Pub Date : 2025-12-26DOI: 10.1109/LCSYS.2025.3648777
Ilia Nasiriziba;Matthew F. Singh
Controlling complex, nonlinear systems, such as the brain, presents a fundamental challenge that requires simplified models for practical controller design. Traditional approaches often fail when these systems operate far from steady states under noise and changing inputs. Different control strategies drive systems into distinct behavioral regimes, each requiring a specific approximation. Rather than imposing a single approximation, this letter introduces ergodic quasilinearization (EQL), which automatically identifies the appropriate linear model for each operating scenario. EQL generates adaptive linear models whose parameters adjust based on the system’s long-term statistical behavior under varying inputs and noise levels. These statistics are derived analytically from the steady-state equalities, eliminating the need for repeated computation of the full nonlinear dynamics. The effectiveness of EQL is demonstrated on large-scale brain network models, where traditional methods encounter difficulties due to complex nonlinearities and high dimensionality. Conventional linearization methods perform well under fixed conditions but lose accuracy when control strategies change the operating regime. In contrast, EQL maintains accuracy across diverse operating scenarios, supporting robust controller design for systems that rarely reach simple steady states. We demonstrate the power of EQL in predicting brain-model responses to complex stimulation protocols and in identifying an optimal open-loop control for reproducing target brain-activity patterns.
{"title":"Ergodic Quasilinearization and Control for Brain Dynamics","authors":"Ilia Nasiriziba;Matthew F. Singh","doi":"10.1109/LCSYS.2025.3648777","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3648777","url":null,"abstract":"Controlling complex, nonlinear systems, such as the brain, presents a fundamental challenge that requires simplified models for practical controller design. Traditional approaches often fail when these systems operate far from steady states under noise and changing inputs. Different control strategies drive systems into distinct behavioral regimes, each requiring a specific approximation. Rather than imposing a single approximation, this letter introduces ergodic quasilinearization (EQL), which automatically identifies the appropriate linear model for each operating scenario. EQL generates adaptive linear models whose parameters adjust based on the system’s long-term statistical behavior under varying inputs and noise levels. These statistics are derived analytically from the steady-state equalities, eliminating the need for repeated computation of the full nonlinear dynamics. The effectiveness of EQL is demonstrated on large-scale brain network models, where traditional methods encounter difficulties due to complex nonlinearities and high dimensionality. Conventional linearization methods perform well under fixed conditions but lose accuracy when control strategies change the operating regime. In contrast, EQL maintains accuracy across diverse operating scenarios, supporting robust controller design for systems that rarely reach simple steady states. We demonstrate the power of EQL in predicting brain-model responses to complex stimulation protocols and in identifying an optimal open-loop control for reproducing target brain-activity patterns.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3101-3106"},"PeriodicalIF":2.0,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11316337","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-25DOI: 10.1109/LCSYS.2025.3648436
Shima Sadat Mousavi;Xiao Tan;Aaron D. Ames
This letter develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient feasibility conditions under which feasible inputs over the convex hull can be obtained per coordinate, with a common input, or via convex blending. We also describe the associated computational methods, based on interval intersections or an offline linear program (LP). Beyond certifying compatibility, we give conditions under which the quadratic-program (QP) safety filter is affine in the state. This enables explicit implementations via convex combinations of vertex-feasible inputs. Case studies illustrate the results.
