Control issues for the Beverton-Holt equation in ecology by locally monitoring the environment carrying capacity: Non-adaptive and adaptive cases

This paper proposes a control algorithm to govern the solution of the Beverton-Holt equation (BHE) under the potentially presence of additive disturbances. The BHE to be controlled is defined by certain intrinsic growth rate and environment carrying capacity sequences, the last one being susceptible of local modifications around nominal values. In fact, the control action provides the carrying capacity which makes that the solution of the current BHE tracks a reference sequence given by another BHE defined by appropriate intrinsic growth rate and environment carrying capacity sequences. In this context, the fact that the inverse of the BHE is a discrete time-varying linear system is taken into account where the inverse of the carrying capacity sequence plays the role of control sequence. The current and the reference BHEs have to be close enough to each other in order that local modifications of the carrying capacity be able to meet the tracking objective. A feedback control law is designed to achieve such an objective with a zero tracking-error in the ideal case of known intrinsic growth rate sequence and no presence of disturbances. An adaptive control law, with the associated parameter estimation algorithm, is considered when the intrinsic growth rate is fully or partially unknown and disturbances are present. Such a control strategy guarantees a bounded tracking-error with the error converging asymptotically to zero in case that additive disturbances also converge to zero. Some results obtained from a simulation example illustrate the effectiveness of this control strategy.     

Active control laws for aeroelasticity

The objective of this paper is to describe a methodology to design control laws in the context of a computational aeroelasticity environment. The technical approach involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. As a control law design techniques, the standard LQG technique is employed. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Numerical results for flutter suppression of the BACT wind-tunnel model are given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Guidance for Quasi-planar Lunar Ascent

The minimum-time controls (thrust pitch angle and thrust yaw angle) for the three-dimensional transfer of a constant-thrust rocket from one state to another over a flat moon are used to develop guidance laws for operation over a spherical moon. The objective is to evaluate the effect of making approximations on the size of the thrust pitch angle on the suitability of the resulting control law as a guidance law. After assuming small out-of-plane motion (small yaw angle), three pitch angle control laws (exact, first-order, and zeroth-order) are developed. The three laws are employed in the sample and hold guidance of a lunar ascent vehicle. All three laws satisfy the final conditions and give essentially the same pitch and yaw control histories. Since the zeroth-order law can be obtained completely analytically (no iteration processes), it merits consideration for ascent guidance.     

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.     

行星悬浮轨道附近的编队

研究了不同类型的地球和火星悬浮轨道附近的相对运动．首先,推导了悬浮轨道附近的相对运动方程并将相对运动方程在悬浮轨道附近线性化．利用两种半自然编队控制率进行编队控制,其中一种为被动控制,对工程应用有很大的价值．在两种控制率下,讨论了每种悬浮轨道的稳定区域．由于两种控制率都不能满足特殊的火星悬浮轨道任务要求,于是,根据该任务的要求设计了一种特殊的半自然控制率．该控制率既能满足编队任务的要求也能使相对运动稳定．     

A STOCHASTIC FEEDBACK MODEL FOR OPTIMAL MANAGEMENT OF RENEWABLE RESOURCES

Analytical expressions for optimal harvest of a renewable resource stock which is subject to a stochastic process are found. These expressions give the optimal harvest as an explicit feedback control law. All relations in the model, including the stochastic process, may be arbitrary functions of the state variable (stock). The objective function, however, is at most a quadratic function in the control variable (yield). A quadratic objective function includes the cases of downward sloping demand and increasing marginal costs which are the most common sources for nonlinearities in the economic part of the model. When it is assumed that there is a moratorium on harvest for stock sizes below a certain level (biological barrier), it is shown that the barrier requirements influence the optimal harvest paths throughout.     

Time-cost trade-off via optimal control theory in Markov PERT networks

We develop a new analytical model for the time-cost trade-off problem via optimal control theory in Markov PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. Then, we construct a multi-objective optimal control problem, in which the first objective is the minimization of the total direct costs of the project, in which the direct cost of each activity is a non-decreasing function of the resources allocated to it, the second objective is the minimization of the mean of project completion time and the third objective is the minimization of the variance of project completion time. Finally, two multi-objective decision techniques, viz, goal attainment and goal programming are applied to solve this multi-objective optimal control problem and obtain the optimal resources allocated to the activities or the control vector of the problem     

On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope

In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.     

Stability analysis and optimization of an inventory system with bounded orders

This paper addresses the control of a one-item inventory system subject to random order lead time and random demand. The key parameter of the control policy is the objective inventory. In each period, the order to be placed brings the inventory position as close as possible to the objective inventory. The order of each period is kept between a lower bound and an upper bound. We show that the distribution of the inventory level converges to its stationary distribution provided that the lower bound is smaller than the average demand, the upper bound is greater than the average demand and some regularity conditions hold. The average inventory cost is shown to be a convex function of the objective inventory level. A simulation-based approach is proposed for the determination of the optimal objective inventory. A method of bisection with derivative is then used to determine the optimal objective inventory. The derivatives needed in various iterations of this method are estimated using a single sample path with respect to a given objective inventory. Numerical results are provided.     

线性系统最优输出转移问题的反馈解

在适当的条件下讨论如何最佳地施加控制将系统的输出转移至目标点,用来度量控制优劣的指标综合反映了转移时间,转移过程所消耗的输入能量与系统自身运动过程所具有的能量的多少,给出了使此指标达到最小的(状态)反馈控制．     

Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems

This paper deals with the adaptive synchronization of two identical hyperchaotic master and slave systems. The master system and the slave system each consists of two subsystems: a hyperchaotic Chen subsystem and a unified chaotic subsystem. The asymptotic convergence of the errors between the states of the master system and the states of the slave system is proven using Lyapunov theory. Simulation results are presented to illustrate the ability of the control law to synchronize the master and slave systems. Moreover, the proposed control scheme is applied to encrypt and decrypt discrete signals such as digital images where computer simulation results are provided to show that the proposed control law works well.     

