We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values of which converge to the value of the control problem. These semi-infinite programs are increasing restrictions of the dual of the nonlinear control problem, which is a maximization problem over the subsolutions of the Hamilton-Jacobi-Bellman (HJB) equation. Our approach is compatible with generic dynamical systems and state constraints. Specifically, we use an oracle that, for a given differentiable function, returns a point at which the function violates the HJB inequality. We solve the semi-infinite programs using a classical convex optimization algorithm with a convergence rate of O(1/k), where k is the number of calls to the oracle. This algorithm yields subsolutions of the HJB equation that approximate the value function and provide a lower bound on the optimal time. We study the closed-loop control built on the obtained approximate value functions, and we give theoretical guarantees on its performance depending on the approximation error for the value function. We show promising numerical results for three non-polynomial systems with up to 6 state variables and 5 control variables.
While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity simulator representing the system at hand. In this work, a new data-driven Lyapunov analysis framework is proposed. Without using the model or its simulator, the proposed approach can learn a piece-wise affine Lyapunov function with a finite and fixed off-line dataset. The learnt Lyapunov function is robust to any dynamics that are consistent with the off-line dataset, and its computation is based on second order cone programming. Along with the development of the proposed scheme, a slight generalization of classical Lyapunov stability criteria is derived, enabling an iterative inference algorithm to augment the region of attraction.
Human facial expressions are a mirror of human thoughts, feelings and human mental states. Facial Emotion Recognition (FER) can provide a social advantage. It's like a form of silent communication. Emotion recognition technology will help to automatically detect the patient's emotions during illness and avoid external acts such as suicide, mental disorders or mental health problems. If we understand all the signs of emotions, we can solve many problems for human beings. Emotion recognition and detection is also useful for healthcare. Through emotional state recognition, we can get information about patients. Recognizing a patient's emotions for a specific disease using artificial intelligence techniques is a challenging task. This article presents recognition, detection and methods for mental health patients. Using artificial intelligence techniques with an emotion detection library and matching emotions to mental health. This article uses an emotional scale to show that there is a link between negative emotions and mental health problems. In this paper, she provided a comprehensive review of AI-based FER methodology, including datasets, feature extraction techniques, algorithms, and recent breakthroughs with their applications in facial expression recognition. In the future, all aspects of FER for different ages would significantly influence the health research community.
