arXiv subjects

Steven J. Kuntz

Publications and source records attributed to Steven J. Kuntz.

4 recordsLinked to original sources

arXiv2026

Background results for robust minmax control of linear dynamical systems

The purpose of this note is to summarize the arguments required to derive the results appearing in robust minmax control of linear dynamical systems using a quadratic stage cost. The main result required in robust minmax control is Proposition 20.a. Moreover, the solution to the trust-region problem given in Proposition 15 and Lemma 16 may be of more general interest. This note has been revised twice. The second version corrected the optimal u and w formulas and combined several results; this third version corrects two typos in the state- ment of Proposition 20.a and adds Lemma 19 and Proposition 21. Theorem numbering is stable across all three versions. The appendix lists the changes in detail. The authors acknowledge Claude (Anthropic), which reviewed the second version line by line, checked the matrix identities numerically, and drafted the corrections listed in the appendix.

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arXiv2025

Maximum Likelihood Identification of Linear Models with Integrating Disturbances for Offset-Free Control

This report addresses the maximum likelihood identification of models for offset-free model predictive control, where linear time-invariant models are augmented with (fictitious) uncontrollable integrating modes, called integrating disturbances. The states and disturbances are typically estimated with a Kalman filter. The disturbance estimates effectively provide integral control, so the quality of the disturbance model (and resulting filter) directly influences the control performance. We implement eigenvalue constraints to protect against undesirable filter behavior (unstable or marginally stable modes, high-frequency oscillations). Specifically, we consider the class of linear matrix inequality (LMI) regions for eigenvalue constraints. These LMI regions are open sets by default, so we introduce a barrier function method to create tightened, but closed, eigenvalue constraints. To solve the resulting nonlinear semidefinite program, we approximate it as a nonlinear program using a Cholesky factorization method that exploits known sparsity structures of semidefinite optimization variables and matrix inequalities. The algorithm is applied to real-world data taken from two physical systems: a low-cost benchmark temperature microcontroller suitable for classroom laboratories, and an industrial-scale chemical reactor at Eastman Chemical's plant in Kingsport, TN.

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arXiv2025

Offset-free model predictive control: stability under plant-model mismatch

We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples.

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arXiv2025

Beyond inherent robustness: strong stability of MPC despite plant-model mismatch

In this technical report, we establish the asymptotic stability of MPC under plant-model mismatch for problems where the origin remains a steady state despite mismatch. This class of problems includes, but is not limited to, inventory management, path-planning, and control of systems in deviation variables. Our results differ from prior results on the inherent robustness of MPC, which guarantee only convergence to a neighborhood of the origin, the size of which scales with the magnitude of the mismatch. For MPC with quadratic costs, continuous differentiability of the system dynamics is sufficient to demonstrate exponential stability of the closed-loop system despite mismatch. For MPC with general costs, a joint comparison function bound and scaling condition guarantee asymptotic stability despite mismatch. The results are illustrated in numerical simulations, including the classic upright pendulum problem. The tools developed to establish these results can address the stability of offset-free MPC, an open and interesting question in the MPC research literature.

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