RBF-ARX model-based two-stage scheduling RPC for dynamic systems with bounded disturbance

A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

“…For comparison, two other algorithms, which are the well-tuned PID with multiple sets of parameters (PID-M) and the RBF-ARX model-based RPC algorithm proposed in Ref. [30] (RBF-ARX-TRPC), are also carried out.…”

“…For fair comparison, the RBF-ARX-TRPC algorithm and the proposed RBF-ARX-RPC algorithm are all based on the same model, which is identified in Section 4.1. e controller parameters and variable constraints of the three algorithms are all given in Table 2. Figure 5 shows the trajectory tracking performances of the three algorithms (PID-M, RBF-ARX-TRPC [30], and RBF-ARX-RPC proposed in this paper). In Figure 5, the pink dotted line denotes the desired trajectory of the liquid level of the lower tank H 2 (t), and it increases from 60 cm to 100 cm at the 20 th second, decreases from 100 cm to 30 cm at the 130 th second, and then increases from 30 cm to 70 cm at the 210 th second.…”

“…Next, it can be verified that the inequality (30) is satisfied if and only if the Lyapunov matrices P ab | a, b � 1, 2, . .…”

“…Zhou et al [29] proposed a one-stage scheduling quasi-min-max MPC algorithm, in which the external bounded disturbance is considered. What is more, Zhou et al [30] further studied a two-stage scheduling quasi-min-max MPC algorithm based on the RBF-ARX model. Although some results have been achieved, the current literatures [28][29][30] are mainly focused on using the parameter bound information of the SD-ARX model to wrap the system's future dynamics, and these types of methods have serious conservatism when constructing the system's state-space model.…”

“…What is more, Zhou et al [30] further studied a two-stage scheduling quasi-min-max MPC algorithm based on the RBF-ARX model. Although some results have been achieved, the current literatures [28][29][30] are mainly focused on using the parameter bound information of the SD-ARX model to wrap the system's future dynamics, and these types of methods have serious conservatism when constructing the system's state-space model. To reduce the conservativeness of these type of methods, the variation range information of the SD-ARX model's parameters is further considered in this paper to compress the size of the convex polytopic sets which are designed to wrap the system's future dynamics.…”