This work introduces a fixed-time adaptive fault-tolerant control approach to tackle the trajectory tracking issues in wheeled mobile robots by accounting for unknown dead zones and actuator faults. Firstly, by introducing smoothing functions, bounded estimates, and adaptive parameters, combined with a fixed-time control strategy, actuator faults and the impacts of unknown dead zones are effectively eliminated. Second, an adaptive fault-tolerant control strategy for nonlinear wheeled mobile robot systems is developed. Subsequently, a fixed-time trajectory tracking controller is designed to guarantee system stability and achieve high-precision control for wheeled mobile robots. Furthermore, leveraging the principles of Lyapunov stability theory, this work rigorously establishes the convergence properties of the controller, offering a robust theoretical foundation for ensuring the precision and reliability of trajectory tracking. Finally, the proposed control strategy’s effectiveness and feasibility are validated through simulation outcomes.

This paper presents event-triggered integral re-inforcement learning methods to solve nonlinear nonzero-sum differential game problems. Firstly, for nonlinear systems, by constructing coupled Hamilton-Jacobi equations, the theoretical basis for solving multi-player nonzero-sum game problems is established. With the help of integral reinforcement learning, the approximate optimal control strategy corresponding to each player can be obtained without knowing the drift dynamics of the system. Then, the event-triggered mechanism with preliminary operation is constructed by designing appropriate triggering condition. The dynamic triggering mechanism is further integrated into the algorithm architecture of online learning method to realize aperiodic adaptive learning and sampling control, and effectively save system computing and communication resources. Finally, the effectiveness of the proposed reinforcement learning method is verified by theory analyses and simulation experiments.

In this article, the optimal control strategy for organism is investigated by using the adaptive dynamic programming (ADP) method under the architecture of nonzero-sum games (NZSGs). First, a tumor model is established to formulate the interaction relationships among normal cells, tumor cells, endothelial cells, and the concentrations of drugs. Then, the ADP-based method of single-critic network architecture is proposed to approximate the coupled Hamilton-Jacobi equations (HJEs) under the medicine dosage regulation mechanism (MDRM). According to the game theory, the approximate MDRM-based optimal strategy can be derived, which is of great practical significance. Owing to the proposed mechanism, the dosages of the chemotherapy and anti-angiogenic drugs can be regulated timely and necessarily. Furthermore, the stability of the closed-loop system with the obtained strategy is analyzed via the Lyapunov theory. Finally, a simulation experiment is conducted to verify the effectiveness of the proposed method.

This article focuses on the Pareto optimal issues of nonlinear game systems with asymmetric input saturation under dynamic event-triggered mechanism (DETM). First, the safe control is guaranteed by transforming the system with safety constraints into the one without state constraints utilizing barrier function. The united cost function integrating nonquadratic utility function is constructed to provide the foundation to achieve the Pareto optimal solutions. Then, the adaptive dynamic programming method with concurrent learning is proposed to approximate the Pareto optimal strategies wherein both current and historical data are utilized. To further lessen the consumptions of computation/communication resources, the DETM is integrated into the adaptive algorithm framework which can avoid Zeno phenomena. All the signals of the closed-loop system are proved to be uniformly ultimately bounded. Finally, the simulation results are given to validate the effectiveness of the proposed method from several aspects.

In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn x = (x₁,…,x_n) ∈ {0,1}ⁿ from a stream of random linear equations over 𝔽₂ that are correct with probability 1/2+ε and flipped with probability 1/2-ε (0 < ε < 1/2), that any learning algorithm requires either a memory of size Ω(n²/ε) or an exponential number of samples. In fact, we study memory-sample lower bounds for a large class of learning problems, as characterized by [Garg et al., 2018], when the samples are noisy. A matrix M: A × X → {-1,1} corresponds to the following learning problem with error parameter ε: an unknown element x ∈ X is chosen uniformly at random. A learner tries to learn x from a stream of samples, (a₁, b₁), (a₂, b₂) …, where for every i, a_i ∈ A is chosen uniformly at random and b_i = M(a_i,x) with probability 1/2+ε and b_i = -M(a_i,x) with probability 1/2-ε (0 < ε < 1/2). Assume that k,𝓁, r are such that any submatrix of M of at least 2^{-k} ⋅ |A| rows and at least 2^{-𝓁} ⋅ |X| columns, has a bias of at most 2^{-r}. We show that any learning algorithm for the learning problem corresponding to M, with error parameter ε, requires either a memory of size at least Ω((k⋅𝓁)/ε), or at least 2^{Ω(r)} samples. The result holds even if the learner has an exponentially small success probability (of 2^{-Ω(r)}). In particular, this shows that for a large class of learning problems, same as those in [Garg et al., 2018], any learning algorithm requires either a memory of size at least Ω(((log|X|)⋅(log|A|))/ε) or an exponential number of noisy samples. Our proof is based on adapting the arguments in [Ran Raz, 2017; Garg et al., 2018] to the noisy case.