Turnpike Sets in Manufacturing Systems: Some Recent Progress

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

Stochastic optimal control for aircraft conflict resolution under wind uncertainty

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

This paper explores a novel stochastic optimal control method to determine 4D (3D space and time) trajectories by considering various uncertainties during flight. 4D trajectory management is a necessary concept to meet future growth in air traffic. However, aircraft may deviate from its planned 4D trajectory due to various uncertainties during flight, and a conflict between aircraft can occur and lead to severe consequences. To resolve an impending conflict, a numerical algorithm incorporating the generalized polynomial chaos into the pseudospectral method is proposed. The proposed stochastic trajectory optimization method is able to take into account various uncertainties during flight and generate optimal conflict-free trajectories by solving the stochastic conflict resolution problem. Through the numerical simulations for the conflict resolution problem, the performance and effectiveness of the proposed algorithm are evaluated and verified.

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of com-positions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as meta learning. This paper presents a new Stochastically Corrected Stochastic Compositional gradient method (SCSC). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate as the stochastic gradient descent (SGD) method for non-compositional stochastic optimization. It is easy to apply SGD-improvement techniques to accelerate SCSC. This helps SCSC achieve state-of-the-art performance for stochastic compositional optimization. In particular, we apply Adam to SCSC, and the exhibited rate of convergence matches that of the original Adam on non-compositional optimization. We test SCSC using the model-agnostic meta-learning tasks.

Contributors

Reliability-based stochastic optimal control of frame building under near-fault ground motions

In optimal design of a permanent magnet (PM) motor, many design variables are required to consider some device properties. These variables are, for example, the shape of core and magnet, the tooth length, the number of turns, and the winding radius. Moreover, many restrictions must be considered in practical PM motor design. These restrictions are, for example, the slot space factor and the cogging torque. However, the optimization problem, which has many design variables by the finite element method (FEM), has not been reported. In this paper, the efficiency of PM motor under the considerations given above is optimized by using FEM and optimization algorithm. In this problem, an objective function has many local minima and it is difficult to calculate its gradient. For these reasons, the genetic algorithm (GA) and simulated annealing method (SA), which are stochastic methods, are used for optimization method, because of the possibility of global range search and because gradient calculation is not required. Adding to both optimization methods, in this paper, SA combined with GA is used for one of the optimization methods. It is found that the solutions optimized by these methods are reasonable from an engineering point of view. © 2001 Scripta Technica, Electr Eng Jpn, 138(3): 72–79, 2002

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

This paper presents a real-time coordinated ramp control approach in response to incident-induced traffic congestion on freeways. The proposed control methodology includes two major functions to alleviate in real time incident impact on multi-segment traffic flows of freeways, i.e. (1) identification of control zone-based congestion patterns, and (2) stochastic optimization of group-based ramp metering control. To reduce congestion, the modified generalized sequential probability ratio testing (M-GSPRT) technology together with stochastic optimal control methods are used, respectively, in the above two mechanisms. With the aid of the Paramics microscopic traffic simulator, numerical results obtained under various simulated incident-induced congestion conditions indicate the feasibility of the proposed method. Numerical test results indicate both the feasibility of the proposed ramp control method in responding to diverse lane-blocking incident conditions, and its efficiency, particularly in improving the averaged hourly throughput by 67.5% in medium-volume incident cases, compared with the no-control strategy.

Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework

Rotorcraft shipboard landing is one of the most challenging operations for rotorcraft pilots owing to the workload associated with the task, which can be attributed to a variety of environmental conditions like random ship motion, heavy sea states and unsteady aerodynamic conditions. This paper explores the effectiveness of Model Predictive Path Integral (MPPI) approach, a stochastic optimal control method, for parallel trajectory optimization as a guidance solution to the rotorcraft shipboard landing problem. Specifically, the computational efficiency for real time guidance solutions afforded by the MPPI approach in comparison to its sequential counterpart is evaluated. Furthermore, a sensitivity analysis of MPPI parameter selection on its performance is carried out. The performance of the developed MPPI algorithms for real time guidance in helicopter ship board landing is demonstrated using nonlinear model simulations of a helicopter executing a symmetric landing profile aligned with the ship deck centerline.

Stochastic control methods for optimization problems in Ornstein-Uhlenbeck spread models

Aggregate production planning by stochastic control