Sub-optimal scheduling in switched systems with continuous-time dynamics: A gradient descent approach

Data-Driven Suboptimal Scheduling of Switched Systems

“…When δt → 0, with first-order Taylor expansion of V * (x(t + δt)) applied in (5) and (6), the HJB equation can be given as [21]:…”

“…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:…”

“…The cost-to-go is solved in policy evaluation (7) and the switching policy is updated in policy improvement (8) iteratively. The stability and convergence are stated in the following theorem which has been proved in [21,38]. Theorem 1.…”

“…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.…”

“…Then further research is conducted for problems with switching cost [19] or state jumps [20]. 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].…”