Solving Control Problems Research Articles

Design of a fractional PIλDμ controller using the cohort intelligence method

The cohort intelligence (CI) method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportionalintegral- derivative (PID) controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.

Methodology and Results of Mathematical Modelling of Complex Technological Processes

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Analytic Controlling Reorientation of a Spacecraft Using a Combined Criterion of Optimality

We consider the problem of optimally controlling the reorientation of a spacecraft (SC) from an arbitrary initial angular state into a given final angular position. We study the case when the minimized functional joins, in the given proportion, the time spent and the integral of the squared modulus of the angular momentum on the reorientation of a SC. The problem is solved in a kinematic setting. We consider two versions of the problem of the optimal rotation of a SC, with bounded and unbounded control. Using the necessary optimality conditions in the form of the Pontryagin maximum principle and the quaternion method for solving control problems on the motion of spacecrafts, we obtain an analytical solution of the posed problem. The solution of the problem is based on the quaternionic differential equation relating the angular momentum vector of a SC with the orientation quaternion of the related coordinate system. We present formalized equations and give computational expressions for constructing the optimal control program. We state the control law as an explicit dependence of the control variables on the phase coordinates. Using the transversality condition as a necessary optimality condition, we determine the maximal value of the modulus of the angular momentum for the optimal motion. For a dynamically symmetric SC, the problem of reorientation in space is solved completely: we obtain the dependences for the optimal law of the change of the angular momentum vector as explicit time functions. We give the results of the mathematical modeling of the motion for optimal control which demonstrate the practical realizability of designed algorithm for controlling the spatial orientation of a SC.

New Control Paradigms for Resources Saving: An Approach for Mobile Robots Navigation.

In this work, an event-based control scheme is presented. The proposed system has been developed to solve control problems appearing in the field of Networked Control Systems (NCS). Several models and methodologies have been proposed to measure different resources consumptions. The use of bandwidth, computational load and energy resources have been investigated. This analysis shows how the parameters of the system impacts on the resources efficiency. Moreover, the proposed system has been compared with its equivalent discrete-time solution. In the experiments, an application of NCS for mobile robots navigation has been set up and its resource usage efficiency has been analysed.

Cyber Security-Oriented Smart Grid State Estimation

Development of Smart Grid involves the introduction of Wide Area Measurement System (WAMS), which provides the use of information, computing and digital technologies for measuring, transmitting and processing operating parameters when solving control problems. In this regard, the increased vulnerability to cyberattacks of the control system was noted. The control of Smart Grid includes monitoring, forecasting and planning of the system operation based on its Electric Power System state estimation results. Therefore, the goal of the paper is to develop a mathematical instrument to bad data detection under cyberattacks. Particular attention is paid to false data injection attacks which result in distortion of state variables estimates. The result of the research is an algorithm developed for state estimation based on the interior point method and test equation obtained by Crout matrix decomposition. The obtained results showed effectiveness of the algorithm in state estimation.

Ψ0 vector reachability domain determination approach for solving control problems using the maximum principle

Abstract An approach is proposed to determine the reachability region of the Ψ0 vector. It will significantly speed up the solution of optimal control problems using the maximum principle for multidimensional dynamic objects.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields – electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

Algorithm to solve linear multipoint problems of control by the method of cascade decomposition

Proposed was a method to solve control problems for the nonstationary heterogeneous linear systems under conditions on the state and control functions at different time points. It consists of a phased transition from of the initial problem to the formula for the determination of some part of the functions of control and a problem similar to the previous one for a system with a smaller number of equations. The suggested method is a modification of the previous method of cascade decomposition, which solves problems using the projectors on the subspace. In the present paper, decomposition was carried out by solving the linear algebraic equations and replacing linearly the desired vector functions. The procedure of differentiation of certain functions was used to construct the controlled process.

