Types Of Control Problems Research Articles

Application of the Tomtit Flock Metaheuristic Optimization Algorithm to the Optimal Discrete Time Deterministic Dynamical Control Problem

A new bio-inspired method for optimizing the objective function on a parallelepiped set of admissible solutions is proposed. It uses a model of the behavior of tomtits during the search for food. This algorithm combines some techniques for finding the extremum of the objective function, such as the memory matrix and the Levy flight from the cuckoo algorithm. The trajectories of tomtits are described by the jump-diffusion processes. The algorithm is applied to the classic and nonseparable optimal control problems for deterministic discrete dynamical systems. This type of control problem can often be solved using the discrete maximum principle or more general necessary optimality conditions, and the Bellman’s equation, but sometimes it is extremely difficult or even impossible. For this reason, there is a need to create new methods to solve these problems. The new metaheuristic algorithm makes it possible to obtain solutions of acceptable quality in an acceptable time. The efficiency and analysis of this method are demonstrated by solving a number of optimal deterministic discrete open-loop control problems: nonlinear nonseparable problems (Luus–Tassone and Li–Haimes) and separable problems for linear control dynamical systems.

Investigation of Various Types of Control Problems for One Nonlinear Model of Filtration

Investigation of Various Types of Control Problems for One Nonlinear Model of Filtration

The feasibility of automated detection of the aligned trunk in sitting directly from raw video using a depth camera

Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

Robust optimal control of stochastic hyperelastic materials

Soft robots are highly nonlinear systems made of deformable materials such as elastomers, fluids and other soft matter, that often exhibit intrinsic uncertainty in their elastic responses under large strains due to microstructural inhomogeneity. These sources of uncertainty might cause a change in the dynamics of the system leading to a significant degree of complexity in its controllability. This issue poses theoretical and numerical challenges in the emerging field of optimal control of stochastic hyperelasticity. This paper states and solves the robust averaged control in stochastic hyperelasticity where the underlying state system corresponds to the minimization of a stochastic polyconvex strain energy function. Two bio-inspired optimal control problems under material uncertainty are addressed. The expected value of the L2-norm to a given target configuration is minimized to reduce the sensitivity of the spatial configuration to variations in the material parameters. The existence of optimal solutions for the robust averaged control problem is proved. Then the problem is solved numerically by using a gradient-based method. Two numerical experiments illustrate both the performance of the proposed method to ensure the robustness of the system and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates

We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. The objective is to transfer a condensate from the ground state to the first-excited state. This type of control problem is typically solved using derivative-based methods in a high-dimensional control space such as gradient-ascent pulse engineering (GRAPE) and Krotov's method or derivative-free methods in a reduced control space such as Nelder-Mead with a chopped random basis (CRAB). We discuss how these methods can be combined in gradient optimization using parametrization (GROUP) including the finite bandwidth of the control electronics. We compare these methods and find that GROUP converges much faster than Nelder-Mead with CRAB and achieves better results than GRAPE and Krotov's method on the control problem presented here.

Control of the Swiss Free Electron Laser: Methods for Precision Control of Pulsed-Mode Accelerator Beams

Free electron laser (FEL) machines generate highpower, coherent, and tunable radiation in the X-ray range. They are used to study molecular structural and dynamic processes at the Ångstrom-femtosecond spatiotemporal scale. The Swiss Free Electron Laser (SwissFEL) facility–under development at the Paul Scherrer Institut and scheduled to begin operation in 2017– will generate intense and short pulses of X-ray light, enabling researchers to observe extremely fast processes, such as the creation of new molecules in chemical reactions or to study the detailed structure of proteins. This article introduces FEL technology from a control systems perspective and provides insight into the types of control problems that arise in pulsedmode accelerators and beams. Although developed here for the SwissFEL machine, the control approaches are expected to be transferable to other systems as well. See Summary for an overview of the article.

Robust Averaged Control of Vibrations for the Bernoulli–Euler Beam Equation

This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.

An Implementation of Predictive Functional Control for Image-Based Satellite Attitude Control

This paper presents an implementation of predictive functional control for image- based satellite attitude control. The approach considers Low Earth Orbit small satellites equipped with an on-board camera for interactive Earth observation. The control goal is to keep a target on the Earth surface in the satellite's camera field of view during orbiting of the satellite above the target. The control error is given in the image frame, therefore in-image interaction with the system is possible. Two types of control problems are considered: target tracking and oriented-target tracking. The system contains a delay that is taken into account in development of the predictive control law. The control problem is solved in the framework of predictive functional control that is based on the kinematic model of the satellite attitude. The presented control algorithm is validated in simulation environment.

