Economic Lyapunov‐based model predictive control with event‐triggered parametric identification

Abstract

This article focuses on the design of model predictive control (MPC) for nonlinear systems with slow time‐dynamic change. To avoid frequent updates of the predictive model and guarantee the state always stays inside of a given feasible region, an event‐triggered parametric estimation mechanism is designed. Firstly, a trigger condition is designed to judge if parameters of the predictive model are out of date and differ a lot from their current true values so that there is no feasible solution to regulate the state within the given bound without predictive model parameter update. This condition also depends on the current state and is deduced from a designed Lyapunov constraint, inputs constraints, and the mismatched predictive model. Then the EMPC is designed based on this condition. If the trigger condition is met, the MPC recursively updates the parameters and imposes the Lyapunov constraint. The Lyapunov constraint is based on the mismatched model and the real state does not need to be convergence. Else, the MPC only optimizes the cost function to derive a good profit. We proved that the proposed EMPC promises that the closed‐loop system state is maintained within a predefined stable region when the model mismatch bound can be estimated accurately. A simulation of a chemical process demonstrates the effectiveness of the proposed method.

A distributed model predictive control with neighborhood state feedback invariant set for reconfigurable networked systems

“…These local optimization problems work together to get the solution of the constrained optimization problem to be solved in centralized MPC. Compared with the centralized MPC, DMPC not only inherits MPC's abilities to obtain good optimization performance, explicitly accommodate constraints, 9‐16 but also can reduce the computational complexity and improve the flexibility and robustness of the overall networked system 7,12,17‐20 …”

“…5,6,8 These local optimization problems work together to get the solution of the constrained optimization problem to be solved in centralized MPC. Compared with the centralized MPC, DMPC not only inherits MPC's abilities to obtain good optimization performance, explicitly accommodate constraints, [9][10][11][12][13][14][15][16] but also can reduce the computational complexity and improve the flexibility and robustness of the overall networked system. 7,12,[17][18][19][20] For the control of reconfigurable networked systems, one problem is how to improve the performance of the entire closed-loop system with feasibility guaranteed even when the network topology changes.…”

Implementable Stability Guaranteed Lyapunov-Based Data-Driven Model Predictive Control with Evolving Gaussian Process

“…5 References 18 and 19 proposed a Lyapunov MPC (LMPC), where a Lyapunov controller is employed to limit the MPC output to guarantee that the state of the closed-loop system asymptotically converges to a small region around the origin. 20 Based on the assumption of the existing stochastic Lyapunovbased controller, ref 21 designs an LMPC for systems with disturbances, which ensures the economic optimality, feasibility, and stability under a certain probability. Moreover, some LMPCs based on the machine learning models appeared in the literature.…”

“…For systems with uncertainties, ref proposed a tube-based MPC which uses a tightened constraint that excludes the boundaries of the possible affect of uncertainties, on states and inputs to guarantee the recursive feasibility of the MPC . References and proposed a Lyapunov MPC (LMPC), where a Lyapunov controller is employed to limit the MPC output to guarantee that the state of the closed-loop system asymptotically converges to a small region around the origin . Based on the assumption of the existing stochastic Lyapunov-based controller, ref designs an LMPC for systems with disturbances, which ensures the economic optimality, feasibility, and stability under a certain probability.…”

Koopman Approximator based Adaptive Model Predictive Control of Continuous Nonlinear Systems

“…Ref. [16] proposed an event-triggered method, which considers a fixed error boundary, and triggered the model update when the state may exceed the state constraints. It assumes the accuracy of the model converges to a certain level in a finite time and does not request the Lyapunov function always decrease for relaxing the stability constraints.…”