Pub Date : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112782
Liwei An , Can Zhao , Guang-Hong Yang
This paper studies the problem of adaptive tracking control for nonlinear strict-feedback systems with parametric uncertainties and safety constraints. A co-design strategy of control barrier functions (CBFs) and barrier Lyapunov functions (BLFs) is proposed, which inherits the robustness and stability of traditional adaptive backstepping controllers. First, a safe virtual control signal is generated by the CBF-induced quadratic programming (QP), which is the suboptimal and smooth solution of the QP with a shifting function. Then, a BLF-based backstepping controller is designed by following the safe virtual control signal. It is shown that the co-design can minimize the damage to the original tracking performance on the premise of safety guarantees. The distinguishing point of the safety design over the existing results is to avoid constructing the high-order CBFs that lead to conservative feasible sets of inputs for ensuring high-relative-degree safety constraints. The simulation results show that the proposed scheme achieves better tracking performance compared with the existing high-order CBF-based method.
{"title":"CBF-based safety design for adaptive control of uncertain nonlinear strict-feedback systems","authors":"Liwei An , Can Zhao , Guang-Hong Yang","doi":"10.1016/j.automatica.2025.112782","DOIUrl":"10.1016/j.automatica.2025.112782","url":null,"abstract":"<div><div>This paper studies the problem of adaptive tracking control for nonlinear strict-feedback systems with parametric uncertainties and safety constraints. A co-design strategy of control barrier functions (CBFs) and barrier Lyapunov functions (BLFs) is proposed, which inherits the robustness and stability of traditional adaptive backstepping controllers. First, a safe virtual control signal is generated by the CBF-induced quadratic programming (QP), which is the suboptimal and smooth solution of the QP with a shifting function. Then, a BLF-based backstepping controller is designed by following the safe virtual control signal. It is shown that the co-design can minimize the damage to the original tracking performance on the premise of safety guarantees. The distinguishing point of the safety design over the existing results is to avoid constructing the high-order CBFs that lead to conservative feasible sets of inputs for ensuring high-relative-degree safety constraints. The simulation results show that the proposed scheme achieves better tracking performance compared with the existing high-order CBF-based method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112782"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-16DOI: 10.1016/j.automatica.2025.112754
Efstratios Stratoglou , Alexandre Anahory Simoes , Anthony Bloch , Leonardo J. Colombo
Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution associated with an affine connection mechanical control system. A Riemannian homogeneous space is, a Riemannian manifold that looks the same everywhere, as you move through it by the action of a Lie group. These Riemannian manifolds are not necessarily Lie groups themselves, but nonetheless possess certain symmetries and invariances that allow for similar results to be obtained. In this work, we introduce the notion of virtual constraint on Riemannian homogeneous spaces in a geometric framework which is a generalization of the classical controlled invariant distribution setting and we show the existence and uniqueness of a control law preserving the invariant distribution. Moreover we characterize the closed-loop dynamics obtained using the unique control law in terms of an affine connection. We illustrate the theory with new examples of nonholonomic control systems inspired by robotics applications.
{"title":"Nonholonomic mechanics and virtual constraints on Riemannian homogeneous spaces","authors":"Efstratios Stratoglou , Alexandre Anahory Simoes , Anthony Bloch , Leonardo J. Colombo","doi":"10.1016/j.automatica.2025.112754","DOIUrl":"10.1016/j.automatica.2025.112754","url":null,"abstract":"<div><div>Nonholonomic systems are, so to speak, mechanical systems with a prescribed restriction on the velocities. A virtual nonholonomic constraint is a controlled invariant distribution associated with an affine connection mechanical control system. A Riemannian homogeneous space is, a Riemannian manifold that looks the same everywhere, as you move through it by the action of a Lie group. These Riemannian manifolds are not necessarily Lie groups themselves, but nonetheless possess certain symmetries and invariances that allow for similar results to be obtained. In this work, we introduce the notion of virtual constraint on Riemannian homogeneous spaces in a geometric framework which is a generalization of the classical controlled invariant distribution setting and we show the existence and uniqueness of a control law preserving the invariant distribution. Moreover we characterize the closed-loop dynamics obtained using the unique control law in terms of an affine connection. We illustrate the theory with new examples of nonholonomic control systems inspired by robotics applications.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112754"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112758
Kaiyun Xie , Junlin Xiong
This paper investigates the existence and computability of the stationary Stackelberg equilibrium (SSE) in two-person zero-sum stochastic Stackelberg games (SSGs). First, an operator-based approach is developed to illustrate that such games admit a fixed-point equilibrium (FPE). It is further proven that the FPE strategy pair constitutes an SSE. Building on this foundation, a value iteration (VI) algorithm is proposed to compute the SSE strategies. However, due to the curse of dimensionality, the exact computation of SSE strategies involves high computational complexity. To address this issue, an -sacrifice strategy is introduced to approximate the leader’s SSE strategy by performing finite iterations, with the degree of approximation quantified by . The relationship between and the number of iterations is established, ensuring a trade-off between computational efficiency and strategic performance. An information flow control example demonstrates the efficiency of the designed strategies.