Some Applications of the Theory of Functions Approximation to the Design of Complex Systems

It is proposed the unified concept of applications of analitical theory of approximation in the development of building materials and flight simulators of modular architecture as complex systems. The annex to the development of simulators of flight dynamics are given the approximation of table - graphically defined functions and functions of several variables by polynomials of higher degrees. It is planned to implement the methods in real-time via parallelization of computational processes. Is given the approximation of aerodynamic factors in simulator of the dynamics of the flight of transport aircraft. It is proposed the description of kinetic processes of formation of physical and mechanical properties of materials to solve control problems of their properties. It indicates the possibility of overcoming the uncertainty targets based on an objective assessment of each of the properties (quality criteria) with their analytical description by polynomial models. The approximation methods are implemented on modern computers. Efficiency was confirmed in the development of training systems for the training of operators of different transport systems and design of composite materials with special properties.

Water exit model and takeoff control for a morphing cross-media vehicle

The water exit of a morphing cross-media vehicle is a nonlinear, multi-coupled, physical process with strong disturbance. It severely affects the subsequent flight of the vehicle after leaving the water. Because of the short duration, it requires very fast response time from the controller. To overcome the shortcomings of existing research on the water exit process of morphing cross-media vehicles, a possible solution of uncontrolled water exit and controlled takeoff is proposed. A water exit dynamic model is established after properly simplifying the complexity and unpredictability of the underwater environment, in consideration of changing variables, such as buoyancy, wetted area, and added mass. A numerical simulation is conducted to prove the validity of the model. Furthermore, an improved sliding-mode controller is designed to ensure that the cross-media vehicle reaches the target conditions after leaving the water and to prevent the vehicle falling back into the water. Simulation results demonstrate the reasonability and feasibility of the proposed solution. These conclusions can provide valuable reference information for solving control problems in morphing cross-media vehicles.

Theoretical analysis of the 2D thermal cloaking problem

Coefficient inverse problems for the model of heat scattering with variable coefficients arising when developing technologies of design of thermal cloaking devices are considered. By the optimization method, these problems are reduced to respective control problems. The material parameters (radial and azimuthal conductivities) of the inhomogeneous anisotropic medium, filling the thermal cloak, play the role of control. The model of heat scattering acts as a functional restriction. A unique solvability of direct heat scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and efficient numerical algorithm of solving thermal cloaking problems is proposed.

Linear parameter-varying modeling and control of the steam temperature in a Canadian SCWR

The Canadian direct-cycle Supercritical Water-cooled Reactor (SCWR) is a pressure-tube type SCWR under development in Canada. The dynamics of the steam temperature have a high degree of nonlinearity and are highly sensitive to reactor power disturbances. Traditional gain scheduling control cannot theoretically guarantee stability for all operating regions. The control performance can also be deteriorated when the controllers are switched. In this paper, a linear parameter-varying (LPV) strategy is proposed to solve such problems. Jacobian linearization and curve fitting are applied to derive the LPV model, which is verified using a nonlinear dynamic model and determined to be sufficiently accurate for control studies. An output feedback H∞ controller is synthesized to stabilize the steam temperature system and reject reactor power disturbances. The LPV steam temperature controller is implemented using a nonlinear dynamic model, and step changes in the setpoints and typical load patterns are carried out in the testing process. It is demonstrated through numerical simulation that the LPV controller not only stabilizes the steam temperature under different disturbances but also efficiently rejects reactor power disturbances and suppresses the steam temperature variation at different power levels. The LPV approach is effective in solving control problems of the steam temperature in the Canadian SCWR.

Batch Mode TD($\lambda$ ) for Controlling Partially Observable Gene Regulatory Networks.

External control of gene regulatory networks (GRNs) has received much attention in recent years. The aim is to find a series of actions to apply to a gene regulation system making it avoid its diseased states. In this work, we propose a novel method for controlling partially observable GRNs combining batch mode reinforcement learning (Batch RL) and TD() algorithms. Unlike the existing studies inferring a computational model from gene expression data, and obtaining a control policy over the constructed model, our idea is to interpret the time series gene expression data as a sequence of observations that the system produced, and obtain an approximate stochastic policy directly from the gene expression data without estimation of the internal states of the partially observable environment. Thereby, we get rid of the most time consuming phases of the existing studies, inferring a model and running the model for the control. Results show that our method is able to provide control solutions for regulation systems of several thousands of genes only in seconds, whereas existing studies cannot solve control problems of even a few dozens of genes. Results also show that our approximate stochastic policies are almost as good as the policies generated by the existing studies.