Vkorc1 variation in house mice during warfarin and difenacoum field trials

Field studies guided by genetic monitoring of Vkorc1 need to be done to implicate mutations conclusively with rodent control problems due to the presence of animals resistant to anticoagulant rodenticides. Rodent control success in relation to Vkorc1 genotypes in house mice (Mus musculus domesticus) was studied on two farms (I and II) in Germany. Tests were carried out to determine whether certain resistance profiles and Vkorc1 genotypes displayed dynamics over the course of sequential treatments with warfarin and difenacoum that were consistent with single nucleotide polymorphisms (SNPs) in Vkorc1 as indicators of resistance. On farms I and II, respectively, three (A to C) and two (A and B) types of control problem with anticoagulants (i.e. proxies for resistance) were encountered in spatially segregated subunits: A = none; B = control problems with warfarin but not with difenacoum; C = control problems with both anticoagulants. Unexpectedly, resistance was encountered in a population where only Vkorc1 wild-type mice were detected. In addition, the Arg58Gly Vkorc1 variant was found not to correlate with observed control failures. Control problems were encountered that cannot be explained by Vkorc1 coding or intronic SNPs, and therefore are likely due to non-coding Vkorc1 SNPs or due to other genetic or non-genetic factors.

極の領域を指定した拡張<i>H</i><sub>∞</sub>制御のLMI解法の導出とその応用

Abstract As well known, extended H ∞ control accepts unstable weighting functions which are included in a generalized plant, so it has wider availability than standard H ∞ control. On the other hand, the root-clustering problem for H ∞ control has been considered by Chilali and Gahinet and the solution is derived. But it is not so easy to apply the solution to extended H ∞ control, because the formulation of the root-clustering controllers is discordant with that of extended H ∞ controllers. Therefore, we can not simply combine the root-clustering conditions with extended H ∞ control. In this paper, we propose a LMI based design method for this control problem by using modified formulation of controllers of the root-clustering problem derived by Chilali and Gahinet. These types of control problems appear in design problems of a vibration isolation controller which attenuates vibrations forced by narrow-band frequency disturbances. A controller for a simple vibration isolation experimental system is designed by the proposed method and performance of a designed controller is verified by experimental results.

On equivalence of pencils from discrete-time and continuous-time control

We study two matrix pencils that arise, respectively, in discrete-time and continuous-time optimal and robust control. We introduce a one-to-one transformation between these two pencils. We show that for the pencils under the transformation, their regularity is preserved and their eigenvalues and deflating subspaces are equivalently related. The eigen-structures of the pencils under consideration have strong connections with the associated control problems. Our result may be applied to connect the discrete-time and continuous-time control problems and eventually lead to a unified treatment of these two types of control problems.

EXTENDED H∞ CONTROL WITH POLE PLACEMENT CONSTRAINTS VIA LMI APPROACH AND ITS APPLICATION

As well known, extended H∞ control accepts unstable weighting functions which are included in a generalized plant, so it has wider availability than standard H∞ control. On the other hand, the root-clustering problem for H∞ control has been considered by Chilali and Gahinet and the solution is derived. But it is not so easy to apply the solution to extended H∞ control, because the formulation of the root-clustering controllers is discordant with that of extended H∞ controllers. Therefore, we can not simply combine the root-clustering conditions with extended H∞ control. In this paper, we propose a LMI based design method for this control problem by using modified formulation of controllers of the root-clustering problem derived by Chilali and Gahinet. These types of control problems appear in design problems of a vibration isolation controller which attenuates vibrations forced by narrow-band frequency disturbances. A controller for a simple vibration isolation experimental system is designed by the proposed method and performance of a designed controller is verified by experimental results.

ON THE SELECTION OF APPROPRIATE CONTROL SYSTEM DESIGN METHODOLOGIES

We will argue in this paper that the nature and magnitude of model uncertainty dictate the appropriateness of the control system design methodology. To obtain these arguments, we will pursue optimality of the control system design. Note this is a philosophical paper, in which we present our arguments in qualitative terms. We will identify the circumstances under which several control system design methodologies are appropriate. The design methodologies that will be considered are (1) optimal control and optimal feedback design, (2) model predictive control (receding horizon control), (3) active and passive adaptive control and (4) robust control. Robust control strategies are conservative and limit the possible improvements that can be obtained over say classical PID control. However, it will turn out that for certain types of control problems, improvements in performance are indeed limited. Roughly speaking, the area where we may expect (significant) improvement from advanced (optimal) control system design is very much limited by the uncertainty of the systems model. Miracles are not to be expected from advanced control. What can be expected is reflected in an active adaptive optimal control scheme introduced and discussed in this paper.

