论文标题
稳健的离散时间Pontryagin最大原理
Robust Discrete-Time Pontryagin Maximum Principle on Matrix Lie Groups
论文作者
论文摘要
本文考虑了矩阵谎言组的离散时间强大最佳控制问题。假定潜在的系统被外源性无法测量的有界干扰扰动，并且控制问题被视为最小值最佳控制，其中，其中的干扰是对手，并试图最大程度地提高控制成本，该控制的成本试图最小化。假设问题中存在鞍点，我们提出了pontryagin最大原理（PMP）的版本，该版本封装了最佳控制和干扰轨迹必须满足的一阶必需条件。该PMP具有哈密顿式的鞍点状态，以及伴随动力学的一组向后差方程。我们还提出了我们在欧几里得空间上结果的特殊情况。最后，我们将PMP应用于刚体的单轴旋转的强大版本。
This article considers a discrete-time robust optimal control problem on matrix Lie groups. The underlying system is assumed to be perturbed by exogenous unmeasured bounded disturbances, and the control problem is posed as a min-max optimal control wherein the disturbance is the adversary and tries to maximise a cost that the control tries to minimise. Assuming the existence of a saddle point in the problem, we present a version of the Pontryagin maximum principle (PMP) that encapsulates first-order necessary conditions that the optimal control and disturbance trajectories must satisfy. This PMP features a saddle point condition on the Hamiltonian and a set of backward difference equations for the adjoint dynamics. We also present a special case of our result on Euclidean spaces. We conclude with applying the PMP to robust version of single axis rotation of a rigid body.
