In model predictive control (MPC), the control input at each time point is determined by solving an optimization problem. Being optimization-based, MPC is known for its limited applicability to systems with complex dynamics. This technical gap could be solved by the recently proposed MPC method based on temporal deep unfolding. Deep unfolding is method derived from deep learning, and it is used to solve an optimization problem. Temporal Deep Unfolding-Based MPC’s effectiveness is not yet thoroughly evaluated in the literature. Therefore, in this paper, we evaluate the effectiveness of the method for multilink pendulum systems by simulation.

Stochastic approximation is an iterative algorithm for solving an unknown equation using noisy observation data. In this paper, we revisit a convergence condition of stochastic approximation for a linear equation, where the noise is assumed to be a sequence whose time average converges to zero. In this case, it is usually assumed that the noisy coefficient matrix of the equation is symmetric, while it is not assumed in this paper. Instead, we slightly strengthen the noise convergence and show that the stochastic approximation gives the exact solution of the equation under this novel condition. The proposed condition is useful for establishing a multi-parameter stochastic approximation.

This paper proposes an acceleration technique using deep unfolding for a matrix completion problem (MCP), which is a problem of estimating missing entries of a matrix. Various algorithms have been proposed for this problem, and their recovery performances depend on parameters used in the algorithms. This paper focuses on the alternating gradient descent (AGD) algorithm for the MCP and shows that its performance depends on step size parameters. Then the deep unfolding is applied to the algorithm and provides a trainable AGD (TAGD) algorithm. Numerical examples show that TAGD algorithm achieves better performance than AGD algorithm.

In the present study, the response of a reference manipulated-variable is estimated directly from data, and the controller parameters of a fixed structure controller are optimized so that a closed-loop system is close to a reference model. Since a regularization method is used in the response estimation method, the estimation accuracy is prevented from deteriorating due to noise effects. In the proposed data-driven design, a pre-filter is designed to compensate for the difference between a model-based model reference problem and the proposed data-driven objective function.