Wang Zhong, Li Yan
Department of Navigation, Guidance, and Control, Northwestern Polytechnical University, Xi'an, 710129, PR China.
ISA Trans. 2021 Feb;108:220-229. doi: 10.1016/j.isatra.2020.08.041. Epub 2020 Sep 1.
The state-dependent Riccati equation (SDRE) method is an efficient approach to solve nonlinear optimal control problems (OCPs), but nonlinear necessary conditions for the first-order optimality are seldom met in the SDRE approach. In this paper, a state-dependent indirect pseudospectral (SDIP) technique is developed to design nonlinear optimal controllers. To preserve the nonlinearity of the system and reduce the computational cost as well, the state-dependent coefficient (SDC) parameterization technique is employed. Then the optimality conditions are derived under input and state constraints, and spectral methods are used to discretize the optimality conditions into a series of mixed linear complementarity problems (MLCPs). The developed SDIP method is able to handle the finite and infinite-horizon nonlinear OCPs in a unified framework. Numerical comparisons also verify the performance of the developed SDIP method.
状态依赖型 Riccati 方程（SDRE）方法是解决非线性最优控制问题（OCP）的一种有效方法，但在 SDRE 方法中很少满足一阶最优性的非线性必要条件。本文提出了一种状态依赖型间接拟谱（SDIP）技术来设计非线性最优控制器。为了保持系统的非线性并降低计算成本，采用了状态依赖系数（SDC）参数化技术。然后在输入和状态约束下推导最优性条件，并使用谱方法将最优性条件离散为一系列混合线性互补问题（MLCP）。所提出的 SDIP 方法能够在统一框架内处理有限和无限时域的非线性 OCP。数值比较也验证了所提出的 SDIP 方法的性能。