{"title":"From Vertices to Convex Hulls: Certifying Set-Wise Compatibility for CBF Constraints","authors":"Shima Sadat Mousavi;Xiao Tan;Aaron D. Ames","doi":"10.1109/LCSYS.2025.3648436","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3648436","url":null,"abstract":"This letter develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient feasibility conditions under which feasible inputs over the convex hull can be obtained per coordinate, with a common input, or via convex blending. We also describe the associated computational methods, based on interval intersections or an offline linear program (LP). Beyond certifying compatibility, we give conditions under which the quadratic-program (QP) safety filter is affine in the state. This enables explicit implementations via convex combinations of vertex-feasible inputs. Case studies illustrate the results.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3011-3016"},"PeriodicalIF":2.0,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-25DOI: 10.1109/LCSYS.2025.3648635
Karthik Elamvazhuthi;Sachin Shivakumar
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that cluster near attractors, resulting in poor coverage of the reachable set. To achieve a more uniform distribution of terminal states, we formulate the problem within an Optimal Transport (OT) framework. In this setting, the goal is to steer the system so that the final state distribution, determined by the chosen controls and initial conditions, matches a desired target distribution. Enforcing this condition exactly is not possible since the reachable set is not known. So we introduce an ${mathrm { L}}_{2}$ -norm based regularization of the terminal distribution that relaxes the constraint while promoting uniform coverage. The resulting formulation can be approximated by a finite-dimensional, particle-based optimal control problem with kernel-coupled terminal cost. We show that this approach converges to the original formulation and demonstrate through a 2D and 6D numerical example that it provides significantly more uniform reachable-set sampling than random control strategies.
{"title":"Uniform Sampling From the Reachable Set Using Optimal Transport","authors":"Karthik Elamvazhuthi;Sachin Shivakumar","doi":"10.1109/LCSYS.2025.3648635","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3648635","url":null,"abstract":"Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that cluster near attractors, resulting in poor coverage of the reachable set. To achieve a more uniform distribution of terminal states, we formulate the problem within an Optimal Transport (OT) framework. In this setting, the goal is to steer the system so that the final state distribution, determined by the chosen controls and initial conditions, matches a desired target distribution. Enforcing this condition exactly is not possible since the reachable set is not known. So we introduce an <inline-formula> <tex-math>${mathrm { L}}_{2}$ </tex-math></inline-formula>-norm based regularization of the terminal distribution that relaxes the constraint while promoting uniform coverage. The resulting formulation can be approximated by a finite-dimensional, particle-based optimal control problem with kernel-coupled terminal cost. We show that this approach converges to the original formulation and demonstrate through a 2D and 6D numerical example that it provides significantly more uniform reachable-set sampling than random control strategies.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3065-3070"},"PeriodicalIF":2.0,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1109/LCSYS.2025.3647842
Liang Wu;Yunhong Che;Richard D. Braatz;Jan Drgona
Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off between certified worst-case and practical average execution times. For example, our previous work (Wu and Braatz 2025) proposed a full-Newton path-following interior-point method (IPM) with data-independent, simple-calculated, and exact $O(sqrt {n})$ iteration complexity, but not as efficient as the heuristic Mehrotra’s predictor–corrector IPM algorithm (which sacrifices global convergence). This letter proposes a new predictor–corrector IPM algorithm that preserves the same certified $O$ ($sqrt {n}$ ) iteration complexity while achieving a $5times $ speedup over (Wu and Braatz 2025). Numerical experiments and codes that validate these results are provided.
在模型预测控制（MPC）等基于实时优化的控制应用中，最小化优化算法的最坏情况和平均执行时间同样至关重要。大多数MPC求解器必须在认证的最坏情况和实际的平均执行时间之间进行权衡。例如，我们之前的工作（Wu和Braatz 2025）提出了一种全牛顿路径跟踪内点法（IPM），具有数据独立，计算简单，精确的$O(sqrt {n})$迭代复杂度，但不如启发式Mehrotra的预测校正IPM算法（牺牲全局收敛性）高效。这封信提出了一种新的预测校正IPM算法，该算法保留了相同的认证$O$ （$sqrt {n}$）迭代复杂度，同时实现了$5times $的加速（Wu and Braatz 2025）。数值实验和代码验证了这些结果。
