Interconnected Subsystems Research Articles

Decentralized discrete adaptive sliding mode control for interconnected nonlinear systems

This article presents a study on controlling a class of large-scale systems composed of interconnected subsystems. The systems are represented by discrete block-oriented models with unknown parameters. This article proposes a novel adaptive sliding mode control strategy to address the tracking control problem and minimize the impact of interconnection. This approach leverages the robustness of sliding mode control against unmodeled dynamics and disturbances with the advantages of adaptive control. To adapt the system’s parameters, a recursive parametric estimation algorithm using least-squares techniques is employed. The proposed method offers benefits such as robustness against parameter uncertainties, handling of nonlinearities, improved tracking accuracy, and reduced chattering phenomena. The effectiveness of the method is demonstrated through the evaluation of two simulation examples.

Dynamic probabilistic risk assessment with K-shortest-paths planning for generating discrete dynamic event trees

Conventional risk assessment methods are often not well suited for fast-changing dynamic and complex systems since the results from the analysis may be averages or valid for a short time before the system’s state changes. A response to this problem is dynamic probabilistic risk assessment (DPRA), which considers the ever-changing nature of such systems and how their dynamic behavior affects the likelihood of future accident scenarios. Performing DPRA is difficult for complex systems — i.e., systems with many interconnected subsystems and components, for example, autonomous systems. There is a combinatorial “explosion” when considering how component failures affect one another and the overall system performance, known in the DPRA literature as the “state explosion problem”, causing DPRA methods to have poor computational performance for large-scale systems. Although solutions to state explosion alleviate the average-case performance, most DPRA methods remain computationally expensive, with exponential worst-case time complexities. In this paper, a method for solving DPRA problems with K-Shortest-Paths planning algorithms is proposed. The method, called KPRA, consists in framing a subset of DPRA problems as relaxed versions of the K-Shortest-Paths (KSP) planning problem, allowing these DPRA problems to be solved by a graph search algorithm called K*, which has a theoretical log-linear worst-case complexity. Therefore, in theory, KPRA with K* solves DPRA problems with computational performance better than exponential. KPRA was implemented and applied to a case study of DPRA for an autonomous ship for validation and comparison with conventional DPRA methods. The case study consists of two ships, one of them autonomous, in a crossing encounter with a possible collision risk. The task is to find the most critical situations for the autonomous ship, i.e., the scenarios where its collision risk is the highest. KPRA’s performance in solving the case study is compared with two conventional DPRA methods. The results show that the KPRA implementation in this work can solve the case study, i.e., produce an output equivalent to the other methods, with a polynomial worst-case computational complexity, i.e., more efficiently than the other methods with exponential complexities.

An improved robust distributed [formula omitted] control method for uncertain interconnected large-scale time-delayed systems

In modern industries, systems have become increasingly large-scale and complex, comprising multiple interconnected subsystems where the performance of each subsystem impacts the others. Ensuring stability and performance under uncertainties, external disturbances, and time delays is crucial for such systems. This paper proposes a new distributed control method that stabilizes a specific type of time-varying input-delayed large-scale system in the presence of uncertainties and external disturbances. The proposed method employs Jensen’s inequality to reduce the number of decision variables and uses reciprocally convex and descriptive methods to minimize conservatism and decrease computation time. The performance of the proposed method is evaluated on a full-car model with an active suspension system as a novel approach to controlling large-scale systems. This paper describes how to divide a large-scale full-car system into several interconnected subsystems, for the first time. The results indicate the potential of the proposed controller in enhancing the performance of the system in comparison with other previous control methods.

