Control Problem In Terms Research Articles

Robust Global Asymptotic Stabilization of Linear Cascaded Systems With Hysteretic Interconnection

We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

Backward Stochastic Volterra Integro-Differential Equations and Applications in Optimal Control Problems

In this article, a class of backward stochastic Volterra integro-differential equations (BSVIDEs) is introduced and studied. It is worthy mentioning that the proposed BSVIDEs cannot be covered by the existing backward stochastic Volterra integral equations (BSVIEs), and they also have the nice flow property such that Itô's formula becomes quite applicable. It is found that BSVIDEs can provide a neat sufficient condition for the solvability of BSVIEs with generator depending on the diagonal value of the solutions. As applications, the optimal control problems in terms of maximum principles and linear quadratic control problems of optimal control for forward stochastic Volterra integro-differential equations are investigated. In contrast with the BSVIEs in current literature, some interesting phenomena and advantages of BSVIDEs are revealed. (A corrected version is attached.)

Application of systematic error detection method to integral parameter measurements in sophisticated production processes and operations

This paper uses the Lagrange multiplier method to substantiate the general solution for validity control problem in terms of independently measured parameters of material flows. The paper shows that the efficiency of the above method can be raised if certain process parameters are measured in a number of independent ways by a dispatcher control system. A technique is described to adjust the initial measurement signals in case some channels have redundant information. Such technique is applicable if the values to be adjusted are identified over a period of time that greatly exceeds the dynamic memory of the object or if the dynamic links between certain channels are completely compensated and the execution of static equations of the studied processes is a prerequisite for the values to be adjusted. A method for systematic error detection in application to aggregate integral uncorrelated measurements was used as part of the NavoiAzot dispatcher control system for adjustment of per-shift and per-day performance indicators as calculated by the system. The paper considers the problem of selecting and retrieving valid data on the basis of redundant measurements of material flows and flow constraint equations. The paper describes a solution for the problem of selecting and retrieving valid data on the basis of redundant measurements of material flows and flow constraint equations in application to a complex fertilizer production monitoring system.

Robust Space Trajectory Design Using Belief Optimal Control

This paper presents a novel approach to the robust solution of optimal impulsive control problems under aleatory and epistemic uncertainty. The novel approach uses belief Markov decision processes to reformulate the control problem in terms of uncertainty distributions, called beliefs, rather than the realizations of the system states. This formulation leads to the definition of a belief optimal control problem where the cost function and constraints are functions of the uncertainty distributions. The control formulation encompasses orbit determination arcs as well. The belief optimization is solved with a shooting-like transcription and a nonlinear programming solver to optimize the resulting discretized problem. Both aleatory and epistemic uncertainties are propagated with a nonintrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimization of a flyby trajectory of the Europa Clipper mission in a scenario characterized by knowledge, execution, and observation uncertainty.

PROBLEMS REGARDING THE USE AND CONTROL OF SOCIAL MEDIA AS A PROPAGANDA TOOL IN CONTEXT OF DIGITAL DEMOCRACY

In the context of digital democracy, the use of social media for propaganda purposes causes control problems in terms of administrative units. Discussions on the control of social media, which is preferred due to advanced message transmission facilities, are stuck between democracy and security concerns. It can be said that the use of such channels by both legal and illegal organizations requires an audit. However, due to their foreign origin and global spread, the control of this field cannot be fully ensured. On the other hand, the fact that local law practices can suppress opposition blocks in favor of the governments makes this area problematic in terms of digital democracy. As a result of this qualitative analytical research conducted with the literature review method, it is seen that legal and illegal organizations use social media effectively to spread their messages within the framework of the concept of democratic rights. Meanwhile, acts incompatible with local law and social morality may occur. Since control mechanisms have a responsibility to establish and maintain social peace, these channels should be kept under control in terms of criminal acts. In a virtual environment where all geographies meet, where the definition of rights and crimes can change, it is inevitable that the supervisory bodies will be forced during the implementation of local legal rules. Despite this, it is essential to provide an audit that protects human rights within the criteria of democracy, justice and equity, encourages the formation of the public sphere, and guarantees organizational and individual freedoms.

Optimal control of microbial production in the chemostat

In this work, we study the problem of maximizing microbial production within a continuous stirred-tank reactor with n ≥ 1 species and one substrate. The interaction between species is described by the chemostat system including a mutation factor. The optimization problem falls into an optimal control problem of Lagrange type in which the control parameter is the dilution rate of the reactor. Thanks to the Pontryagin Maximum Principle, we obtain necessary conditions on optimal controls that involve a singular arc. These computations are highlighted thanks to numerical simulations via a direct method. We also study the related optimization problem at steady-state which provides an insight into optimal solutions of the optimal control problem in terms of turnpike phenomenon.

On the structure of the singular set of solutions in one class of 3D time-optimal control problems

A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.

Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations

<p style='text-indent:20px;'>The convective Brinkman-Forchheimer (CBF) equations describe the motion of incompressible viscous fluids through a rigid, homogeneous, isotropic, porous medium and is given by</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \partial_t{\boldsymbol{u}}-\mu \Delta{\boldsymbol{u}}+({\boldsymbol{u}}\cdot\nabla){\boldsymbol{u}}+\alpha{\boldsymbol{u}}+\beta|{\boldsymbol{u}}|^{r-1}{\boldsymbol{u}}+\nabla p = {\boldsymbol{f}},\ \nabla\cdot{\boldsymbol{u}} = 0. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>In this work, we consider some distributed optimal control problems like total energy minimization, minimization of enstrophy, etc governed by the two dimensional CBF equations with the absorption exponent <inline-formula><tex-math id="M1">\begin{document}$ r = 1,2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>. We show the existence of an optimal solution and the first order necessary conditions of optimality for such optimal control problems in terms of the Euler-Lagrange system. Furthermore, for the case <inline-formula><tex-math id="M3">\begin{document}$ r = 3 $\end{document}</tex-math></inline-formula>, we show the second order necessary and sufficient conditions of optimality. We also investigate an another control problem which is similar to that of the data assimilation problems in meteorology of obtaining unknown initial data, when the system under consideration is 2D CBF equations, using optimal control techniques.</p>

Application of internal point methods in cybersecurity problems of intelligent energy systems

The paper considers approaches to the creation of intelligent energy systems based on WAMS monitoring systems, using information technology in metrology, in the means of receiving, processing and transmitting information and determining parameters in control tasks. The paper analyzes the existing cyberattacks on the SCADA and WAMS system and considers possible ways to solve control problems in terms of information security violations of intelligent energy systems. DoS-attacks are considered in more detail, which lead to the failure of devices that measure currents, voltages and capacities, as well as to the disruption of information processing equipment. The paper proposes an algorithm for estimating the state of cyber defense of the intelligent energy system based on mathematical modeling of the internal states of the system, which allows to obtain the required accuracy of calculations in terms of incomplete information, which is the inability to access measurement data.

Complexity of control in judgment aggregation for uniform premise-based quota rules

The task of aggregating individual judgments over logically interconnected propositions is called judgment aggregation. Manipulation of judgment aggregation procedures has first been studied by List [45] and Dietrich and List [27], and Endriss et al. [30] were the first to study it from a computational perspective. Baumeister et al. [7] extended their results on manipulation and introduced the concept of bribery in judgment aggregation, again focusing on algorithmic and complexity-theoretic properties. Complementing this previous work on strategic scenarios, we introduce the concept of control in judgment aggregation, making use of the preference types introduced by Dietrich and List [27] and studying the class of uniform premise-based quota rules for these control problems in terms of their computational complexity.

Design and experimental testing of an optimization-based flow control algorithm for Energy Harvesting Wireless Sensor Networks

In this paper a distributed flow control law is proposed to maximize throughput and to minimize energy consumption in Energy Harvesting Wireless Sensor Networks (EH-WSNs). We preliminary recast the control problem in terms of primal–dual optimization one taking into account the bandwidth and energy autonomy node constraint. Then, we devise a distributed flow rate control implemented at each node that allows the overall network to converge to the optimal solution of the original problem. The closed loop EH-WSN stability and convergence to the optimal equilibrium are proven. The effectiveness of the proposed control law in terms of throughput and network lifetime performance is experimentally validated by a small representative EH-WSN. The experimental results are in a good agreement with the theoretical ones.

Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls

The article considers a two-level open quantum system whose dynamics is driven by a combination of coherent and incoherent controls. Coherent control enters into the Hamiltonian part of the dynamics whereas incoherent control enters into the dissipative part. The goal is to find controls which move the system from an initial density matrix to a given target density matrix as fast as possible. To achieve this goal, we reformulate the optimal control problem in terms of controlled evolution in the Bloch ball and then apply Pontryagin maximum principle and gradient projection method to numerically find minimal time and optimal coherent and incoherent controls. General method is provided and several examples of initial and target states are explicitly considered.

Dynamic Modelling and Control of Thermal Energy Storage

Thermal energy storage (TES) is a critical element in district heating systems and having a good understanding of its dynamic behaviour is necessary for effective energy management. TES supports heat sources in achieving a steady power supply. Achieving heat and electric load demand translates into a discharging and charging control problem in terms of stored heat energy. To this end, an accurate dynamic model is essential to design effective controllers to improve district heating performance. A thermal dynamic model of a water tank, together with controllers for energy charging and discharging processes, are presented in this paper. The model is based on a computational fluid dynamics approach. It is developed using thermal stratification. The hot or cold-water stream which vertically crosses each tank section is considered to describe heat transfer. This is a non-linear process represented by partial differential equations, which are linearised to obtain a suitable model for control system design. State-space and transfer function representations of the system are obtained. The non-linear model is implemented in MATLAB/Simulink to design a linear controller that regulates the mass flow rate of cold and hot water to fill or empty the tank’s energy according to performance specifications. The design of regulation and tracking controllers is explained. Simulation results show that a good performance in terms of the mass flow rate input demands is achieved with the proposed controllers.

