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Since the multi-time scales and strong nonlinearity are objectively existed in the practical industrial processes, it is extremely challenging to design control policy for optimizing the industrial operation. Therefore, this paper focuses on the multi-time scale optimal operational control (OOC) problem with unmodeled dynamics. Under the framework of reinforcement learning (RL) technology, a self-learning model-free method by integrating zero-sum game and singular perturbation (SP) theories is proposed in this paper, such that composite controllers with signal compensation can be found under which the suboptimal operation of the whole process can be achieved using only measured data. The remarkable highlight in this paper is the novel design method of the composite controllers with signal compensations for unknown nonlinear systems with multi-rate operations. Finally, the effectiveness of the proposed method is verified by a practical example and a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel deep learning approach for predicting saddle points in stochastic two-player zero-sum games. Our method combines neurodynamic optimization and deep neural networks. First, we model the stochastic two-player zero-sum game as an ordinary differential equation (ODE) system using neurodynamic optimization. Second, we develop a neural network to approximate the solution to the ODE system, which includes the saddle point prediction for the game problem. Third, we introduce a specialized algorithm for training the neural network to enhance the accuracy of the saddle point prediction. Our experiments demonstrate that our model outperforms existing approaches, yielding faster convergence and more accurate saddle point predictions. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of fault tolerant control (FTC) for reentry vehicles (RV) subject to actuator fault and perturbation. In contrast to the majority of papers assuming bounded and exogenous actuator fault effect, the adaptive dynamic programming (ADP) control algorithm has been considered here to tackle with the dependence of closed-loop states induced by the setup of an active FTC strategy. By this way, the FTC problem formulation takes theoretically into account the fact that an actuator fault can destabilize a closed-loop. First, the FTC problem in attitude tracking is transformed into an error-optimal control problem. Next, a cost function based on zero-sum game theory is considered to achieve tracking under the joint influence of state-dependent actuator faults and perturbations. Lyapunov theory has been next used to prove the stability of FTC architecture and the network weight convergence. Benefits of proposed ADP-FTC algorithm is finally highlighted on a numerical benchmark of RV. [ABSTRACT FROM AUTHOR]

Stable operations of control systems play a vital role in mission accomplishments of the second-order nonlinear systems, such as six-axis robots used in intelligent production lines, industrial equipment and control systems. In this paper, a fault-tolerant control scheme is developed for a class of second-order nonlinear control system under actuator bias faults and loss of effectiveness faults via the zero-sum differential game method. Based on the backstepping method, a controller is designed to ensure system tracking performance. Then by the zero-sum differential game method, a fault-tolerant controller is designed for the equivalent error system. Simulation results show the validity of the designed fault-tolerant control scheme. • The stability of the system and the optimality of control consumption are achieved. • Both unknown bias and loss of effectiveness faults are solved. • Uncertainty of the control gain matrix caused by the fault pattern matrix is solved. [ABSTRACT FROM AUTHOR]

This paper aims to investigate an innovative framework to handle emergency response scheme selection (ERSS) issues by integrating TODIM and TPZSG (two-person zero-sum game) methods under novel T-spherical hesitant probabilistic fuzzy set (T-SHPFS) environments. First, T-SHPFS is defined as an extension of the existing tools, which can depict the complex assessment information including several possible values of the various membership functions' degrees and the associated statistical uncertainty information. Concomitantly, T-SHPFS's normalization method, comparison laws, operation rules, cross-entropy measure and Hausdorff distance are explored. Then, an objective attribute weight determining model is constructed, considering the credibility of T-SHPF evaluations and the divergence degrees between attribute assessments simultaneously. Next, an integrated TODIM-TPZSG decision-making approach is developed to select the most desirable emergency response scheme. Finally, an illustrative example concerning the selection of the best medical waste disposal method during the COVID-19 epidemic is conducted to verify the effectiveness of the proposed TODIM-TPZSG method. Sensitivity analysis and comparisons between the TODIM-TPZSG and other representative methods are also provided to demonstrate the superiorities of the proposed method. The results reveal that the developed T-SHPFSs give DMs more assessment freedom; the proposed TODIM-TPZSG approach considers the decision makers' psychological behaviors; the ranking results of the proposed method can reflect the specific divergence degrees among the alternatives; and the needed computation burden and computational complexity are low and less affected by the number of alternatives and criteria than most current ERSS methods. • Proposing T-spherical hesitant probabilistic fuzzy set (T-SHPFS), a novel fuzzy set, to describe intricate information, which renders experts more freedom in evaluation processes. • Establishing the normalization method, comparison laws, operation rules, cross-entropy measure and Hausdorff distance of T-SHPFSs. • Constructing an objective attribute weight determining model, considering the credibility of T-SHPF evaluations and the divergence degree between attribute assessments simultaneously. • Devising an integrated TODIM-TPZSG decision-making approach for selecting the most desirable emergency response scheme. [ABSTRACT FROM AUTHOR]