Distributed Control for Multiagent Consensus Motions with Nonuniform Time Delays

This paper solves control problems of agents achieving consensus motions in presence of nonuniform time delays by obtaining the maximal tolerable delay value. Two types of consensus motions are considered: the rectilinear motion and the rotational motion. Unlike former results, this paper has remarkably reduced conservativeness of the consensus conditions provided in such form: for each system, if all the nonuniform time delays are bounded by the maximal tolerable delay value which is referred to as “delay margin,” the system will achieve consensus motion; otherwise, if all the delays exceed the delay margin, the system will be unstable. When discussing the system which is intended to achieve rotational consensus motion, an expanded system whose state variables are real numbers (those of the original system are complex numbers) is introduced, and corresponding consensus condition is given also in the form of delay margin. Numerical examples are provided to illustrate the results.

Evolutionary Fixed-Structure Controller Tuning Against Multiple Requirements

This work deals with a new Matlab tool for computing fixed-structure controller against multiple requirements. Based on evolutionary computation, it allows solving control problems based on complex specifications, i.e. criterion whose gradients or sub gradients can’t be easily formulated: thus it appears to be well adapted to the industrial framework. The tool is described and few examples show its efficiency in computing fixed-structure controller against complex specifications.

Control System Design for a Five-Degree-of-Freedom Electrospindle Supported With AC Hybrid Magnetic Bearings

This study investigates a five-degree-of-freedom (5-DOF) electrospindle that is supported with ac hybrid magnetic bearings (HMBs). Compared with electrospindles supported with magnetically suspended dc magnetic bearings, an electrospindle supported with ac magnetic bearings is cost effective and efficient. Therefore, the application value of the latter to the project is higher than that of the former. An analysis from a previous work on the 5-DOF ac HMB-supported electrospindle had determined its insufficiencies. Based on this analysis, this study focuses on solving control problems in practical applications by designing a control system. The control system design includes the overall schematic, prototype, hardware, and software designs. Several performance tests have been conducted to verify the effectiveness of the proposed control system design. Results of the tests indicate that the rotor has excellent characteristics, such as good start-of-suspension performance, stable suspension characteristics with and without load, excellent antidisturbance characteristics, and faultless suspension characteristics within the supercritical speed range with an improved controller. Finally, subsequent measures for future research on the 5-DOF ac HMB-supported electrospindle are also provided.

Analytical methods in technological and environmental studies

The possibilities of modern analytical techniques to solve control problems in high-technology and environmental studies are considered. The first part of the article provides a review of the key concepts of the analytica. The second part is devoted to the problems associated with the analytical software technologies for high-purity substances and evaluation of the detection limits of elements by atomic spectrometry methods. The final part describes the analytical methods used in environmental monitoring. The main attention is paid to the studies that have been intensively conducted at the Research Institute of Chemical Reagents and Special Purity Chemical Substances, starting with 1970s. The institute has preserved traditional approaches and comprehensive research programs until present, even though the range of research topics is not so wide and the problems to be solved are not so ambitious.

Hybrid optimization schemes for quantum control

Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a holonomic phasegate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotov's method yields considerably better results than either one of the two methods alone.

Control of the phase boundary evolution in solidification

An approach to solving control problems for thermal processes with phase transitions is proposed. The problem of controlling the phase boundary evolution in the course of solidification in metal casting is studied by following this approach. A mathematical model of this process is underlain by a three-dimensional nonstationary two-phase initial–boundary value problem of the Stefan type. The control function is determined by solving the optimal control problem formulated in this work.

The Bubnov–Galerkin method in control problems for bilinear systems

We suggest to apply the Bubnov---Galerkin method to solving control problems for bilinear systems. We reduce the solution of a control problem to a finite-dimensional system of linear problem of mo...