A Dual-level Model Predictive Control Scheme for Multi-timescale Dynamical Systems--Extended Version

Abstract

This paper presents a dual-level model predictive control (MPC) scheme for two-timescale dynamical systems subject to input and state constraints, with the scope to enforce closed-loop separable dynamics. A novel dual-level MPC (i.e., D-MPC) algorithm is initially presented. At the high level of the control structure, a stabilizing MPC regulator minimizes the deviation of the output and its setpoint at a slow time scale. A shrinking horizon MPC is designed at the low level to refine the computed control actions in the basic time scale so as to generate satisfactory short-term transient of the output associated with the "fast" dynamics. To further improve the closed-loop control performance, an incremental D-MPC algorithm is also proposed, via introducing at the high level of the D-MPC an integral action and an explicit design of the "fast" output reference. The proposed algorithms are not only suitable for systems characterized by different dynamics, but also capable of imposing separable closed-loop performance for dynamics that are nonseparable and strongly coupled. The recursive feasibility and convergence properties of the D-MPC and incremental D-MPC closed-loop control systems are proven. The simulation results concerning the use of the proposed approaches for the control of a Boiler Turbine (BT) system, including the comparisons with a decentralized PID controller and a multirate MPC, are reported to show the effectiveness of the proposed algorithms in imposing closed-loop separable dynamics and the advantages in generating satisfactory control performance.

Intent-Aware Optimal Collision Avoidance and Trajectory Planning for a Pursuit Vehicle

“…[21] which has been found to improve the ergodicity of a hybrid system in real-time operation. Receding horizon control strategy has also been explored in underwater surveillance [22] and in a modified form in dynamical systems with unknown, bounded and stochastic disturbances [23,24].…”

A Dual-Level Model Predictive Control Scheme for Multitimescale Dynamical Systems

“…For completeness, the proposed controllers were applied to the original nonlinear systems and compared with classic nonlinear MPC algorithms and the SMC in [47]. The implementing steps and simulation results are neglected here for space limitations, interested readers may refer [48] for a detailed report. The simulation results have verified the effectiveness of the proposed approaches.…”

“…In view of (25), it is possible to write (48) (28) and Low-Level Problem (33)]: As N α is assumed to be reachable by Algorithm 2 such that ( 28) is feasible at time k = 0, along the same line of Appendixes-A and -B, we first prove the recursive feasibility for problem (33) in the fast time scale. To this end, note that (33) is feasible at a time instant h ∈ [kN, kN +N) means that one can find the candidate control sequence u(kN), .…”