This article considers the finite-horizon H $_{\infty}$ tracking problem for a class of discrete linear time-varying systems. Two reinforcement learning (RL) methods—policy iteration (PI) and $Q$ -learning—are proposed to solve this problem. The latter can obtain the H $_{\infty}$ controller without system dynamics. In the field of RL control, most studies focus on infinite-horizon control and time-invariant systems, and few studies have investigated finite-horizon control or time-varying systems. In contrast to infinite-horizon H $_{\infty}$ tracking control, finite-horizon H $_{\infty}$ tracking control involves a time-varying value function. While this introduces challenges, it empowers the algorithm to effectively handle time-varying problems. Within the finite-horizon framework, the value function is bounded, allowing the removal of the discount factor, thereby enhancing control performance. Additionally, there is no longer a need for an admissible control law for initialization, providing the proposed algorithms with the combined advantages of both PI and value iteration (VI). Two simulation examples are used to verify the effectiveness of the proposed algorithms.

In real industrial processes, both outliers and missing data are very common. Owing to the assumption that the data sampled from a normal process follow the Gaussian distribution, the regular datadriven process monitoring methods, such as the probabilistic partial least square (PPLS) method and the probabilistic principal component analysis method, are sensitive to outliers. By introducing heavy-tailed t distribution instead of Gaussian distribution to capture the distribution of normal data, the robust data-driven method can significantly reduce the influence of outliers on the development of the model. To reduce the influence of missing data, this paper proposes a process modeling and monitoring method with incomplete data based on the robust PPLS method. In the proposed method, to use more useful information in modeling, incomplete data along with complete data are employed in the parameter estimation using the maximum likelihood method; according to the robust PPLS model and the Bayes' rule, the distributions of latent variables and missing data are derived, and subsequently, the expectation-maximization algorithm is used to achieve the parameter estimation. In addition, based on the conditional distribution of missing data, two monitoring indices are developed to evaluate the deviation of latent variables and residuals. A simulation case illustrates the application of the proposed method, and the results of application demonstrate its efficacy.

This paper addresses the infinite-region linear quadratic regulation problem of the discrete two-dimensional (2-D) Roesser model, drawing inspiration from reinforcement learning principles. It introduces a novel proof establishing that expressing the optimal control law in 2-D through state feedback is unattainable. Subsequently, a policy iteration framework is proposed to derive suboptimal state feedback, followed by an exploration of the true optimal policy through value iteration. The efficacy of these methodologies is demonstrated via two numerical examples, enhancing the practical understanding of these innovative approaches.