Suboptimal Scheduling in Switched Systems With Continuous-Time Dynamics: A Least Squares Approach

Abstract

Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are presented. The first solution formulates a policy iteration (PI) algorithm for the switched systems with recursive least squares. To reduce the computational burden imposed by the PI algorithm, a second solution, called single loop PI, is presented. Online and concurrent training algorithms are discussed for implementing each solution. At last, effectiveness of the presented algorithms is evaluated through numerical simulations.

Data-Driven Suboptimal Scheduling of Switched Systems

“…For the optimal problem, the admissible switching policy should be introduced and the relevant assumption is made as [22]. Definition 1.…”

“…Then, a PI approach can be applied to solve the optimal scheduling problem. Given an admissible switching policy v 0 , the PI approach [21,22] is stated as follows:…”

“…By utilizing control inputs to represent the switching policy, embedding approaches transform the optimal control problems of switched systems to traditional optimal control problems to address [12][13][14]. Adaptive dynamic programming (ADP) [15] approaches are introduced to solve the optimal control problems for switched systems with different initial conditions directly [16][17][18][19][20][21][22]. For optimal scheduling of switched systems with infinite-horizon cost functions, ADP approaches perform well to provide approximate global optimal solutions directly.…”

“…For optimal scheduling of switched systems with continuous-time dynamics, an approximate feedback solution is proposed based on policy iteration (PI) algorithm with its offline, online, and concurrent implementation [21]. Then, a PI algorithm with recursive least squares is proposed and modified into a single loop PI algorithm to reduce the computational burden [22].…”

Sub-Optimal Control of Autonomous Wheel Loader With Approximate Dynamic Programming

“…The behavior of a WL in an SLC portrays a switched system with controlled subsystems and a fixed mode sequence [1]. Switched systems are systems comprised of several subsystems/modes and a switching rule that assigns the active mode [2]- [4]. The sequence of active modes in a switched system is called the mode sequence.…”