A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this paper. An extension of the vector-measurement-sensor selection of the greedy algorithm is proposed and is applied to particle-image-velocimetry data to reconstruct the full state based on the information given by sparse vector-measurement sensors.

Optimization approaches that determine sensitive sensor nodes in a large-scale, linear time-invariant, and discrete-time dynamical system are examined under the assumption of independent and identically distributed measurement noise. This study offers two novel selection algorithms, namely an approximate convex relaxation method with the Newton method and a gradient greedy method, and confirms the performance of the selection methods, including a convex relaxation method with semidefinite programming (SDP) and a pure greedy optimization method proposed in the previous studies. The matrix determinant of the observability Gramian was employed for the evaluations of the sensor subsets, while its gradient and Hessian were derived for the proposed methods. In the demonstration using numerical and real-world examples, the proposed approximate greedy method showed superiority in the run time when the sensor numbers were roughly the same as the dimensions of the latent system. The relaxation method with SDP is confirmed to be the most reasonable approach for a system with randomly generated matrices of higher dimensions. However, the degradation of the optimization results was also confirmed in the case of real-world datasets, while the pure greedy selection obtained the most stable optimization results.

Complexity of online computation is a drawback of model predictive control (MPC) when applied to the Navier–Stokes equations. To reduce the computational complexity, we propose a method to approximate the MPC with an explicit control law by using regression analysis. In this paper, we extracted two state-feedback control laws and two output-feedback control laws for flow around a cylinder as a benchmark. The state-feedback control laws that feed back different quantities to each other were extracted by ridge regression, and the two output-feedback control laws, whose measurement output is the surface pressure, were extracted by ridge regression and Gaussian process regression. In numerical simulations, the state-feedback control laws were able to suppress vortex shedding almost completely. While the output-feedback control laws could not suppress vortex shedding completely, they moderately improved the drag of the cylinder. Moreover, we confirmed that these control laws have some degree of robustness to the change in the Reynolds number. The computation times of the control input in all the extracted control laws were considerably shorter than that of the MPC.

The characteristics of the sensor selection method based on various algorithms for state estimation in a high-dimensional system using the Kalman filter were investigated. Sensors were selected based on the error covariance matrix of the Kalman filter. The performance of the sensor selection methods based on different algorithms, semidefinite programming, approximate convex relaxation, and greedy algorithm, including newly formulated methods, were compared by varying the number of potential sensor locations and the number of sensors to be selected under several noise ratio conditions. Two sensor selection methods for state estimation in a high-dimensional system using a Kalman filter were newly proposed based on the SDP with gain formulation and approximate convex relaxation, and the characteristics of the method including the previously proposed method were compared in a high-dimensional system. Although the condition was limited at n < O (10 ³ ), the approximate convex relaxation method and its randomized method are effective in terms of computational time and objective value for a small-scale problem. The objective value obtained by the greedy method shows the best performance compared to the other methods in almost all investigated conditions. Particularly, the greedy method outperforms other methods when the number of selected sensors is small. In addition, only the greedy method can handle the large-scale problem of n > O (10 ⁴ ). Overall, the greedy-based method is found to be favorable in large-scale problems in terms of computation time and the performance of the obtained sensor set.

Controlling a mobile robot in a space with obstacles is a well-known problem in robotics. The control objective is for the mobile robot to reach a goal point with obstacle avoidance. In this paper, we specially consider the multiple obstacle avoidance problem for particularly a four-wheeled vehicle. Assuming that the shapes and locations of the obstacles are known, we propose a design method of a nondifferentiable navigation function, which guides a vehicle at the desired point. The control law for the four-wheeled vehicle is obtained from the extended function of the navigation function. As four-wheeled vehicles cannot move sideways because of their nonholonomic constraint, the proposed control law addresses this difficulty by considering a decrease in the control Lyapunov function, and can be applied to vehicles with steering limitations. Moreover, the control law makes it possible for the vehicles to achieve an -point turn automatically without the need for any rule-based decision-making or heuristic method. The four-wheeled vehicle can reach the goal point from any initial point under the proposed control law. Our experimental results with a small four-wheeled vehicle are presented at the end of this paper. Graphical Abstract