Configuration-Constrained Tube Model Predictive Control for Tracking Varying Setpoint References

المفاهيم الأساسية

This paper proposes a novel configuration-constrained tube-based Model Predictive Control (MPC) framework for tracking varying setpoint references with linear systems subject to additive and multiplicative uncertainties.

الملخص

The paper introduces a variant of Configuration-Constrained Tube MPC (CCTMPC) for tracking varying setpoint references. The proposed approach is developed using a tracking MPC formulation, which enables the synthesis of reference tracking controllers that guarantee asymptotic stability for piecewise constant references.
The key highlights are:

The use of configuration-constrained polytopes for parameterizing the Robust Forward Invariant Tubes (RFITs) results in a controller that exhibits superior properties compared to existing rigid-tube and elastic-tube MPC methods for reference tracking. Notably, the need for a robust affine feedback law is eliminated, and the resulting RFITs exhibit an improved representational capability, leading to less conservativeness.

The ability to handle multiplicative uncertainty, coupled with the removal of the requirement for precomputing a terminal set, renders the proposed scheme apt for designing tracking controllers for practical systems that can be represented by linear parameter-varying (LPV) models.

The scheme can seamlessly incorporate model refinement while preserving asymptotic stability, making it well-suited for the development of adaptive MPC schemes.

Theoretical guarantees are provided regarding recursive feasibility in the presence of reference changes, robustness, and stability for piecewise constant references.

The efficacy of the approach is demonstrated through two numerical examples, including an autonomous vehicle lane change maneuver.

الإحصائيات

The paper presents the following key figures and metrics:

The Hausdorff distance between the feasible regions of the proposed CCTMPC controller and the maximal RCI set is 0.0179, compared to 0.2816 for ETMPC and 1.1056 for RTMPC.
The projection of the RFIT along the lateral deviation (ey) and angular deviation (eψ) states for the autonomous vehicle lane change maneuver, showing the reduction in uncertainty as the vehicle moves into the faster lane.

اقتباسات

"The use of configuration-constrained polytopes for parameterizing the RFITs results in a controller that exhibits superior properties compared to [10, 6]. Notably, the need for a robust affine feedback law is eliminated, and the resulting RFITs exhibit an improved representational capability, leading to less conservativeness."
"The ability of our approach to handle multiplicative uncertainty, coupled with the removal of the requirement for precomputing a terminal set, renders it apt for designing tracking controllers for practical systems that can be represented by linear parameter-varying (LPV) models [7]."

الرؤى الأساسية المستخلصة من

Configuration-Constrained Tube MPC for Tracking

by Filippo Bada... في arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.03629.pdf

استفسارات أعمق

How can the proposed CCTMPC framework be extended to handle time-varying references or references with more complex dynamics

The proposed Configuration-Constrained Tube MPC (CCTMPC) framework can be extended to handle time-varying references or references with more complex dynamics by incorporating adaptive mechanisms into the control scheme. One approach is to introduce online optimization techniques that continuously update the RFIT parameters based on the evolving reference signals. This adaptation can be achieved by modifying the terminal cost and constraints in the optimization problem to account for the changing references. By dynamically adjusting the RFITs to track time-varying references, the CCTMPC controller can effectively handle more complex reference trajectories.

What are the potential challenges and trade-offs in implementing the CCTMPC scheme in real-time applications, and how can they be addressed

Implementing the CCTMPC scheme in real-time applications may pose challenges related to computational complexity, especially as the number of optimization variables and constraints increases with the prediction horizon and the dimensionality of the system. To address these challenges, efficient optimization algorithms and high-performance computing resources can be utilized to reduce the computational burden. Additionally, trade-offs between the complexity of the RFITs and the conservativeness of the predictions need to be carefully considered. By optimizing the RFIT parameters judiciously, the conservativeness can be minimized without compromising stability and feasibility. Real-time implementation also requires robustness to disturbances and uncertainties, which can be addressed through appropriate modeling and control design techniques.

What are the theoretical connections between the economic MPC formulation and the tracking MPC formulation presented in this work, and how can they be further explored

Theoretical connections between the economic Model Predictive Control (MPC) formulation and the tracking MPC formulation presented in this work lie in the optimization objectives and constraints. Economic MPC typically aims to minimize a cost function over a finite horizon, considering economic objectives such as energy efficiency or cost optimization. On the other hand, tracking MPC focuses on tracking a reference signal while ensuring stability and feasibility. By exploring the relationship between the cost functions and constraints in both formulations, researchers can potentially develop hybrid MPC schemes that integrate economic considerations with tracking requirements. This integration could lead to more versatile and efficient control strategies that balance performance objectives with tracking accuracy. Further exploration of these connections can enhance the understanding of the interplay between economic optimization and reference tracking in MPC frameworks.