{"title":"A Time-Certified Predictor-Corrector IPM Algorithm for Box-QP","authors":"Liang Wu;Yunhong Che;Richard D. Braatz;Jan Drgona","doi":"10.1109/LCSYS.2025.3647842","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3647842","url":null,"abstract":"Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off between certified worst-case and practical average execution times. For example, our previous work (Wu and Braatz 2025) proposed a full-Newton path-following interior-point method (IPM) with data-independent, simple-calculated, and exact <inline-formula> <tex-math>$O(sqrt {n})$ </tex-math></inline-formula> iteration complexity, but not as efficient as the heuristic Mehrotra’s predictor–corrector IPM algorithm (which sacrifices global convergence). This letter proposes a new predictor–corrector IPM algorithm that preserves the same certified <inline-formula> <tex-math>$O$ </tex-math></inline-formula>(<inline-formula> <tex-math>$sqrt {n}$ </tex-math></inline-formula>) iteration complexity while achieving a <inline-formula> <tex-math>$5times $ </tex-math></inline-formula> speedup over (Wu and Braatz 2025). Numerical experiments and codes that validate these results are provided.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3059-3064"},"PeriodicalIF":2.0,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1109/LCSYS.2025.3648321
Nahid Binandeh Dehaghani;Rafal Wisniewski;A. Pedro Aguiar
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. A quantum subroutine is incorporated to efficiently solve the Schur complement step using block-encoding and Quantum Singular Value Transformation techniques. We formally analyze the time complexity and convergence behavior under the cumulative effect of quantum errors, establishing local input-to-state stability and convergence to a neighborhood of the stationary point, with explicit error bounds in terms of the barrier parameter and quantum solver accuracy. The proposed framework enables computational complexity to scale polylogarithmically with the system dimension demonstrating the potential of quantum algorithms to enhance classical optimization routines in nonlinear control applications.
{"title":"Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control","authors":"Nahid Binandeh Dehaghani;Rafal Wisniewski;A. Pedro Aguiar","doi":"10.1109/LCSYS.2025.3648321","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3648321","url":null,"abstract":"We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. A quantum subroutine is incorporated to efficiently solve the Schur complement step using block-encoding and Quantum Singular Value Transformation techniques. We formally analyze the time complexity and convergence behavior under the cumulative effect of quantum errors, establishing local input-to-state stability and convergence to a neighborhood of the stationary point, with explicit error bounds in terms of the barrier parameter and quantum solver accuracy. The proposed framework enables computational complexity to scale polylogarithmically with the system dimension demonstrating the potential of quantum algorithms to enhance classical optimization routines in nonlinear control applications.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3005-3010"},"PeriodicalIF":2.0,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1109/LCSYS.2025.3647987
Yu Yang;Andreas Oliveira;Louis L. Whitcomb;Felipe Pait;Mario Sznaier;Noah J. Cowan
The weakly electric fish Eigenmannia virescens naturally swims back and forth to stay within a moving refuge, tracking its motion using visual and electrosensory feedback. Previous experiments show that when the refuge oscillates as a low-frequency sinusoid (below about 0.5 Hz), the tracking is nearly perfect, but phase lag increases and gain decreases at higher frequencies. Here, we model this nonlinear behavior as an adaptive internal model principle (IMP) system. Specifically, an adaptive state estimator identifies the a priori unknown frequency, and feeds this parameter estimate into a closed-loop IMP-based system built around a lightly damped harmonic oscillator. We prove that the closed-loop tracking error of the IMP-based system, where the online adaptive frequency estimate is used as a surrogate for the unknown frequency, converges exponentially to that of an ideal control system with perfect information about the stimulus. Simulations further show that our model reproduces the fish refuge tracking Bode plot across a wide frequency range. These results establish the theoretical validity of combining the IMP with an adaptive identification process and provide a basic framework in adaptive sensorimotor control.
