Abstract
In this paper, a data-driven optimal scheduling approach is investigated for continuous-time switched systems with unknown subsystems and infinite-horizon cost functions. Firstly, a policy iteration (PI) based algorithm is proposed to approximate the optimal switching policy online quickly for known switched systems. Secondly, a data-driven PI-based algorithm is proposed online solely from the system state data for switched systems with unknown subsystems. Approximation functions are brought in and their weight vectors can be achieved step by step through different data in the algorithm. Then the weight vectors are employed to approximate the switching policy and the cost function. The convergence and the performance are analyzed. Finally, the simulation results of two examples validate the effectiveness of the proposed approaches.
Highlights
Switched systems consisting of several subsystems and a switching policy ruling the switching among them [1,2] arise in certain application situations [3,4] such as a system which has to collect data sequentially from a number of sensory sources and switches its attention among the data sources [5,6].The switching among subsystems complicates the control problems and many of the problems remain to be open such as the optimal control problems
policy iteration (PI)-based algorithm inspired by the off-policy learning method [35,36] is proposed to approximate the optimal solution quickly for optimal scheduling problems with known system models first and based on that, a data-driven PI-based algorithm is formulated for optimal scheduling of continuous-time switched systems with infinite-horizon cost functions, which don’t require that dynamic equations can be evaluated or known at some sets
The offline, online and concurrent implementation of the aforementioned PI approach for switched systems with known dynamics has been investigated in references [21,22,38]
Summary
Switched systems consisting of several subsystems and a switching policy ruling the switching among them [1,2] arise in certain application situations [3,4] such as a system which has to collect data sequentially from a number of sensory sources and switches its attention among the data sources [5,6]. PI-based algorithm inspired by the off-policy learning method [35,36] is proposed to approximate the optimal solution quickly for optimal scheduling problems with known system models first and based on that, a data-driven PI-based algorithm is formulated for optimal scheduling of continuous-time switched systems with infinite-horizon cost functions, which don’t require that dynamic equations can be evaluated or known at some sets. The contribution of this paper is stated as follows: (1) with the data produced by the initial switching policy, an online PI-based algorithm is proposed to approximate the optimal solution quickly for optimal scheduling of known switched systems. (2) A data-driven PI-based algorithm is designed to solve optimal scheduling problems for switched systems with infinite-horizon cost functions and unknown subsystems, solely from the data produced by the initial switching policy, which has not been achieved well in existing literature as far as we know.
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