Finding and analysing the minimum set of driver nodes required to control multilayer networks

It is difficult to control multilayer networks in situations with real-world complexity. Here, we first define the multilayer control problem in terms of the minimum dominating set (MDS) controllability framework and mathematically demonstrate that simple formulas can be used to estimate the size of the minimum dominating set in multilayer (MDSM) complex networks. Second, we develop a new algorithm that efficiently identifies the MDSM in up to 6 layers, with several thousand nodes in each layer network. Interestingly, the findings reveal that the MDSM size for similar networks does not significantly differ from that required to control a single network. This result opens future directions for controlling, for example, multiple species by identifying a common set of enzymes or proteins for drug targeting. We apply our methods to 70 genome-wide metabolic networks across major plant lineages, unveiling some relationships between controllability in multilayer networks and metabolic functions at the genome scale.

Optimal Distributed Control of a Generalized Fractional Cahn–Hilliard System

In the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” by the same authors, general well-posedness results have been established for a class of evolutionary systems of two equations having the structure of a viscous Cahn–Hilliard system, in which nonlinearities of double-well type occur. The operators appearing in the system equations are fractional versions in the spectral sense of general linear operators A, B having compact resolvents, which are densely defined, unbounded, selfadjoint, and monotone in a Hilbert space of functions defined in a smooth domain. In this work we complement the results given in the quoted paper by studying a distributed control problem for this evolutionary system. The main difficulty in the analysis is to establish a rigorous Frechet differentiability result for the associated control-to-state mapping. This seems only to be possible if the state stays bounded, which, in turn, makes it necessary to postulate an additional global boundedness assumption. One typical situation, in which this assumption is satisfied, arises when B is the negative Laplacian with zero Dirichlet boundary conditions and the nonlinearity is smooth with polynomial growth of at most order four. Also a case with logarithmic nonlinearity can be handled. Under the global boundedness assumption, we establish existence and first-order necessary optimality conditions for the optimal control problem in terms of a variational inequality and the associated adjoint state system.

Optimal position targeting via decoupling fields

We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle, we characterize a solution of the unconstrained control problem in terms of a fully coupled forward–backward stochastic differential equation (FBSDE). We use the method of decoupling fields for proving that the FBSDE has a unique solution. We exploit a monotonicity property of the decoupling field for solving the original constrained problem and characterize its solution in terms of an FBSDE with a free backward part.

Adaptive nonlinear ship tracking control with unknown control direction

SummaryThis paper is to suggest a novel design for ship tracking control of the benchmark Norrbin nonlinear ship model under relaxed conditions. The challenges of the problem under investigation include the uncertain or absent information of the model time constant, the uncertain reference course, and the intrinsic environmental disturbances. We formulate the ship tracking control problem in terms of a nonlinear output regulation problem with unknown control direction and uncertain exosystems. To solve the problem, we first adopt a novel internal model candidate to convert the output regulation problem into a stabilization problem for an augmented system. Then, a Nussbaum‐gain‐based stabilizer is developed for the augmented system to complete the design. Simulation results are presented to show the effectiveness of the proposed controller.

Optimal control in teleoperation systems with time delay: A singular perturbation approach

The main goal of controller design in teleoperation systems is to achieve optimal performance, transparency and stability in presence of factors such as time delay in communication channel and modeling uncertainties. The teleoperation systems usually have complex dynamic. Consequently, differential equation solution of optimal control problem is difficult and complex for them. This paper presents a novel method for designing optimal controller based on singular perturbation framework for these systems. Firstly, we use the Taylor expansion to model the time delay, with considering time delay term; we derive a singular perturbation formulation for the teleoperation system. Using singular perturbation model and Chang decoupling transformation, singularly perturbed differential equations of optimal control problem is decomposed into the reduced order slow and fast differential equations. A formula is obtained that produces the solution of original differential equations of optimal control problem in terms of solutions of the slow and fast reduced order matrix differential equations. The reduced-order differential equations decrease the complexity of the optimal control problem for teleoperation systems. The simulations verify the effectiveness of the proposed control method and excellent performances tracking with high speed and small control signal.

On a Class of Path-Dependent Singular Stochastic Control Problems

This paper studies a class of non-Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a Z-constrained BSDE, with dynamics associated to a non singular underlying forward process. Due to the non-Markovian environment, our main argumentation relies on the use of comparison arguments for path dependent PDEs. Our representation allows in particular to quantify the regularity of the solution to the singular stochastic control problem in terms of the space and time initial data. Our framework also extends to the consideration of degenerate diffusions, leading to the representation of the solution as the infimum of solutions to Z-constrained BSDEs. As an application, we study the utility maximization problem with transaction costs for non-Markovian dynamics.

Discrete-Time Fractional Optimal Control

A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α .