Decentralized QFT Controller Design Based on the Equivalent Subsystems Method

Since the 1970s various decentralized control methodologies have been developed to deal with the challenge of controlling complex and/or spatially distributed systems with multiple inputs and multiple outputs (MIMO), e.g., chemical plants, power systems, water systems, etc. In general, the use of distributed information and control structures requires the synthesis of control laws in a constrained (decentralized) information structure. The article presents a novel frequency domain robust decentralized controller design method that is appropriate for uncertain dynamic MIMO systems with equal numbers of input and output variables, which consist of interconnected physical subsystems and are given as a set of square transfer function matrices. The main framework of the proposed method provides the Equivalent Subsystems Method (ESM), whereby the overall closed-loop system under a decentralized controller is stable if, and only if, all the individual closed-loop equivalent subsystems are stable. By generating equivalent subsystems for all transfer matrices, which describe the uncertain MIMO system, the individual uncertain equivalent subsystems are obtained as sets of respective frequency responses. Such representation allows the application of the QFT (quantitative feedback theory) approach to independently design local single-input single-output (SISO) robust controllers which constitute the resulting decentralized controller implemented in real subsystems. The designed controller ensures robust stability of the overall closed-loop system and the required performance as specified by the standard QFT performance specification types in both the equivalent subsystems and the overall closed-loop system. Compared to the existing method and references therein, the proposed method reduces the conservatism of the robust stability conditions and enables the exploitation of the benefits by the SISO QFT approach in the independent design of the robust decentralized controller. The developed design procedure is verified and illustrated in a case study on the robust decentralized level controller design of the quadruple tank process.

Formation of information decision support system in the diagnostics of management efficiency of enterprise’s financial and economic activity

The complexity management of financial and economic activity of the enterprise requires the search for qualitatively new approaches to the formation, systematization and analysis of information in order to identify and solve the problems of developing a strategy and tactics for the development of the enterprise. The purpose of the paper is the formation and justification of the structure of information support system’s formation concerning decisions in the diagnostics of financial and economic activity of the enterprise management efficiency, which is aimed at increasing the effectiveness of management decision-making of a strategic and tactical nature. The tasks of the information support system for diagnostics of financial and economic activity of the enterprise management efficiency have been determined, which allows to eliminate a number of causes of information uncertainty in the process of managing the enterprise's activities. It is proved that the system of information support for decision-making in the diagnosis of financial and economic activity of the enterprise management efficiency should be considered in the form of three interconnected subsystems, which are lower-order systems, namely: the financial and information system, the system of financial and information diagnostics and the system of detected financial problems. The author proposed a comprehensive functionality of all components of the information support system for decision-making support in the diagnosis of the management of the financial and economic activities of the enterprise, which will increase the validity and effectiveness of the management decisions made, taking into account the influence of the instability of the external and internal environment of its functioning.

Non-iterative multi-area coordinated energy and reserve allocation model for hybrid AC/DC power systems with flexible frequency operation

As the result of renewable energy natural intermittency, load shedding and renewables curtailment are inevitable to keep supply and demand balance in high penetration level power systems. Luckily, with accurate estimation and proper allocation of the reserve, power fluctuation can be smoothed appreciably. Therefore, this study presents a novel coordinated day-ahead economic dispatch model for both energy and reserve in bulk hybrid AC/DC power systems. Flexible frequency operation for each regional sub AC system is applied to estimate reserve demand, while renewable energy forecast error is described by the versatile probability distribution. Considering practical operation structure in China, a non-iterative bi-layer dispatch algorithm is proposed to share power and reserve between interconnected subsystems by applying DC tie-lines’ flexibility. This bi-layer structure is achieved through the upper layer deciding the boundary variables with aggregated generation information provided by the lower layer. Then each lower layer regional AC grid solves its own programming with the boundary variables. Simulation is carried out to verify the efficacy of the proposed dispatch model and distributed solution methodology.

Adaptive Output Feedback Control for Nonholonomic Chained Systems with Integral Input State Stability Inverse Dynamics.

This paper investigates a class of nonholonomic chained systems with integral input-to-state stable (iISS) inverse dynamics subject to unknown virtual control directions and parameter uncertainty included in drift terms. First, the system is divided into two interconnected subsystems according to the system's structure. Second, one controller is designed using a switch strategy for state finite escape. Then, another controller and adaptive law are designed by combining a reduced-order state observer and backstepping method after input-state scaling. Finally, simulation results validate the feasibility of the proposed control algorithm.

Distributed Model Predictive Control and Coalitional Control Strategies—Comparative Performance Analysis Using an Eight-Tank Process Case Study

Complex systems composed of multiple interconnected sub-systems need to be controlled with specialized control algorithms. In this paper, two classes of control algorithms suitable for such processes are presented. Firstly, two distributed model predictive control (DMPC) strategies with different formulations are described. Afterward, a coalitional control (CC) strategy is proposed, with two different communication topologies, i.e., a default decentralized topology and a distributed topology. All algorithms were tested on the same simulation setup consisting of eight water tanks. The simulation results show that the coalitional control methodology has a similar performance to the distributed algorithms. Moreover, due to its simplified formulation, the former can be easily tested on embedded systems with limited computation storage.

