we obtain the approximate solution of the equation indirectly, which is proved to be uniquely solvable and the optimal cost function in our paper, and so does the optimal control law. 2. The adaptive optimal control based on the GDHP technique for dynamic s... |
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