Control Of Large-scale Systems Research Articles

Behavioral Analysis of Various Techniques of Model Order Reduction Used in the Reduction of Large Scale Control System

It is very important task to study the behavior of the processes occurring in the industry. To attain this task, the knowledge of the transfer function of the system should be there. When working in robust environment, these transfer functions becomes so tedious that it becomes very difficult to obtain these transfer functions and hence affects the study of the behavior of these system. Due to this, the requirement for reduction of these transfer function becomes a necessity to analyze the behavior of foresaid systems and it becomes easy to do the desired modifications in the system i.e addition of any feature, desired changes in the behavior etc., furthermore the thing to be kept in consideration while doing the reduction in transfer function that the behavior viz. peak overshoot, settling time, steady state error of the two systems (reduced and the original system) should be approximately same, so it is prime importance that the applied model order reduction technique should provide a more accurate approximation of original higher order system. The paper presents here the different categories of model order reduction techniques that can be applied to achieve the motto of model order reduction of higher order systems. The techniques presented are categorized into the four different categories to understand them and their merits and demerits and these will help in proper selection of the model order reduction technique to obtain the most accurate reduced order approximation of large scale system.

On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks

In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20–200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.

Optimization for Reinforcement Learning: From a single agent to cooperative agents

This article reviews recent advances in multi-agent reinforcement learning algorithms for large-scale control systems and communication networks, which learn to communicate and cooperate. We provide an overview of this emerging field, with an emphasis on the decentralized setting under different coordination protocols. We highlight the evolution of reinforcement learning algorithms from single-agent to multi-agent systems, from a distributed optimization perspective, and conclude with future directions and challenges, in the hope to catalyze the growing synergy among distributed optimization, signal processing, and reinforcement learning communities.

Lazy reinforcement learning for real-time generation control of parallel cyber–physical–social energy systems

To learn human intelligence, the social system/human system is added to a cyber–physical energy system in this paper. To accelerate the configuration process of the parameters of the cyber–physical energy system, parallel systems based on artificial societies-computational experiments-parallel execution are added to the cyber–physical energy system, i.e., a parallel cyber–physical–social energy system is proposed in this paper. This paper proposes a real-time generation control framework to replace the conventional generation control framework with multiple time scales, which consist of long-term time scale, short-term time scale, and real-time scale. Since a lazy operator employed into reinforcement learning, a lazy reinforcement learning is proposed for the real-time generation control framework. To reduce the real simulation time, multiple virtual parallel cyber–physical–social energy systems and a real parallel cyber–physical–social energy system are built for the real-time generation control of large-scale multi-area interconnected power systems. Compared with a total of 146016 conventional generation control algorithms and a relaxed artificial neural network in the simulation of IEEE 10-generator 39-bus New-England power system, the proposed lazy reinforcement learning based real-time generation control controller can obtain the highest control performance. The active power between two areas and the systemic frequency deviation can be reduced by the lazy reinforcement learning, and the simulation results verify the effectiveness and feasibility of the proposed lazy reinforcement learning based real-time generation control controller for the parallel cyber–physical–social energy systems.

Coordinated design of PSS and unified power flow controller using the combination of CWT and Prony methods with the help of SPEA II multi‐objective optimisation algorithm

Since the initial objective of power system stabiliser (PSS) units and flexible AC transmission system (FACTS) devices is the damping of inter-area and local oscillations, it is very substantial that the network electromechanical oscillatory modes are identified for tuning the controller of large-scale interconnected power systems. In this research, a method based on the combination of continuous wavelet transform and Prony algorithm is presented to study low-frequency electromechanical oscillations of the power system. The coordinated design of PSS and FACTS parameters become a multi-objective optimisation problem that will be solved using the SPEA II. The residue method is used to improve damping and satisfy the controller constraints of the suggested power systems. Finally, the proposed method of mode estimation and controller design is simulated on the two well-known test case systems, namely IEEE 2-area 4-generator and New England- New York 68-bus 16-generator systems using MATLAB software. The results represent accurate performance and validity of the proposed method to improve oscillation damping, dynamic stability of the power systems.