A Non-Equilibrium Thermodynamic Approach for Analysis of Power Conversion Efficiency in the Wind Energy System

This article proposes an approach and develops an appropriate method of applying linear non-equilibrium thermodynamics to analyze energy processes, in particular using the example of the wind energy conversion system (WECS) with a directly connected vertical axis wind turbine (VAWT) and vector-controlled permanent magnet synchronous generator (PMSG). The main steps of the proposed approach are the description of the component subsystems as universal linear or linearized energy converters (ECs), which are characterized by several dimensionless parameters, the main one of which is the degree of coupling between their input and output. According to their value, as well as justified efficiency criteria, the optimal operating points of each ECs can be easily found. Such an approach makes it possible to abstract from physical laws of a different nature and equally assess the work of each of the subsystems. The next step is a connection of the received ECs. As shown in the paper, for the most common cascade connection of ECs, there are the best conditions for their connection, under which the newly formed equivalent EC can have maximum efficiency. This opens up an opportunity to analyze the influence of already real parameters of cascaded interconnected subsystems on the quality of their connection and justify specific solutions that would not have been seen without this approach. For example, in this study, from all parameters of the PMSG, only the selection of the optimal rated inductance of the armature winding made it possible to improve the quality of the connection of the PMSG with a specific VAWT and approximate the efficiency of the entire WECS to the maximum possible, especially in medium and high winds.

PROPERTIES OF SCHWARZ MATRICES IN DISCRETE-TIME LINEAR SYSTEMS

In this paper, we investigate the properties of the Schwarz matrix, a specific type of matrix that appears in the stability analysis of discrete-time linear time-invariant systems. We derive a formula for the determinant of the Schwarz matrix and a formula for its permanent. We also provide conditions on the entries of the Schwarz matrix that ensure the system described by the state update equation $x_{k+1} = Bx_k$ is stable, as well as conditions that guarantee the eigenvalues of the Schwarz matrix are real. These findings provide insights into the stability properties of systems characterized by Schwarz matrices and offer new tools for the analysis of interconnected subsystems in a cascaded structure.

Purpose and prospects for the development of cyberphysical systems for technoligical processes

The article is devoted to a new way of organizing production that is actively developing in the conditions of the industry's information transformation associated with the introduction of cyber-physical systems. Market analysis shows a positive trend in the growth of capitalization of this industry, indicating the widespread use of digital transformation tools for production and increased investment in the development of information technologies, including the creation and implementation of cyber-physical systems. The article analyzes the existing definitions of "cyber-physical systems" and "cyber-physical complexes." It also reveals the concept of a cyber-physical control system for the technological processes" and describes its main structure. The cyber-physical control system is considered a number of interconnected subsystems that perform strictly defined functions. The article presents a description of each of these subsystems, a generalized scheme of their hierarchical connections, and interactions. The article also considers the role of cyber-physical control systems in the information transformation of the industry and discusses the prospects for their future development.

A Co-Estimation Framework for State of Charge and Parameters of Lithium-Ion Battery With Robustness to Aging and Usage Conditions

Aging and usage conditions affect the battery parameters such as capacity and changes in the open-circuit voltage and internal resistance dependencies on the state of charge. This paper proposes an on-board strategy for the simultaneous estimation of these parameters and their robust evaluation during the battery life. The proposed co-estimation framework consists of a set of interconnected subsystems grounded on the integration of recursive least-squares techniques and a Luenberger-like observer which are independently designed by relying on moving averages of voltage and current measurements. Each subsystem is separately activated through logic variables which select the operating conditions proper for the estimation purposes and allows tracking of model parameters variations. The effectiveness of the solution is shown over experiments with a cylindrical LG M50T INR21700 Li-ion cell with NMC cathode and graphite/silicon anode.

Integral Quadratic Constraints with Infinite-Dimensional Channels.

Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinite-dimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinite-dimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity.

