Suboptimal Control of Time-Varying Neutral Control Systems

In this paper,the optimal control of time-varying neutral control systems is investigated by means of the Maxmium Principle of time-delay systems.optimal control law is given. Then sub-optimal control of time-varying neutral control systems is studied by using sensitivity approach. Algorithm for suboptimal control is given.     

Model Based Control of a Parallel Robot – A Comparison of Control Algorithms

In this contribution the control behavior of a special construction of a parallel robot, called multi-axes test facility, is investigated. After a brief discussion of the different tasks of the robot the construction of the robot is briefly presented. To solve the tasks, different control algorithms are derived based on model equations of different complexity of the robot. Depending on the task to be performed by the robot, the controllers compensate the kinematic and/or kinetic coupling of the degrees of freedom of the robot, stabilize the system and achieve the desired spatial motion of each degree of freedom as well as sufficient robustness with respect to parameter uncertainties and load variations. A few results obtained in computer simulations and laboratory experiments are presented and judged with respect to the quality of control, the closeness to reality of the computer simulations, and the amount of costs and work needed to realize the different solutions.     

Ergodic Control in L∞

The infinite horizon discounted L ^∞ problem is studied as the discount factor goes to zero. It is related to the limit of the finite horizon problem as the horizon becomes infinite. The deterministic problem with and without a running cost is considered.     

Semi-Smooth Newton Methods for Optimal Control of the Dynamical Lamé System with Control Constraints

Optimal control problems governed by the dynamical Lamé system with additional constraints on the controls are analyzed. Different types of control action are considered: distributed, Neumann boundary and Dirichlet boundary control. To treat the inequality control constraints semi-smooth Newton methods are applied and their convergence is analyzed. Although semi-smooth Newton methods are widely studied in the context of PDE-constrained optimization little has been done in the context of the dynamical Lamé system. The novelty of the article is the proof that in case of distributed and Neumann boundary control the Newton method converges superlinearly. In case of Dirichlet control superlinear convergence is shown for a strongly damped Lamé system. The results are an extension of [14 A. Kröner , K. Kunisch , and B. Vexler ( 2011 ). Semi-smooth Newton methods for optimal control of the wave equation with control constraints . SIAM J. Control Optim. 49 : 830 – 858 .[Crossref], [Web of Science ®] , [Google Scholar]], where optimal control problems of the classical wave equation are considered. The control problems are discretized by finite elements and numerical examples are presented.     

Optimal Control of Non-well-posed Heat Equations

This work is concerned with Pontryagin＇s maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.     

A Primal-Dual Active Set Method for Bilaterally Control Constrained Optimal Control of the Navier–Stokes Equations

Abstract

This paper is devoted to the analysis and numerical solution of distributed optimal control of the Navier–Stokes equations in presence of bilateral pointwise control constraints. The analysis of the problem involves the proof of existence of an optimal solution, as well as the presentation of necessary and sufficient conditions for optimality. For the numerical solution of the problem we apply a primal-dual active set strategy and show global and local convergence properties of the method. Finally, some numerical experiments, which illustrate the performance of the method, are discussed.     

The Fuzzy Solution of Multiobjective Optimization Control

It is impossible to make all objectives achieve optimization in solving multiobjective optimization control. These objectives contradict each other. The optimal solution of multiobjective optimization control is generally a set, so the optimal solution which satisfies     

Control Synthesis for Čaplygin Polynomial Systems

This paper discusses new control synthesis for certain cascade type polynomial systems addressed in the paper as aplygin systems. A numerical control synthesis as well as characterization of reachability set are presented. The results of the paper are important for various branches of system theory, where the control synthesis is concerned.     

Optimal Control of Elliptic Variational–Hemivariational Inequalities

This paper establishes a bridge between set optimization problems and vector Ky Fan inequality problems. We introduce a general model, called the bifunction-set optimization problem, that provides a unifying framework for the above-mentioned problems. An existence result in our model is obtained, with the help of KKM–Fan’s lemma. As applications, we derive some new or sharper existence results for set optimization problems and generalized vector Ky Fan inequalities with efficient solutions.     

Null-free False Discovery Rate Control Using Decoy Permutations

The traditional approaches to false discovery rate(FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical, permutation-based and empirical ones, have some inherent drawbacks. For example, the theoretical null might fail because of improper assumptions on the sample distribution. Here, we propose a null distributionfree approach to FDR control for multiple hypothesis testing in...     