{"title":"Modeling Adaptive Tracking of Predictable Stimuli in Electric Fish","authors":"Yu Yang;Andreas Oliveira;Louis L. Whitcomb;Felipe Pait;Mario Sznaier;Noah J. Cowan","doi":"10.1109/LCSYS.2025.3647987","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3647987","url":null,"abstract":"The weakly electric fish Eigenmannia virescens naturally swims back and forth to stay within a moving refuge, tracking its motion using visual and electrosensory feedback. Previous experiments show that when the refuge oscillates as a low-frequency sinusoid (below about 0.5 Hz), the tracking is nearly perfect, but phase lag increases and gain decreases at higher frequencies. Here, we model this nonlinear behavior as an adaptive internal model principle (IMP) system. Specifically, an adaptive state estimator identifies the a priori unknown frequency, and feeds this parameter estimate into a closed-loop IMP-based system built around a lightly damped harmonic oscillator. We prove that the closed-loop tracking error of the IMP-based system, where the online adaptive frequency estimate is used as a surrogate for the unknown frequency, converges exponentially to that of an ideal control system with perfect information about the stimulus. Simulations further show that our model reproduces the fish refuge tracking Bode plot across a wide frequency range. These results establish the theoretical validity of combining the IMP with an adaptive identification process and provide a basic framework in adaptive sensorimotor control.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3077-3082"},"PeriodicalIF":2.0,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1109/LCSYS.2025.3647981
Margarita A. Guerrero;Braghadeesh Lakshminarayanan;Cristian R. Rojas
Model predictive control is a well established control technology for trajectory tracking. Its use requires the availability of an accurate model of the plant, but obtaining such a model is often time consuming and costly. Data-Enabled Predictive Control (DeePC) addresses this shortcoming in the linear time-invariant setting, by skipping the model building step and instead relying directly on input-output data. Unfortunately, many real systems are nonlinear and exhibit strong operating-point dependence. Building on classical linear parameter-varying control, we introduce DeePC-GS, a gain-scheduled extension of DeePC for unknown, regime-varying systems. The key idea is to allow DeePC to switch between different local Hankel matrices–selected online via a measurable scheduling variable–thereby uniting classical gain scheduling tools with identification-free, data-driven MPC. We test the effectiveness of our DeePC-GS formulation on a nonlinear ship-steering benchmark, demonstrating that it outperforms state-of-the-art data-driven MPC while maintaining tractable computation.
{"title":"Gain-Scheduled Data-Enabled Predictive Control: A DeePC Approach for Nonlinear Systems","authors":"Margarita A. Guerrero;Braghadeesh Lakshminarayanan;Cristian R. Rojas","doi":"10.1109/LCSYS.2025.3647981","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3647981","url":null,"abstract":"Model predictive control is a well established control technology for trajectory tracking. Its use requires the availability of an accurate model of the plant, but obtaining such a model is often time consuming and costly. Data-Enabled Predictive Control (DeePC) addresses this shortcoming in the linear time-invariant setting, by skipping the model building step and instead relying directly on input-output data. Unfortunately, many real systems are nonlinear and exhibit strong operating-point dependence. Building on classical linear parameter-varying control, we introduce DeePC-GS, a gain-scheduled extension of DeePC for unknown, regime-varying systems. The key idea is to allow DeePC to switch between different local Hankel matrices–selected online via a measurable scheduling variable–thereby uniting classical gain scheduling tools with identification-free, data-driven MPC. We test the effectiveness of our DeePC-GS formulation on a nonlinear ship-steering benchmark, demonstrating that it outperforms state-of-the-art data-driven MPC while maintaining tractable computation.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3041-3046"},"PeriodicalIF":2.0,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1109/LCSYS.2025.3647069
Yang Zhao;Elikplim Gah;Sze Zheng Yong
This letter presents an output-feedback tube-based model predictive control (MPC) framework for linear sampled-data control systems subject to external disturbances and non-convex constraints. The proposed approach rigorously incorporates inter-sample reachability analysis to account for the continuous-time evolution of system trajectories between discrete sampling instances and to ensure constraint satisfaction in the continuous time domain. The resulting continuous-time tube-based MPC scheme is demonstrated to ensure that trajectories remain within (potentially non-convex) safe sets throughout the continuous-time evolution.