UDE-Based Dynamic Surface Control for Quadrotor Drone Attitude Tracking under Non-Ideal Actuators

Quadrotor drone attitude tracking is inevitably affected by the combination of model uncertainties, external disturbances, and non-ideal actuator dynamics during stable flight and complex maneuvers. In order to achieve precise attitude control in these situations, a cascade-structured dynamic surface control (DSC) strategy is proposed based on an uncertainty and disturbance estimator (UDE), considering the actuator dynamics as represented by a first-order plus time-delay model. The DSC scheme is used to transform the original attitude dynamics system into a set of interconnected subsystems. On the one hand, the mismatched disturbances in the attitude kinematics and dynamics loops are converted into matched disturbances to accommodate the structural constraints of the UDE so that these disturbances, as well as the non-ideality caused by the actuator time delay, are estimated and compensated for by the approach. On the other hand, the “complexity explosion” problem is addressed by the first-order filter employed by DSC. The ultimate boundedness of the closed-loop system is proven while the parameter design constraints are provided. MATLAB Simulink simulations are conducted to demonstrate the desirability of considering actuator dynamics and to verify that the proposed control strategy can relax the constraints of the control parameters and enable a higher accuracy.

PHARMACEUTICAL MARKETING AS A MARKETING SYSTEM AT THE MACRO LEVEL: STRUCTURE AND FEATURES

The article addresses theoretical and methodological foundations of the marketing systems of the pharmaceutical market at the macro level. The size and social significance of this market determine the need to ensure its proper functioning as a whole system, but the systemic approach to marketing in general and to that of a specific industry remains underdeveloped. Marketing policy still mainly relies on the classical marketing mix, developing in the framework of marketing management approach that is in the micro-framework. Thus, issues related to societal interests in the functioning of markets, such as ensuring sustainability, development of human capital, and quality of life, remain without a proper apparatus of studying and action, on the margin of interests of market actors. This determines the relevance of the study. Based on the systematisation and generalisation of specific features of the pharmaceutical market and using the apparatus and approaches of macro marketing, the general structure of the marketing system is shaped grounded in a specific difference in mechanisms of creation and delivery of consumer value, attributed to the mechanism of drug prescription. Therefore, two interconnected subsystems of the pharmaceutical market marketing system are suggested: prescription and over-the-counter (OTC) drugs. Managing the first subsystem requires the use of approaches and tools inherent in B2B marketing. The creation and realisation of consumer value here is based on the objective needs of end consumers and is strongly influenced by the expert and professional environment. Taking into account the importance of the pharmaceutical market for ensuring social well-being, the need to create new pharmaceutical products may not always be justified by the significance of the market size, anticipating the need for non-market financing, support from market externalities The subsystem relies both the mechanisms of competition and that of cooperation; uses innovative management and marketing, to a certain extent this subsystem depends on the ability to ensure network of interaction between market participants. Such features of the first subsystem obviously have an impact on the second, where the need to ensure social well-being determines the general direction and sets guidelines and restrictions for marketing programmes of individual market participants. The effective functioning of the whole system is based on a combination of mechanisms of cooperation, vital considering a strong need for externalities, and competitive marketing based on specific characteristics of the pharmaceutical industry and market. Key aspects of macromarketing of the pharmaceutical market have been identified to ensure the management of the marketing system of the market system at the macro level.

ОСНОВНІ СКЛАДОВІ ЕЛЕМЕНТИ АДМІНІСТРАТИВНО-ПРАВОВОГО ЗАБЕЗПЕЧЕННЯ ПРАВ І СВОБОД ЛЮДИНИ

The article defines the main constituent elements of the administrative and legal provision of human and citizen rights and freedoms. The content of administrative and legal support is clarified, in particular, it is proposed to understand how the activity of state authorities is determined and regulated by legislation, in order to ensure the optimal mechanism for organizing, consolidating, implementing, protecting and protecting social relations with respect to human rights and freedoms. An analysis of concepts similar in content in different variable combinations was carried out. It is noted that under "collateral" should be understood the conditions of guarantee. Legal support is the activity of the state regulated, established and aimed at realizing the rights, freedoms and legitimate interests of its citizens. It is emphasized that the mechanism of administrative and legal protection of human rights and freedoms is a single integral system of legal means, with the help of which legal regulation of social relations is carried out. The author traditionally proposes to include the norms of administrative law among the elements of the mechanism of administrative and legal support; legal fact; acts of direct implementation of the right; acts of application of the law, which establish and implement the provisions of administrative and legal norms. It is said that administrative and legal norms are the primary structural elements of administrative regulation of social relations in the sphere of ensuring the rights and freedoms of a person and a citizen. It is emphasized that they occupy the central link, since their absence leads to inactivity of the entire system of functioning of administrative law. In conclusion, it is outlined that the mechanism of administrative and legal protection of human rights and freedoms has its own specifics, in particular: the structure of the mechanism, which includes two interconnected subsystems; the mechanism acts as a means of implementing state power in relation to the management of public relations as a whole; the mechanism of administrative and legal support is characterized by its own, specific content.