{"title":"Stationary Stackelberg equilibrium in two-person zero-sum stochastic Stackelberg games","authors":"Kaiyun Xie , Junlin Xiong","doi":"10.1016/j.automatica.2025.112758","DOIUrl":"10.1016/j.automatica.2025.112758","url":null,"abstract":"<div><div>This paper investigates the existence and computability of the stationary Stackelberg equilibrium (SSE) in two-person zero-sum stochastic Stackelberg games (SSGs). First, an operator-based approach is developed to illustrate that such games admit a fixed-point equilibrium (FPE). It is further proven that the FPE strategy pair constitutes an SSE. Building on this foundation, a value iteration (VI) algorithm is proposed to compute the SSE strategies. However, due to the curse of dimensionality, the exact computation of SSE strategies involves high computational complexity. To address this issue, an <span><math><mi>ϵ</mi></math></span>-sacrifice strategy is introduced to approximate the leader’s SSE strategy by performing finite iterations, with the degree of approximation quantified by <span><math><mi>ϵ</mi></math></span>. The relationship between <span><math><mi>ϵ</mi></math></span> and the number of iterations <span><math><mi>n</mi></math></span> is established, ensuring a trade-off between computational efficiency and strategic performance. An information flow control example demonstrates the efficiency of the designed strategies.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112758"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112794
Ming Li , Zhaojian Wang , Mengshuo Jia , Feng Liu , Bo Yang , Xinping Guan
In this paper, we propose a distributed feedback controller to steer a multi-agent dynamical system to the generalized Nash equilibrium (GNE) for an aggregative game with only a monotone pseudo-gradient. First, a monotone aggregative game among the agents is formulated, which considers operational constraints in both the transient process and the steady state. Then, a distributed controller based on primal–dual gradient dynamics is designed for each agent to steer the system to track the GNE of the predefined game autonomously. The controller relaxes the requirement of the strictly/strongly monotone pseudo-gradient. At the same time, the hard limits of the control input are satisfied both at equilibrium and during the transient process. We further prove that the closed-loop system is asymptotically stable and its equilibrium attains the GNE. Finally, a practical example of frequency control on IEEE 68-bus system verifies the effectiveness of the proposed method.
