Optimal Transport Over Deterministic Discrete-Time Nonlinear Systems Using Stochastic Feedback Laws
Optimal Transport Over Deterministic Discrete-Time Nonlinear Systems Using Stochastic Feedback Laws
复制标题
使用随机反馈定律的确定性离散时间非线性系统的最优传输
作者：
Karthik Elamvazhuthi;P. Grover;S. Berman
这封信考虑了一般非线性控制系统的运输问题的放松版本，其目标是设计时变反馈律，将给定的初始概率测度在闭环系统的作用下运输到目标概率测度。为了使问题易于分析，我们考虑随机的控制律，即，控制律是从控制系统的状态空间到容许控制输入集合上的概率测度空间的映射。根据一些控制系统的可控性假设定义在状态空间上，我们表明，运输问题，被认为是一个可控性问题的提升控制系统的概率措施的空间，是适定性的一大类的初始和目标措施。我们用它来证明定义在概率测度空间上的固定端点最优控制问题的适定性，其中沿着终端约束，目标是沿着控制系统的轨迹优化目标泛函沿着。这个优化问题可以看作是一个无限维线性规划问题。这种提法有利于数值解的低维控制系统的运输问题，我们在两个数值例子。
This letter considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability measure under the action of the closed-loop system. To make the problem analytically tractable, we consider control laws that are stochastic, i.e., the control laws are maps from the state space of the control system to the space of probability measures on the set of admissible control inputs. Under some controllability assumptions on the control system as defined on the state space, we show that the transport problem, considered as a controllability problem for the lifted control system on the space of probability measures, is well-posed for a large class of initial and target measures. We use this to prove the well-posedness of a fixed-endpoint optimal control problem defined on the space of probability measures, where along with the terminal constraints, the goal is to optimize an objective functional along the trajectory of the control system. This optimization problem can be posed as an infinite-dimensional linear programming problem. This formulation facilitates numerical solutions of the transport problem for low-dimensional control systems, as we show in two numerical examples.
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
通讯作者：
Pavon, Michele