Stabilizing Model Predictive Control without Terminal Constraints for Switched Nonlinear Systems

Knüfer, Sven; Müller, Matthias A.; Allgöwer, Frank

doi:10.1016/j.ifacol.2016.10.141

Cited by 13 publications

(6 citation statements)

References 10 publications

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“…Theoretical studies on switched MPCs have been actively conducted since the 2000s [26]. The prediction model [27] and cost function [28] can be switched to improve performance and reduce computational complexity depending on the situation. However, ensuring stability, robustness, and persistent feasibility is difficult.…”

Section: Smooth Transition Between Mpcs Using Intermediate‐mpcmentioning

confidence: 99%

Connection of nonlinear model predictive controllers for smooth task switching in autonomous driving

Honda

Okuda

Suzuki

et al. 2022

Asian Journal of Control

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Motion planning, decision making, and control are vital functions in autonomous driving for accomplishing the desired driving task while considering passenger comfort, road infrastructure, and surrounding traffic participants. Model predictive control (MPC) is a promising method for simultaneously realizing these functions. However, formulating a single MPC that can run through all driving scenarios is difficult, and previous research has often been conducted to design an MPC for a specific driving task. To extend the availability of MPC for all driving tasks, smooth switching between different MPCs designed for each driving task must be addressed. One of the difficulties in switching between MPCs is guiding the state to a feasible set of optimization problems after switching. In this paper, we present a new framework to realize the smooth connection of MPCs, that is, to reduce the optimization infeasibility at the time of MPC switching. In our proposed method, two general nonlinear MPCs with different state spaces, cost functions, constraints, and formulations can be systematically switched via automatically generated intermediate‐MPCs without requiring any particular alterations. This can help reduce the system complexity of the hybrid MPC system.

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Section: Smooth Transition Between Mpcs Using Intermediate‐mpcmentioning

confidence: 99%

Connection of nonlinear model predictive controllers for smooth task switching in autonomous driving

Honda

Okuda

Suzuki

et al. 2022

Asian Journal of Control

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“…Equation 12provides an additive bound on the change of the optimal value functions at the same state when a switch takes place. Note that the main difference between (9) and (12) is that the right hand side of the latter does not depend on the optimization of two different controllers, but on the fixed value of the current state. In view of (12), the following result holds.…”

Section: A Mdt For Stabilizing Switchingmentioning

confidence: 99%

“…First of all note that (12) puts a finite bound on the increase of the optimal value function produced by a switch at any given state. Secondly, from (12) and algebraic manipulation of (3) and (4) it follows that…”

Section: A Mdt For Stabilizing Switchingmentioning

confidence: 99%

“…The bound in (12), however explicit, might lead to unnecessary conservativeness given that at any switching time t k there is only one MPC controller active. An alternative is to compare the corresponding optimal value functions at dynamically adjacent states.…”

Section: A Mdt For Stabilizing Switchingmentioning

confidence: 99%

“…A conceptually different technique is presented in [11], [12], where Lyapunov functions of neighbouring modes are compared in order B. Hernandez Vicente is supported by the Chilean Ministry of Education (CONICYT PFCHA/Concurso para Beca de Doctorado en el Extranjero -72150125).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Switching Tube-Based MPC: Characterization of Minimum Dwell-Time for Feasible and Robustly Stable Switching

Vicente

Trodden

2019

IEEE Trans. Automat. Contr.

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Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

Zamani

Bolandi

2023

Asian Journal of Control

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This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete‐time nonlinear systems capable to deal with changing setpoints and unknown non‐additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non‐additive non‐slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed‐loop input‐to‐state stability and recursive feasibility of the optimization problem for any piece‐wise constant setpoint and non‐additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.

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Stabilizing Model Predictive Control without Terminal Constraints for Switched Nonlinear Systems

Cited by 13 publications

References 10 publications

Connection of nonlinear model predictive controllers for smooth task switching in autonomous driving

Connection of nonlinear model predictive controllers for smooth task switching in autonomous driving

Switching Tube-Based MPC: Characterization of Minimum Dwell-Time for Feasible and Robustly Stable Switching

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non‐additive unknown disturbance

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