Mixture‐based adaptive probabilistic control

AbstractQuasi‐Bayes algorithm, combined with stabilized forgetting, provides a tool for efficient recursive estimation of dynamic probabilistic mixture models. They can be interpreted either as models of closed‐loop with switching modes and controllers or as a universal approximation of a wide class of non‐linear control loops.Fully probabilistic control design extended to mixture models makes basis of a powerful class of adaptive controllers based on the receding‐horizon certainty equivalence strategy.Paper summarizes the basic elements mentioned above, classifies possible types of control problems and provides solution of the key one referred to as ‘simultaneous’ design. Results are illustrated on mixtures with components formed by normal auto‐regression models with external variable (ARX). Copyright © 2003 John Wiley & Sons, Ltd.

Trimmed deep stall on the F-16 Fighting Falcon

Abstract High performance fighter aircraft have problems with handling qualities, at high angles of incidence. Pilots are limiting combat effectiveness by cautiously avoiding hazardous regions of the flight envelope. This paper presents and extends existing work on the F-16 aircraft's handling characteristics during the deep stall condition. Inflight experience shows that there are two types of control problems when flying at high angles-of-attack, the ‘pitch departures’ and the ‘deep stall trim’. This paper investigates the critical deep stall condition, assesses the effectiveness of the proposed method of recovery and suggests an augmented and reliable method of returning to normal flight.

A practical algorithm for diagnosing control loop problems

This paper describes an algorithm for detecting and diagnosing poor performance in feedback control loops. The performance of the control loop is assessed based on criteria derived from parameters that can be estimated from superficial knowledge of the controlled process. The algorithm can distinguish between three types of control problems: oscillatory response, sluggish response, and plant failure. The method is particularly applicable to heating, ventilating, and air-conditioning (HVAC) systems where linear (PI) control law is normally used despite the existence of often quite non-linear operating characteristics. In these systems, the control performance varies as the plant is exercised across its operating range. In practice, periodical re-tuning of HVAC control loops during the yearly load cycle may be necessary in order to obtain consistent control performance. The algorithm presented in this paper can act as the basis for determining when re-tuning is necessary in addition to detecting plant failure. Potential advantages of detecting control problems in HVAC systems are energy savings, reduced maintenance costs, and improved thermal comfort conditions. The paper describes the techniques comprising the algorithm and presents results from tests carried out on a simulated air-handling unit (AHU).

Organisational Change and Responsive Management Accounting Practice

The primary purpose of management accounting is to help maintain organisational control (Emmanuel, Otley and Merchant 1990). However, different types of problems can be controlled in different ways (of which the management accounting system is one). Organisational control probably becomes most problematic when a fundamental change, such as total quality management, is introduced because problems can manifest themselves in new and unexpected ways. This article uses two complementary field studies to argue that management accountants need to understand these different types of control problems, how they change when TQM is introduced and how they can be controlled.

H control attenuating initial-state uncertainties

H A generalized type of control problem, which treats a mixed attenuation of disturbance and initial-state uncertainty for linear time-invariant systems in the H infinite-horizon case, is examined. The mixed attenuation supplys controls H with good transients or assures controls of robustness against initial-state H uncertainty. A necessary and sufficient condition for an control to attain the H mixed attenuation is given. On the basis of this condition, the robustness of controls against initial-state uncertainty is discussed.

Generalised H∞ multivariable controllers

The design of multivariable controllers to minimise a H∞ cost function is considered. The cost function to be minimised is specially selected to enable both control and error signal spectra to be minimised, and also to provide a simple controller structure. Because of the different cost function, the problem is not the same as that usually considered but still allows sensitivity and complementary sensitivity terms to be minimised in a certain sense. The polynomial systems approach is taken to the solution of the H∞ control problem. This involves the use of the solution to the more LQG type of control problem to provide the solution to the desired H∞ problem.

Feedback linearization families for nonlinear systems

Characterizations are developed for parameterized, linear, dynamic feedback control laws that can arise when linearizing a nonlinear, dynamic feedback control law for a specified nonlinear system about a family of constant operating points. Such characterizations are important in applying the recently-developed extended linearization design approach to various types of control problems. To illustrate, the input-output decoupling problem is considered.