{"title":"Distributed control to steer dynamical systems to the generalized Nash equilibria for monotone aggregative games with operational constraints","authors":"Ming Li , Zhaojian Wang , Mengshuo Jia , Feng Liu , Bo Yang , Xinping Guan","doi":"10.1016/j.automatica.2025.112794","DOIUrl":"10.1016/j.automatica.2025.112794","url":null,"abstract":"<div><div>In this paper, we propose a distributed feedback controller to steer a multi-agent dynamical system to the generalized Nash equilibrium (GNE) for an aggregative game with only a monotone pseudo-gradient. First, a monotone aggregative game among the agents is formulated, which considers operational constraints in both the transient process and the steady state. Then, a distributed controller based on primal–dual gradient dynamics is designed for each agent to steer the system to track the GNE of the predefined game autonomously. The controller relaxes the requirement of the strictly/strongly monotone pseudo-gradient. At the same time, the hard limits of the control input are satisfied both at equilibrium and during the transient process. We further prove that the closed-loop system is asymptotically stable and its equilibrium attains the GNE. Finally, a practical example of frequency control on IEEE 68-bus system verifies the effectiveness of the proposed method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112794"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-23DOI: 10.1016/j.automatica.2025.112760
Reza Samsami, Mohammad Mehdi Arefi
This paper introduces a novel policy iteration (PI) reinforcement learning (RL) technique for a hierarchical Stackelberg dynamic game for a class of continuous-time nonlinear dynamical systems including one-leader-multi-followers that concurrently handles both zero-sum (ZS) and nonzero-sum (NZS) games in the game model. At first, the leader makes decisions to learn optimal strategies of all followers. Meanwhile, each follower independently reacts optimally to the leader’s strategy by playing a Nash game with followers and a ZS game with the disturbances simultaneously. To overcome the difficulty of solving the Hamilton–Jacobi (HJ) equation resulting from this hierarchical game, and consequently finding the multiplayer Stackelberg–Nash-saddle (MSNS) equilibrium solution of the game, an adaptive dynamic programming (ADP) algorithm that employs neural network (NN) is developed. An actor-critic NNs framework is presented to solve HJ equations by estimating value functions, control policies, and disturbances. To obtain the leader’s optimal strategy, an optimal adaptive control method using NN is proposed. The convergence of NN weights and the states of the closed-loop optimal system are shown to be uniformly ultimately bounded (UUB). Finally, an example is provided to show the effectiveness of the proposed algorithm in solving the MSNS equilibrium solution with input constraints.
{"title":"Robust reinforcement learning-based controller for a class of nonlinear multiplayer Stackelberg game with input constraints","authors":"Reza Samsami, Mohammad Mehdi Arefi","doi":"10.1016/j.automatica.2025.112760","DOIUrl":"10.1016/j.automatica.2025.112760","url":null,"abstract":"<div><div>This paper introduces a novel policy iteration (PI) reinforcement learning (RL) technique for a hierarchical Stackelberg dynamic game for a class of continuous-time nonlinear dynamical systems including one-leader-multi-followers that concurrently handles both zero-sum (ZS) and nonzero-sum (NZS) games in the game model. At first, the leader makes decisions to learn optimal strategies of all followers. Meanwhile, each follower independently reacts optimally to the leader’s strategy by playing a Nash game with followers and a ZS game with the disturbances simultaneously. To overcome the difficulty of solving the Hamilton–Jacobi (HJ) equation resulting from this hierarchical game, and consequently finding the multiplayer Stackelberg–Nash-saddle (MSNS) equilibrium solution of the game, an adaptive dynamic programming (ADP) algorithm that employs neural network (NN) is developed. An actor-critic NNs framework is presented to solve HJ equations by estimating value functions, control policies, and disturbances. To obtain the leader’s optimal strategy, an optimal adaptive control method using NN is proposed. The convergence of NN weights and the states of the closed-loop optimal system are shown to be uniformly ultimately bounded (UUB). Finally, an example is provided to show the effectiveness of the proposed algorithm in solving the MSNS equilibrium solution with input constraints.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112760"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-12-24DOI: 10.1016/j.automatica.2025.112761
Licheng Wang , Zidong Wang
This paper investigates the event-based probability guaranteed tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.
{"title":"Event-based probability-guaranteed tracking control with amplify-and-forward relay schemes","authors":"Licheng Wang , Zidong Wang","doi":"10.1016/j.automatica.2025.112761","DOIUrl":"10.1016/j.automatica.2025.112761","url":null,"abstract":"<div><div>This paper investigates the event-based probability guaranteed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> tracking control problem for a class of discrete-time systems with a relay-aided communication scheme. The uncertainties of the system matrices are taken into account, which is described by mutually independent uniformly distributed random variables. An adaptive event-triggering scheme is introduced during the signal exchange from the sensor to the relay where the triggering threshold is dynamically regulated. Moreover, an amplify-to-forward relay is employed to improve the communication quality between the sensor and the controller. With the help of the Lyapunov stability theory, sufficient conditions are established to guarantee that the tracking error dynamics achieves the asymptotical stability and the <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance with probability constraints. The desired controller parameters are derived by means of the solution to certain optimization problem subject to matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the developed tracking control scheme.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112761"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145822795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a network of agents, we say that the agents achieve a -agreement when their state variables converge to a point that corresponds to the projection of the agents’ states onto a -dimensional linear subspace. The -agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in -agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed -dimensional subspace through local coordination algorithms. We show that achieving -agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve -agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for -agreement, deriving insights into the relationship between the subspace dimension and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.