Distributed Economic MPC for Dynamically Coupled Linear Systems: A Lyapunov-Based Approach

This article develops a distributed economic model predictive control (EMPC) method which is applied in a group of interconnected linear subsystems subject to unknown bounded disturbances. Multiple subsystems are coupled through the dynamics, and the control objective is to optimize some general performance criteria of the whole system which may take economic considerations into account. First, a two operation modes EMPC optimization problem is formulated, which incorporates the constraints derived from the Lyapunov technique. In the first mode, each subsystem focuses on the optimization of the economic performance while maintaining the state in a certain region. In the second mode, the system states are steered to a neighborhood of a steady state by making use of the Lyapunov-based constraints. Furthermore, a consensus alternating direction method of multipliers (ADMM) is adopted to solve the model predictive control optimization problems with a coupled predicted model constraint in a distributed way. By introducing consensus constraints, the resulting local optimization problem does not depend on real-time optimal solutions from neighboring subsystems and allows subsystems to solve it in parallel. Moreover, the closed-loop system is ensured to be input-to-state stable (ISS) with respect to the disturbances. To demonstrate the effectiveness of the algorithm, we conduct numerical simulations on a thermal power interconnected system.

Scalable Regret for Learning to Control Network-Coupled Subsystems With Unknown Dynamics

In this article, we consider the problem of controlling an unknown linear quadratic Gaussian (LQG) system consisting of multiple subsystems connected over a network. Our goal is to minimize and quantify the regret (i.e., loss in performance) of our learning and control strategy with respect to an oracle who knows the system model. Upfront viewing the interconnected subsystems globally and directly using existing LQG learning algorithms for the global system results in a regret that increases super-linearly with the number of subsystems. Instead, we propose a new Thompson sampling-based learning algorithm which exploits the structure of the underlying network. We show that the expected regret of the proposed algorithm is bounded by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tilde{\mathcal {O}} (n \sqrt{T})$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of subsystems and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> is the time horizon. Thus, the regret scales linearly with the number of subsystems. We present numerical experiments to illustrate the salient features of the proposed algorithm.

Dynamics of a coupled socio-environmental model: An application to global CO2 emissions

In this article, a novel coupled socio-environmental model is proposed and analysed using real data. The model is formulated with two interconnected subsystems: a human–environment model that describes the state of forest cover, human population, and atmospheric carbon dioxide (CO2) concentration; and a socio-economic model that represents human behaviour as a dynamical variable. Human behaviour focuses on their opinion about forest conservation, which affects the harvesting rate per unit area. We examine the mathematical model analytically and numerically to gain insight into the dynamics of the coupled system. By plotting the basin of attractions, we show that when an initial abundance of forest cover is small, and there is a low fraction of conservationists, the system eventually stays at a higher density of forest cover and a higher fraction of conservationists. However, for intermediate to high values of initial forest cover, the system stays at a low forest cover and a low fraction of conservationists among people. With an increase in the economic cost, after a certain threshold, we observe that the number of cooperators increases despite the forest cover being very low. Further, the model is validated using yearly data on forest cover and atmospheric CO2 in the period 1990–2016. The fitting to the data is performed using a MATLAB optimization technique, and the quality of the fitting is quantified using accuracy metrics. Numerical simulations using estimated parameters show that increasing forest cover is essential in reducing the CO2 level in the atmosphere. From a policy-making point of view, it is important to increase the proportion of conservationists in the community, which will eventually result in increased forest cover and consequently decrease the burden of atmospheric CO2 concentration.

Dissipativity Analysis of Large-Scale Networked Systems

This paper investigates the dissipativity analysis of large-scale networked systems with linear time-invariant dynamics. The networked system is composed of a large number of subsystems whose connections are arbitrary, and each subsystem can have different dynamics. A sufficient and necessary condition for the strict dissipativity analysis of the networked system is derived, which takes advantage of the block-diagonal structure of the system parameter matrix and the sparseness characteristics of the subsystem interconnections. Then, a necessary condition and a sufficient condition that depend only on a single subsystem parameter are given separately. Numerical simulations illustrate that compared with the existing results, the conditions suggested in this paper have higher computational efficiency in the dissipative analysis of large-scale networked systems.