{"title":"Tube-Based MPC for Uncertain Sampled-Data Control Systems With Inter-Sample Reachability Analysis","authors":"Yang Zhao;Elikplim Gah;Sze Zheng Yong","doi":"10.1109/LCSYS.2025.3647069","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3647069","url":null,"abstract":"This letter presents an output-feedback tube-based model predictive control (MPC) framework for linear sampled-data control systems subject to external disturbances and non-convex constraints. The proposed approach rigorously incorporates inter-sample reachability analysis to account for the continuous-time evolution of system trajectories between discrete sampling instances and to ensure constraint satisfaction in the continuous time domain. The resulting continuous-time tube-based MPC scheme is demonstrated to ensure that trajectories remain within (potentially non-convex) safe sets throughout the continuous-time evolution.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3047-3052"},"PeriodicalIF":2.0,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1109/LCSYS.2025.3646686
Siqi Du;Heling Zhang;Roy Dong
Classical data-driven methods can be conceptualized as mappings from data distributions to decisions. However, in practice, decisions can influence the data distributions themselves. One of the common methods for handling unknown decision-dependent distribution shift is repeated optimization. In this letter, we model repeated optimization as a discrete-time feedback interconnection system. Our framework enables convergence analysis based on dissipation inequalities and integral quadratic constraints, which provides a novel method to show convergence under unknown decision-dependent distribution shift. We bound the suboptimality when using repeated gradient descent and ignoring the distribution shift when taking gradient steps. Additionally, our framework provides a method to bound the distance between performatively stable points and performatively optimal points.
{"title":"Convergence Analysis of Repeated Optimization in Performative Prediction","authors":"Siqi Du;Heling Zhang;Roy Dong","doi":"10.1109/LCSYS.2025.3646686","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3646686","url":null,"abstract":"Classical data-driven methods can be conceptualized as mappings from data distributions to decisions. However, in practice, decisions can influence the data distributions themselves. One of the common methods for handling unknown decision-dependent distribution shift is repeated optimization. In this letter, we model repeated optimization as a discrete-time feedback interconnection system. Our framework enables convergence analysis based on dissipation inequalities and integral quadratic constraints, which provides a novel method to show convergence under unknown decision-dependent distribution shift. We bound the suboptimality when using repeated gradient descent and ignoring the distribution shift when taking gradient steps. Additionally, our framework provides a method to bound the distance between performatively stable points and performatively optimal points.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"2999-3004"},"PeriodicalIF":2.0,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1109/LCSYS.2025.3646701
Erik I. Verriest
Geometric insight may lead to a quick solution for a class of non-LQ optimal control problems. We illustrate this with a simple, inconspicuous-looking example. While necessary conditions for optimality are easily obtained, their analytic solution may not be easy. But some problems are locally reducible to an Euclidean distance problem, but not necessarily globally due to the underlying topology. This insight leads to the additional realization that in some cases, optimality may require impulsive inputs. However, Dirac deltas cannot be compatible with nonlinear operations in Schwartz’s distribution theory. Thus, it seems that we may have a solution but not a theory. Since the solution is transparent in its geometric form, it suggests that another approach to generalized functions, as proposed by Colombeau, should be used. This is very valuable as it corroborates our earlier work. Generalizations are then sought for other problems reducible to Euclidean minimum distance problems, and even more general Riemannian spaces. We make some connections with the notion of persistence of behavior, where these results apply.
{"title":"Geometric Insight in Solving Optimal Control Problems and the Emergence of Generalized Functions","authors":"Erik I. Verriest","doi":"10.1109/LCSYS.2025.3646701","DOIUrl":"https://doi.org/10.1109/LCSYS.2025.3646701","url":null,"abstract":"Geometric insight may lead to a quick solution for a class of non-LQ optimal control problems. We illustrate this with a simple, inconspicuous-looking example. While necessary conditions for optimality are easily obtained, their analytic solution may not be easy. But some problems are locally reducible to an Euclidean distance problem, but not necessarily globally due to the underlying topology. This insight leads to the additional realization that in some cases, optimality may require impulsive inputs. However, Dirac deltas cannot be compatible with nonlinear operations in Schwartz’s distribution theory. Thus, it seems that we may have a solution but not a theory. Since the solution is transparent in its geometric form, it suggests that another approach to generalized functions, as proposed by Colombeau, should be used. This is very valuable as it corroborates our earlier work. Generalizations are then sought for other problems reducible to Euclidean minimum distance problems, and even more general Riemannian spaces. We make some connections with the notion of persistence of behavior, where these results apply.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"9 ","pages":"3053-3058"},"PeriodicalIF":2.0,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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