Production planning and control I. The decision problem

The application of the linear-quadratic-gaussian (LQG) tracking problem to production planning and control systems is discussed. Decision concepts are developed from an examination of the structure of a generalized production control system. The decision problem is modelled as a LQG tracking problem operating in the presence of persistent disturbances—the disturbances representing the demand for finished goods. The development of a solution leads to a linear, time-invariant decision policy which is a decomposition of the decision input into separate and nearly independent decision tasks. Sufficient conditions for the existence of a solution are presented. An open-loop, closed-loop decision system is presented to show how the decision model can be used to analyse relationships among system structure, performance, and information requirements.     

Production planning and control III. The sampling problem

Concepts from bayesian decision theory and control theory are combined to address the question of how long a decision-maker should wait between samples of the stale of a dynamic production system. Expressions defining expected performance are derived for open-loop, continuous, and sampled information modes of operation. These results are used to define the value of sampled information. The main results support the intuition of decision-makers and serve as qualitative guides for information system design.     

The obstacle avoidance motion planning problem for autonomous vehicles: A low-demanding receding horizon control scheme

The paper addresses the obstacle avoidance motion planning problem for ground vehicles operating in uncertain environments. By resorting to set-theoretic ideas, a receding horizon control algorithm is proposed for robots modelled by linear time-invariant (LTI) systems subject to input and state constraints and disturbance effects. Sequences of inner ellipsoidal approximations of the exact one-step controllable sets are pre-computed for all the possible obstacle scenarios and then on-line exploited to determine the more adequate control action to be applied to the robot in a receding horizon fashion. The resulting framework guarantees Uniformly Ultimate Boundedness and constraints fulfilment regardless of any obstacle scenario occurrence.     

Receding horizon control applied to optimal mine planning

In this paper we show that the problem of optimal mine planning can be cast in the framework of receding horizon control. Traditional formulations of this problem have cast it in the framework of mixed integer linear programming. In this paper, we present an alternative formulation of the mine planning problem using the “language” of control engineering. We show that this alternative formulation gives rise to new insights which have the potential to lead to improved computational procedures. The advantages are illustrated by an example incorporating many practical features of an actual mine planning problem.     

Detecting planning horizons in deterministic infinite horizon optimal control

A deterministic infinite horizon optimal control problem with discounted cost is investigated. Under some assumptions we give a method to detect a planning horizon which is guaranteed to exist. When forward dynamic programming can be applied, the procedure does not require extra computations. An inventory control example is presented.     

线性时序逻辑约束下的滚动时域控制路径规划

针对有限确定性系统中的路径规划问题,本文提出了一种线性时序逻辑约束下的在线实时求解滚动时域控制的新方法。该方法将滚动时域控制方法和满足线性时序逻辑公式的策略相结合,控制目标是在满足高级别任务规范的同时,使收集的累积回报值最大化。其中,在有限时域内的每个时间步长上局部优化回报值,并应用当前时刻计算获得的最优控制序列。通过执行适当的约束,保证控制器产生的无限轨迹满足期望的时序逻辑公式。而且,由于地势影响因子的引入,所建议的方案更接近于真实情况。仿真实验结果验证了文中提出方法的可行性和有效性。     

Production planning and control: A personal philosophy

This paper looks at the author's beliefs, concerning the ways in which Production Planning and Control should be developed in the future. He sees the way forward as one which includes small factories - even if the companies are large - less specialisation; simple materials flow systems; Flexible programming; PBC or Kanban and the development of systems theory.     

Discrete optimization by optimal control methods. II. The static traveling salesman problem

The static minisum traveling salesman problem is formulated as an optimal control problem. Two-sided algorithms based on the sufficient conditions for global optimality for solving this problem and a new algorithm for approximating the quality criterion from above to its optimal value are designed.     

Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem

In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real-time the solution to the optimal control design HJ equation. This method finds in real-time suitable approximations of both the optimal cost and the optimal control policy, while also guaranteeing closed-loop stability. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks. We call this ‘synchronous’ policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra nonstandard terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and the stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm.     

The regulator problem with indefinite quadratic cost for boundary control systems: the finite horizon case

In this paper we study the finite horizon non-standard LQ-problem for an abstract dynamics, which models a large class of hyperbolic-like partial differential equations. We provide necessary/sufficient conditions for finiteness of the value function corresponding to the control problem. Sharpness of sufficient conditions is shown by means of counterexamples. The specific features of the finite, in contrast to infinite, horizon case are illustrated.     