{"title":"The role of network connectivity in distributed k-agreement protocols","authors":"Gianluca Bianchin , Miguel Vaquero , Jorge Cortés , Emiliano Dall’Anese","doi":"10.1016/j.automatica.2025.112753","DOIUrl":"10.1016/j.automatica.2025.112753","url":null,"abstract":"<div><div>Given a network of agents, we say that the agents achieve a <span><math><mi>k</mi></math></span>-<em>agreement</em> when their state variables converge to a point that corresponds to the projection of the agents’ states onto a <span><math><mi>k</mi></math></span>-dimensional linear subspace. The <span><math><mi>k</mi></math></span>-agreement problem generalizes the classical consensus problem; unlike in consensus, where the agents’ states must asymptotically coincide, in <span><math><mi>k</mi></math></span>-agreement the agents reach an agreement in a generalized sense (within a linear subspace, where the states do not necessarily coincide). In this paper, we investigate which interaction topologies enable a network of agents to reach an agreement on a prescribed <span><math><mi>k</mi></math></span>-dimensional subspace through local coordination algorithms. We show that achieving <span><math><mi>k</mi></math></span>-agreement requires communication over highly connected graphs; specifically, the number of edges in the interaction graph must grow linearly with the dimension <span><math><mi>k</mi></math></span> of the agreement subspace. Our characterization reveals that the presence of cycles in the communication graph (particularly, independent families of cycles) constitutes the fundamental structural feature enabling the agents to achieve <span><math><mi>k</mi></math></span>-agreement. We also investigate the use of common graph topologies, such as path and circulant graphs, for <span><math><mi>k</mi></math></span>-agreement, deriving insights into the relationship between the subspace dimension <span><math><mi>k</mi></math></span> and the required network connectivity. The effectiveness of the proposed framework is demonstrated through simulations in robotic formation control problems.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112753"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-08DOI: 10.1016/j.automatica.2026.112822
Renshuo Cheng, Chengpu Yu, Yao Li
This paper studies the inverse optimal control for discrete-time finite-horizon linear quadratic tracking with unknown target states. Due to the time-varying feedback policies caused by the finite-horizon setting and the unknown system dynamics, the concerned inverse optimal control becomes challenging. To deal with it, a novel data driven inverse identification approach is developed, for which the corresponding identifiability conditions are provided and the statistical consistency is analyzed in the presence of observation noise. Compared to the existing solutions, the proposed approach requires only optimal trajectories, possibly corrupted by additive observation noise with zero mean and bounded covariance, and achieves consistent results without knowledge of the noise covariance. Finally, simulation examples are presented to show the effectiveness of the proposed approach.
{"title":"Data-driven inverse optimal control for linear quadratic tracking with unknown target states","authors":"Renshuo Cheng, Chengpu Yu, Yao Li","doi":"10.1016/j.automatica.2026.112822","DOIUrl":"10.1016/j.automatica.2026.112822","url":null,"abstract":"<div><div>This paper studies the inverse optimal control for discrete-time finite-horizon linear quadratic tracking with unknown target states. Due to the time-varying feedback policies caused by the finite-horizon setting and the unknown system dynamics, the concerned inverse optimal control becomes challenging. To deal with it, a novel data driven inverse identification approach is developed, for which the corresponding identifiability conditions are provided and the statistical consistency is analyzed in the presence of observation noise. Compared to the existing solutions, the proposed approach requires only optimal trajectories, possibly corrupted by additive observation noise with zero mean and bounded covariance, and achieves consistent results without knowledge of the noise covariance. Finally, simulation examples are presented to show the effectiveness of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112822"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-09DOI: 10.1016/j.automatica.2026.112821
Ruiqing Zhang, Huaiyuan Jiang, Bin Zhou
In this paper, a bias-policy iteration (Bias-PI) method is proposed to relax the requirement of the policy iteration method on the initial admissible control and achieve optimal control for unknown continuous-time nonlinear systems. First, a model-based Bias-PI method is introduced that uses a bias value function to ease the constraints of the initial admissible control. The boundedness of the bias value function and the convergence of the algorithm are demonstrated through rigorous mathematical proofs. Further, the data-driven implementation of the Bias-PI method is detailed, highlighting its ability to learn an optimal controller without prior system information, and simultaneously retaining the fast convergence properties of the traditional policy iteration algorithm. The effectiveness of the data-driven Bias-PI method is illustrated through two simulation examples.
