Article
Automation & Control Systems
Tobias Breiten, Karl Kunisch
Summary: Nonlinear observers based on the minimum energy estimation concept are discussed, with an output injection operator approximated by a neural network. An optimization problem is proposed to learn the network parameters and numerically investigate linear and nonlinear oscillators.
SYSTEMS & CONTROL LETTERS
(2021)
Article
Automation & Control Systems
Keyan Miao, Richard Vinter
Summary: This article discusses an optimal control problem in neo-classical macroeconomics, aiming to maximize expenditure on social programs by balancing investment for growth and consumption. A nonstandard verification technique is introduced and applied to handle singularities caused by fractional singularities, providing a detailed solution and analysis of the problem.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2021)
Article
Computer Science, Artificial Intelligence
Mehdi Mohammadi, Mohammad Mehdi Arefi, Navid Vafamand, Okyay Kaynak
Summary: This paper proposes a novel model-free optimal controller for nonlinear AUVs, utilizing an integral reinforcement learning strategy to address the optimal control problem for completely unknown dynamics, and employs a neural network structure for modeling and control implementation.
NEURAL COMPUTING & APPLICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Bo Xu, Yuan-Xin Li, Zhongsheng Hou, Choon Ki Ahn
Summary: In this paper, a novel approach is proposed to address the event-triggered optimized consensus tracking control problem in a class of uncertain nonlinear multi-agent systems (MASs). An adaptive reinforcement learning algorithm based on the actor-critic architecture and the backstepping method is utilized to optimize control performance. The proposed optimized controller employs a novel event-triggered strategy to dynamically adjust sampling errors online and reduce communication resource usage and computational complexity.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Environmental Sciences
Lu Xiao, Ya Chen, Chaojie Wang, Jun Wang
Summary: This paper discusses the cooperation between asymmetric countries in transboundary pollution control, with a focus on the impact of assistant investments provided by developed countries. The study finds that the provision of assistant investments can reduce common pollution stock and increase economic benefits for both countries by raising equilibrium emission strategies.
ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH
(2022)
Article
Engineering, Mechanical
Guoping Zhang, Quanxin Zhu
Summary: This paper investigates the event-triggered optimal control (ETOC) for nonlinear Ito-type stochastic systems using the adaptive dynamic programming (ADP) approach. The value function of the Hamilton-Jacobi-Bellman (HJB) equation is approximated using critical neural network (CNN), and a new event-triggering scheme is proposed. The Lyapunov direct method is used to prove that the ETOC based on ADP approach guarantees that the CNN weight errors and system states are semi-globally uniformly ultimately bounded in probability.
NONLINEAR DYNAMICS
(2021)
Article
Automation & Control Systems
Javier de Frutos, Julia Novo
Summary: This paper provides error bounds for fully discrete approximations of infinite horizon problems using the dynamic programming approach. The paper revises the error bound of the fully discrete method and proves that, under assumptions similar to the time discrete case, the error of the fully discrete case is O(h+k), giving first order accuracy in time and space for the method. This error bound matches numerical experiments in the literature where the behavior predicted by the O(k/h) bound has not been observed.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Karl Kunisch, Donato Vasquez-Varas
Summary: This article analyzes a learning technique for finite horizon optimal control problems and its approximation based on polynomials, and illustrates the practicality and efficiency of the method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Automation & Control Systems
Lukas Koelsch, Pol Jane Soneira, Albertus Johannes Malan, Soeren Hohmann
Summary: This paper presents an adaptive control strategy for multi-player noncooperative differential games by extending a single-player feedback Nash strategy and using the Hamiltonian of the port-Hamiltonian system. Numerical simulations demonstrate the effectiveness of the proposed control laws.
INTERNATIONAL JOURNAL OF CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Hao-Yang Zhu, Yuan-Xin Li, Shaocheng Tong
Summary: This article investigates the event-triggered optimized tracking control problem for stochastic nonlinear systems based on reinforcement learning (RL). By using an adaptive RL algorithm and a dynamically adjustable event-triggered mechanism, it achieves optimized control while saving network resources and reducing computation burden. The effectiveness of the proposed ETOC algorithm is demonstrated through a simulation example.
IEEE TRANSACTIONS ON FUZZY SYSTEMS
(2023)
Article
Automation & Control Systems
Lina Xia, Qing Li, Ruizhuo Song, Hamidreza Modares
Summary: This paper considers the asymmetric input-constrained optimal synchronization problem of heterogeneous unknown nonlinear multi-agent systems. By performing a state-space transformation and designing a novel distributed observer, the satisfaction of asymmetric input constraints is guaranteed. With the help of a network of augmented systems and a data-based off-policy reinforcement learning algorithm, the constrained Hamilton-Jacobi-Bellman equation is solved. Simulation results demonstrate the correctness and validity of the theoretical results.
IEEE-CAA JOURNAL OF AUTOMATICA SINICA
(2022)
Article
Automation & Control Systems
Hao-Yang Zhu, Yuan-Xin Li, Shaocheng Tong
Summary: This paper proposes a simple and efficient adaptive event-triggered optimized control scheme using reinforcement learning for stochastic nonlinear systems. The scheme includes an online state observer to estimate unmeasured states and a dynamically adjustable event-triggered mechanism that reduces communication resources. The theoretical analysis proves that all closed-loop signals remain bounded under the proposed output-feedback ETOC method.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2023)
Article
Mathematics, Applied
Linlin Tian, Zhaoyang Liu
Summary: This paper investigates the optimal dividend problem for the renewal risk model with phase-type distributed interclaim times and exponentially distributed claim sizes. By proposing an algorithm and analyzing the theoretical properties, the optimal strategy is found, and the optimality of phasewise barrier strategy as well as the convergence of the algorithm is proved.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Mathematics, Applied
Gaofeng Zong
Summary: This paper considers the transition semigroup related to the stochastic Burgers-Huxley equation, which describes the interaction between reaction mechanisms, convection effects, and diffusion transports. It is proved that the transition semigroup possesses a regularizing effect in the Banach space of continuous functions and some estimates on the derivative of the transition semigroup are established. An application in the Hamilton-Jacobi-Bellman equation arising from a stochastic optimal control problem is provided.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Emiliano Cristiani, Arianna De Santo, Marta Menci
Summary: This paper investigates a model for pedestrian flow wherein each individual in the crowd aims to minimize a given cost functional by moving in a known domain. The dynamics of the pedestrians and the cost functional depend on the position of the entire crowd. Pedestrians are assumed to have predictive abilities limited up to a certain time, leading to different modeling assumptions and theoretical questions.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2023)
