非对称输入约束非线性系统的最优控制及其在UAV环航问题中的应用
Optimal control of nonlinear systems with unsymmetrical input constraints and its applications to the UAV circumnavigation problem
摘要：
本文提出了一种新的设计方案，用于解决具有非对称和状态依赖输入约束的非线性系统的最优控制问题。通过引入一个初始稳定控制策略作为所构造的最优控制策略的基线，我们消除了当前研究中对自适应最优控制的假设，即当系统的状态处于原点时，内部动态应保持为零。特别地，研究了动态部分未知的非线性控制系统，给出了获得相应最优控制策略的方法。证明了闭环系统的稳定性和控制策略的最优性。此外，我们应用所提出的控制设计框架来解决固定翼无人机（UAV）的最优环球航行问题的基础上积累的Fisher信息。通过数值仿真，将该算法的控制性能与现有的环航控制策略进行了比较。
英文摘要：
In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of the constructed optimal control policy, we remove the assumption in the current study for the adaptive optimal control, that is, the internal dynamics should hold zero when the state of the system is in the origin. Particularly, nonlinear control systems with partially-unknown dynamics are investigated and the procedure to acquire the corresponding optimal control policy is presented. The stability for the closed-loop dynamics and the optimality of the obtained control policy are both proved. Besides, we apply the proposed control design framework to solve the optimal circumnavigation problem based on the accumulative Fisher information for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our algorithm is compared with that of the existing circumnavigation control policy in a numerical simulation.
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