{"title":"Adaptive dynamic programming for unknown continuous-time nonlinear systems via bias-policy iteration","authors":"Ruiqing Zhang, Huaiyuan Jiang, Bin Zhou","doi":"10.1016/j.automatica.2026.112821","DOIUrl":"10.1016/j.automatica.2026.112821","url":null,"abstract":"<div><div>In this paper, a bias-policy iteration (Bias-PI) method is proposed to relax the requirement of the policy iteration method on the initial admissible control and achieve optimal control for unknown continuous-time nonlinear systems. First, a model-based Bias-PI method is introduced that uses a bias value function to ease the constraints of the initial admissible control. The boundedness of the bias value function and the convergence of the algorithm are demonstrated through rigorous mathematical proofs. Further, the data-driven implementation of the Bias-PI method is detailed, highlighting its ability to learn an optimal controller without prior system information, and simultaneously retaining the fast convergence properties of the traditional policy iteration algorithm. The effectiveness of the data-driven Bias-PI method is illustrated through two simulation examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112821"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-09DOI: 10.1016/j.automatica.2026.112824
Na Li , Lei Zou , Jiayue Sun , Derui Ding
The federated-filtering-based (FFB) fusion estimation problem is investigated in this paper for networked multi-rate systems, where the measurement signals are transmitted over a wireless network with limited transmission power. A probabilistic quantization mechanism is introduced to handle the raw measurement signals for the purpose of facilitating digital communication over network. Certain transmission models are proposed to describe the behaviors under the effects of multi-rate dynamics, probabilistic quantization and limited transmission power. A delicately designed FFB fusion scheme is proposed to acquire the desired state estimates, where the local filters will receive feedback from the fusion center to reset their estimates. The parameters for the local filters are calculated by recursively minimizing their upper-bounds for the estimation error covariances. Furthermore, new conditions have been derived to analyze the ultimately boundedness of the estimation error covariance for the fusion center. Subsequently, a power allocation strategy is designed by minimizing such ultimate bound subject to the given transmission power constraint. Finally, the effectiveness of the proposed fusion estimation strategy and its optimal power allocation scheme is verified through a simulation example.
{"title":"Fusion estimation for multi-rate systems with probabilistic quantization and transmission power constraints: A federated-filtering-based method","authors":"Na Li , Lei Zou , Jiayue Sun , Derui Ding","doi":"10.1016/j.automatica.2026.112824","DOIUrl":"10.1016/j.automatica.2026.112824","url":null,"abstract":"<div><div>The federated-filtering-based (FFB) fusion estimation problem is investigated in this paper for networked multi-rate systems, where the measurement signals are transmitted over a wireless network with limited transmission power. A probabilistic quantization mechanism is introduced to handle the raw measurement signals for the purpose of facilitating digital communication over network. Certain transmission models are proposed to describe the behaviors under the effects of multi-rate dynamics, probabilistic quantization and limited transmission power. A delicately designed FFB fusion scheme is proposed to acquire the desired state estimates, where the local filters will receive feedback from the fusion center to reset their estimates. The parameters for the local filters are calculated by recursively minimizing their upper-bounds for the estimation error covariances. Furthermore, new conditions have been derived to analyze the ultimately boundedness of the estimation error covariance for the fusion center. Subsequently, a power allocation strategy is designed by minimizing such ultimate bound subject to the given transmission power constraint. Finally, the effectiveness of the proposed fusion estimation strategy and its optimal power allocation scheme is verified through a simulation example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112824"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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