A Sparse ADMM-Based Solver for Linear MPC Subject to Terminal Quadratic Constraint

Model predictive control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC, this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal te...

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Bibliographic Details
Published in:IEEE transactions on control systems technology Vol. 32; no. 6; pp. 2376 - 2384
Main Authors: Krupa, Pablo, Jaouani, Rim, Limon, Daniel, Alamo, Teodoro
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Artificial intelligence
Closed loops
Complexity theory
Convex functions
Ellipsoids
Embedded optimization
Embedded systems
Feedback control
model predictive control (MPC)
Optimization
Predictive control
Programming
quadratic constraints
second-order cone (SOC) programming
Slack variables
Solvers
Terminal constraints
Vectors
ISSN:1063-6536, 1558-0865
Online Access:Get full text
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Summary:Model predictive control (MPC) typically includes a terminal constraint to guarantee stability of the closed-loop system under nominal conditions. In linear MPC, this constraint is generally taken on a polyhedral set, leading to a quadratic optimization problem. However, the use of an ellipsoidal terminal constraint may be desirable, leading to an optimization problem with a quadratic constraint. In this case, the optimization problem can be solved using second-order cone (SOC) programming solvers, since the quadratic constraint can be posed as a SOC constraint, at the expense of adding additional slack variables and possibly compromising the simple structure of the solver ingredients. In this brief, we present a sparse solver for linear MPC subject to a terminal ellipsoidal constraint based on the alternating direction method of multipliers (ADMM) algorithm in which we directly deal with the quadratic constraints without having to resort to the use of a SOC constraint nor the inclusion of additional decision variables. The solver is suitable for its use in embedded systems, since it is sparse, has a small memory footprint, and requires no external libraries. We compare its performance against other approaches from the literature.
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ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2024.3386062