Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

斜孔气膜冷却数值模拟分析

本文通过数值模拟分析圆柱孔和扩散孔的单斜孔气膜冷却特性,考察复合角、孔型和吹风比对流场和气膜冷却效果的影响。结果表明,复合角的引入使气膜侧向分布更宽,但冷却效果沿主流方向衰减更快。适中吹风比得到的气膜能更有效的保护壁面。在相同吹风比和复合角条件下,扩散孔的气膜冷却效率比圆柱孔更好,且冷却更为均匀持久。     

Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems

A method for the numerical solution of state-constrained optimal control problems subject to higher-index differential-algebraic equation (DAE) systems is introduced. For a broad and important class of DAE systems (semiexplicit systems with algebraic variables of different index), a direct multiple shooting method is developed. The multiple shooting method is based on the discretization of the optimal control problem and its transformation into a finite-dimensional nonlinear programming problem (NLP). Special attention is turned to the mandatory calculation of consistent initial values at the multiple shooting nodes within the iterative solution process of (NLP). Two different methods are proposed. The projection method guarantees consistency within each iteration, whereas the relaxation method achieves consistency only at an optimal solution. An illustrative example completes this article.     

Active control of extended Van der Pol equation

We study in this paper the active control of a driven class of Van der Pol oscillator which exhibits three limit cycles. We begin by investigating the dynamics and stability analysis of the system under active control. We also analyze the effects of a time periodic perturbation included in the control process. In all these cases the domain of control gain parameters leading to a good control is obtained and verified numerically.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Vehicle density and velocity estimation on highways for on-ramp metering control

A scheme for vehicle density and velocity estimation in a stretch of highway based on a modified cell transmission model [C. F. Daganzo, Transportation Research, Part B, 28B(4),269–287, 1994. Elsevier is presented. The scheme is intended for use with on-ramp metering control algorithms, providing local knowledge of densities and velocities that is helpful to improve on-ramp metering control performance. Estimation of density is obtained by nonlinear estimators, while velocity estimation is obtained by gradient algorithms. There is one density–velocity estimator for free traffic flow and other for congested traffic flow. Both estimator schemes work in parallel. The final estimation of density and velocity results from a convex combination of the predictions of the two estimators. This combination depends on occupancy or density measurements at the boundaries of the stretch and is produced by a fuzzy inference system. Stability and convergence of the density and velocity estimation scheme is proved by Lyapunov based techniques. Simulation results comparing measured and estimated traffic data are presented. They confirm good performance of the estimators. Research sponsored by grants UNAM PAPIIT IN110403 and CONACYT 47583.     

正定矩阵标准型的复合矩阵的一般形式

实对称正定矩阵的复合矩阵正定性的研究已有结论,但对于一般意义下的正定矩阵的复合矩阵是否仍然是正定的研究需要利用一般的正定矩阵的标准形的复合矩阵进行讨论,给出了一般公式及具体算法,为讨论其复合矩阵的正定性提供了基础条件.     

Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.     

Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.