A Multiple Exponential Smoothing Scheme For Quality Control

1. INTRODUCTIONRoberts (1959) first introduced the exponentially weighted movingaverage (EWMA) control scheme. Such a scheme is useful for detectingsmall shifts in the mean of a process. Like Shewhart and cumulativesum (CUSUM) control schemes, an EWMA control scheme is easy toimplement and interpret. For the purpose of providing signals the clas-sical Shewhart chart has no memory, i. e. it ignores the immediate history. The CUSUM chart, however, has too much memory, giving equalwe…     

“Invariance-Inducing” Control of Nonlinear Discrete-Time Dynamical Systems

The present study aims at the derivation of model-based control laws that attain the invariance objective for nonlinear skew-product discrete-time dynamical systems. The problem under consideration naturally arises in a variety of control problems pertaining to physical/chemical systems, and in the present study, it is conveniently formulated and addressed in the context of functional equations theory. In particular, the mathematical formulation of the problem of interest is realized via a system of nonlinear functional equations (NFEs), and a rather general set of necessary and sufficient conditions for solvability is derived. The solution to the above system of NFEs can be proven to be a unique locally analytic one, and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package such as MAPLE. It is also shown that, on the basis of the solution to the above system of NFEs, a locally analytic manifold and a nonlinear control law can be explicitly derived that renders the manifold invariant for the class of skew-product systems considered. Furthermore, the restriction of the system dynamics on the aforementioned invariant manifold represents exactly the target controlled system dynamics. Finally, the proposed method is applied to the HF molecular system classically modeled as a rotationless Morse oscillator in the presence of an external laser-field, where the primary objective is molecular dissociation.     

Optimal Control for non–isothermal crystallization of polymers

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non–isothermal Avrami–Kolmogorov model. The boundary temperature serves as control variable. The cost functional takes the spatial variation of the crystallinity and the final degree of crystallization into account. The resulting boundary control problem for a parabolic equation coupled with two ordinary differential equations is treated by an adjoint variable approach. A steepest descent algorithm is used to solve the problem numerically. Simulations illustrate the applicability and performance of the optimization algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Necessary and Suffcient Conditions for Distinguishability of Linear Control Systems

Distinguishability plays a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.     

Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N -person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.     

Stochastic H2/H∞ Control with Random Coefficients

This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefcients,which is actually a control combining the H2 optimization with the H∞robust performance as the name of H2/H∞ reveals.Based on the classical theory of linear-quadratic(LQ,for short)optimal control,the sufcient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation(BSRE,for short)associated with H∞ robustness are derived.Then the sufcient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Riccati equations.     

Control of McKean–Vlasov dynamics versus mean field games

We discuss and compare two investigation methods for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which optimization and passage to the limit are performed. When optimizing first, the asymptotic problem is usually referred to as a mean-field game. Otherwise, it reads as an optimization problem over controlled dynamics of McKean–Vlasov type. Both problems lead to the analysis of forward–backward stochastic differential equations, the coefficients of which depend on the marginal distributions of the solutions. We explain the difference between the nature and solutions to the two approaches by investigating the corresponding forward–backward systems. General results are stated and specific examples are treated, especially when cost functionals are of linear-quadratic type.     

The Stock Control of Engineering Spares—A Case Study

This paper discusses the experience of an operational research group in developing a practical scheme for the control of spares in an organization with many central and subsidiary stores. It covers the development of the scheme from the choice of the method of control to the publication of control tables for use throughout the organization; it is complementary to earlier papers on the methods of cost measurement and the mathematical analysis.Reasons are given for choosing a re-order level scheme rather than a cyclical review scheme, and for using run out costs rather than levels of service. The effect of errors in estimating physical and economic parameters is discussed; in practice not all the parameters need to be considered explicitly. Several modifications made to meet practical objections are described. The paper ends with some comments on possible future developments.     

Control of chaotic solutions of the Hindmarsh–Rose equations

Irregular bursting and spiking solutions of the Hindmarsh–Rose model for the electrical activity of neuron cell bodies have been converted by a chaos control algorithm to periodic spike trains. A proportional feedback method is used to control both chaotic spike trains and chaotic bursting by applying controlling perturbations to membrane parameters.     

Optimal Control Problem for Cancer Invasion Reaction–Diffusion System

Abstract

An optimal control problem constrained by a reaction–diffusion mathematical model which incorporates the cancer invasion and its treatment is considered. The state equations consisting of three unknown variables namely tumor cell density, normal cell density, and drug concentration. The main goal of the considered optimal control problem is to minimize the density of cancer cells and decreasing the side effects of treatment. Moreover, existence of a weak solution of brain tumor reaction–diffusion system and the corresponding adjoint system of optimal control problem is also investigated. Further, existence of minimizer for the optimal control problem is established and also the first-order optimality conditions are derived.