Automatica· 2026Q1
A model predictive control framework with robust stability guarantees under unbounded disturbances
- 2citations
- Q1SCImago
- 2026year
Short summary
A novel model predictive control (MPC) framework relaxes initial state constraints with a penalty, offering input-to-state stability and bounded cumulative constraint violations under unbounded disturbances, outperforming current soft-constrained MPC.
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Key points
- Proposes an MPC framework that penalizes initial state constraint relaxation instead of state constraints.
- Achieves input-to-state stability and bounds cumulative constraint violation for unbounded disturbances.
- Offers near-optimal performance in nominal conditions and outperforms state-of-the-art soft-constrained MPC.
- Reduces to a quadratic program for linear systems with only marginally increased computational complexity.
AI-generated from the title and abstract; the full text is not read.
Abstract
To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state constraint with a penalty. Compared to state-of-the-art soft constrained MPC formulations, the proposed formulation has two key features: (i) input-to-state stability and bounds on the cumulative constraint violation for unbounded disturbances; (ii) close-to-optimal performance under nominal operating conditions. To address unbounded disturbances with compact input constraints, we focus on open-loop stable systems; however, the method applies equally to stabilizable systems when soft input constraints are used. In the special case of linear systems, the proposed MPC formulation reduces to a quadratic program, and the offline design and online computational complexity are only marginally increased compared to a nominal design. Numerical examples demonstrate benefits compared to state-of-the-art soft-constrained MPC formulations.
The authors' abstract, as published at the source. Automatica, 2026 · DOI ↗
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Field: Control and Systems Engineering
Control and Systems EngineeringEngineering