复杂网络混沌系统的最优控制

考虑到控制系统能量限制的要求,确定了一个二次目标函数,基于最优控制理论给出了复杂网络混沌系统的最优控制律,利用Lyapunov稳定性理论证明了闭环系统的稳定性,数值结果证明了该方法的有效性.     

Assessing alternative control strategies for systems with asymptotically stable equilibrium positions

In a number of optimal control applications, it is possible to arrange control guided only by an analysis of a system’s dynamic properties. These controls are customarily referred to as alternatives to those that satisfy the Pontryagin maximum principle. This work considers autonomous systems of ordinary differential equations with a terminal objective functional that at each fixed value of the control parameter have unique and asymptotically stable equilibrium positions. It is shown that the problem of arranging alternative control can then be reduced to a finite-dimensional problem of mathematical programming. An estimate of the alternative control error in terms of the objective functional is obtained. Sufficient conditions for obtaining this estimate are given. A mathematical model of leukemia therapy is considered as an example.     

On a negative-equivalency theorem in associative optimal path problems

In this we study a wide class of optimal path problem in acyclic digraphs, where path lengths are defined through associative binary operations:addition, multiplication, multiplication-addition, fraction and so on. Solving a system of two interrelated recur-sive equations, we simultaneously find both shortest and longest path lengths, Further, for every problem (primal problem), we associate the other related problem (negative-equivalent problem) where each path length is defined through the associative operation connected to it in the primal problem by DeMorgan’s law. The main objective of this paper is to derive a negative-equivalency theorem between the primal problem and the negative-equivalent one     

Bayesian analysis of repairable systems with modulated power law process

As a compromise between nonhomogeneous Poisson process and renewal process, the modulated power law process is more appropriate to model the failures of repairable systems. In this article, objective Bayesian methods are proposed to analyze the modulated power law process. Seven reference priors, one of which is also the Jeffreys prior, are derived. However, only four of them are taken into consideration because of their practicality. Propriety of the posterior densities considering the four reference priors is proved. Predictive distribution of the future failure time is obtained additionally. For the purpose of comparison, the simulation work and real data analysis are carried out based on both the objective Bayesian and maximum likelihood approaches, which show that the objective Bayesian estimation and prediction have much better statistical properties in a frequentist context, and outperforms the maximum likelihood method even with small or moderate sample sizes.     

量测带噪声的多个体二阶系统聚集控制

考虑在含有量测噪声情况下的二阶多个体系统聚集控制问题.目的是使得系统中每个个体根据邻居信息构造控制,在只有部分个体能够观测到目标的情况下到达目标.和以前许多多个体同步及聚集问题的研究模型中所考虑的一阶系统不同, 系统的每个个体都只能量测到其邻居个体的部分状态信息,如位置, 并且这些量测还带有噪声.根据这些信息设计了基于局部规则的分散控制律,并且证明当量测噪声和状态量测本身相关时,只要系统在任意给定的时间区域段之内能够保持联合连通,就能够实现系统对目标的跟踪和达到目标.     

Control of nonlinear underactuated systems

In this paper we introduce a new method to design control laws for nonlinear, underactuated systems. Our method produces an infinite‐dimensional family of control laws, whereas most control techniques only produce a finite‐dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system that is open‐loop unstable and cannot be stabilized using any linear control law and demonstrate that our method produces a stabilizing control law. © 2000 John Wiley & Sons, Inc.     

Transient and steady-state analysis of a manufacturing system with setup changes

This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.     

Optimal synthesis in a two-dimensional problem with asymmetric constraints on the control

A two-dimensional optimal control problem is considered on the assumption that the terminal time of the process is not fixed and the integral objective functional depends on a parameter. Asymmetric constraints are imposed on the control parameter. Two cases are considered: constraints of the same sign and constraints of different signs. In the case of constraints of different signs, if the parameters of the problem satisfy certain relations, one obtains chattering control, alternating with a control with two switchings and a first-order singular are when these relations are violated. In the case of sign-definite control the controllability domain is part of the plane bounded by two semiparabolas. Three types of control law are then possible, in two of which the system will hit the boundary of the controllability domain and move along it, while the third features a first-order singular are. As the parameter of the problem is varied, the phase portrait undergoes evolution and one of these three types is interchanged with another. The optimality of these control laws is rigorously established using a dynamic programming method.     

Multiobjective optimal control of a four-body kinematic chain

Optimal control of mechanical systems is an active area of research. However, so far, most contributions are taking only one single objective into account, whereas for many practical problems, one is interested in optimizing several conflicting objectives at the same time. Applying singleobjective optimization to each of them leads to several trajectories each being optimal for one objective, but ignoring all others. In contrast to that, combining all objectives and using multiobjective optimization leads to a variety of trade off solutions taking all objectives into account simultaneously. We use the direct discretization method DMOCC (Discrete Mechanics and Optimal Control for Constrained systems) to approximate trajectories of the underlying optimal control problems, resulting in restricted optimization problems of high dimension. For the multiobjective part, we apply a reference point technique which successively utilizes an auxiliary distance function to gain the trade off solutions. The presented approach is illustrated by the multiobjective optimal control of a constrained multibody system. A four-body kinematic chain is controlled in a rest to rest maneuver, for which minimal control effort and minimal required maneuver time are the conflicting objectives. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)