The stability of constrained receding horizon control

An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed. For both stable and unstable linear plants, feasibility of the contraints guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law. The constraints' feasibility can be checked efficiently with a linear program. It is always possible to remove state constraints in the early portion of the infinite horizon to make them feasible. The controller's implementation requires only the solution of finite-dimensional quadratic programs     

The finite horizon investor problem with a budget constraint

We study a model that incorporates a budget constraint in a decision making problem. Our goal is to maximize the expected wealth, where in each time period we can either stop the business getting our current wealth or to continue one additional time period and getting a random revenue. We show that when the wealth is scalar, the problem is NP-hard and we provide an FPTAS. However, when the wealth is vector with at least two components the problem cannot be approximated.     

Production planning and control for remanufacturing: a state-of-the-art survey

Remanufacturing is rapidly emerging as an important form of waste prevention and environmentally conscious manufacturing. Firms are discovering it to be a profitable approach while at the same time enhancing their image as environmentally responsible, for a wide range of products. In this paper the characteristics of the remanufacturing environment are discussed first to distinguish this environment from other manufacturing environments. The production planning and control function of the remanufacturing firm is examined in this environment. The research in the various decision-making areas that comprise the production planning and control function is evaluated. There are many areas where the research is still scant. The lack of any overall integrated framework and models for the production planning and control function is noted. It is also pointed out that most firms are still grappling with these problems and do not have any formal mechanisms in place. There is a need to develop models and frameworks grounded in the problems and needs of these remanufacturing firms.     

Moving horizon observers and observer-based control

In this paper two topics are explored. A new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed. The moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing, or approximately minimizing, a cost function over the preceding interval (horizon) [t-T,t]; as t advances, so does the horizon. Convergence of the estimator is established under the assumption that the corresponding global optimization problem can be (approximately) solved and a uniform reconstructability condition is satisfied; the latter condition is automatically satisfied for linear observable systems. The utility of the estimator for receding horizon control is explored. In particular, stability of a composite moving horizon system, comprising a moving horizon regulator and a moving horizon observer, is established     

The electrical distribution network planning problem

In this paper we are dealing with the electrical distribution network planning problem where a network configuration has to be specified in order to meet demand, to satisfy the operating constraints, and to minimize investment, operating, and power–loss costs. The iterative procedure includes several heuristic algorithms to generate a radial network, to choose a set of open feeders to meet the reliability constraint, and to solve the reconfiguration problem in order to reduce the power–loss costs. Furthermore, in order to compare the reliability of potential solutions, a predictive reliability assessment measure is established.     

A faster solution to the horizon problem

An algorithm is developed for calculating the horizons for each point in a digital terrain grid in order N iterations, whereas all previous methods seem to be of O(N²) time complexity. The new method makes horizon computations reasonable, and ought to improve the accuracy of surface climate models in rugged terrain.     

On receding horizon feedback control

Receding horizon feedback control (RHFC) was originally introduced as an easy method for designing stable state-feedback controllers for linear systems. Here those results are generalized to the control of nonlinear autonomous systems, and we develop a performance index which is minimized by the RHFC (inverse optimal control problem). Previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the RHFC horizon distance a function of the state. That functional dependence was implicit and difficult to implement on-line. Here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state.     

基于滚动时域的无人机动态航迹规划

针对带有动力学约束的多旋翼无人机航迹规划问题,提出了一种基于滚动时域控制和快速粒子群优化(RHC-FPSO)方法。该方法引入了基于VORONOI图的代价图方法说明从航迹端点到达目标点的距离估计。根据滚动时域和人工势场法的思想,将路径规划问题转化为优化问题,以最小距离和其他性能指标为代价函数。设计评价函数准则,按照评价准则使用变权重粒子群优化算法求解。针对无人机靠近危险区飞行的问题,将斥力场引入到代价函数中,提升其安全性。仿真实验结果显示,使用文中方法可以有效地在满足约束条件下穿过障碍物区域,以及在复杂环境下可以动态计算。     

Infinite horizon stable predictive control

Terminal constraints guarantee the stability of predicted trajectories and form the basis of predictive control algorithms with guaranteed stability. Earlier work in the literature uses terminal constraints which define sufficient but not necessary conditions for the stability of predicted trajectories. In this paper we deploy conditions which are both necessary and sufficient and hence release more degrees of freedom for optimizing performance and/or meeting constraints. Also an alternative means of computing the implied infinite horizon GPC cost, avoiding the need for solving a Lyapunov equation, is presented     

An application of control theory to a problem in educational planning

The paper treats an example arising from a problem in educational planning. The provision of places in a sector of education to satisfy an unknown social demand is treated as a "dual-control" process. Dynamic programming is used to determine the sequence of decisions which extremizes a performance criterion. Results are obtained for different forms of a priori distributions of the unknown demand. Because answers can be obtained analytically without approximation, the optimum policy can be compared with the nonoptimum policy of optimizing stage by stage. The paper also discusses the effect of the decision maker's a priori knowledge upon the infinite stage process.