A Predictive Control Scheme for Large-Scale Grid-Connected PV System Using High-Level NPC Inverter

This paper focuses on the control of large-scale grid-connected photovoltaic system. The proposed system is composed of two conversion stages: the first stage contains four PV arrays, each one connected to an individual DC/DC converter (boost converter), while the second stage is a five-level neutral point clamped (NPC) inverter tied to the grid. Each DC-link capacitor input of the NPC inverter is connected to the output of the DC/DC boost converter. In order to enhance the energy harvesting capability of the proposed system, different controllers based on finite-set model predictive control (FS-MPC) are developed and presented. A fast voltage-oriented maximum power point tracking performed by FS-MP current controller (FS-MPCC) is investigated and applied for each boost converter to maximize the produced power from each PV array. Furthermore, a FS-MPC algorithm is proposed to control the centralized five-level NPC inverter. The purposes of the developed controllers are: track the MPP rapidly and accurately under sudden irradiation changes, ensure the balance of the four DC-link capacitor voltages whatever the difference between the extracted powers from each PV system unit, inject the reactive power demanded by the grid operator and also minimize the switching frequency of the five-level NPC inverter. The results obtained through MATLAB/Simulink and Simpower toolbox packages prove that the proposed control scheme provides better performance in comparison with conventional control scheme. Moreover, a high grid current quality and perfect DC-link capacitor voltages balancing are ensured under contrast of extract powers from each PV system.

Observer-Based Adaptive Decentralized Fault-Tolerant Control of Nonlinear Large-Scale Systems With Sensor and Actuator Faults

This paper investigates the problem of decentralized fault-tolerant tracking control for nonlinear large-scale systems with sensor and actuator faults. Due to the adverse coupling effects that unknown sensor faults and output interconnections coexist, the previous methods fail to achieve decentralized tracking controls. Focus of this paper is particularly on addressing this issue. First, a decentralized fault-tolerant observer is constructed to simultaneously estimate unmeasured state and compensate the actuator faults. Then, an adaptive signal compensation mechanism is presented to mitigate the effects of sensor faults and output interconnections. By applying the cubic absolute-value Lyapunov function analysis method, it is shown that all the signals are bounded and the tracking error of each subsystem converges to an adjustable neighborhood of zero. An example of a large-scale power system is adopted to illustrate the effectiveness of the obtained scheme.

Globally Optimal State-Feedback LQG Control for Large-Scale Systems With Communication Delays and Correlated Subsystem Process Noises

This paper studies the optimal decentralized state-feedback control of large-scale systems. The large-scale system is composed of subsystems and defined over a connected digraph. One step time is required for information to travel across an edge in the graph. Under the above-mentioned setup, when subsystem process noises are uncorrelated, the explicit optimal state-feedback controller can be designed by independence decomposition based on information hierarchy graph. However, this decomposition method fails when the subsystem process noises are correlated. In this paper, we propose a new decomposition method for system state and control input, and split the optimal state-feedback control problem with correlated process noises into two subproblems that can be solved separately. The solution to the first subproblem can be obtained by solving a linear matrix equation. The second subproblem is solved by algebraic Ricatti equation.

Observer-based decentralized control of large-scale stochastic high-order feedforward systems with multi time delays

This paper investigates the problem of observer-based decentralized control for a class of large-scale stochastic high-order feedforward systems with multi time delays. By using the homogeneous domination idea and constructing the implementable observer, the decentralized output-feedback controller design scheme is firstly proposed. Then, with the aid of stochastic time delay system stability theory, the globally asymptotically stable in probability of the closed-loop system is verified by selecting an appropriate Lyapunov–Krasoviskii functional. Finally, an example is provided to demonstrate the efficiency of the proposed design method.

ADMM-based problem decomposition scheme for vehicle routing problem with time windows

Emerging urban logistics applications need to address various challenges, including complex traffic conditions and time-sensitive requirements. In this study, in the context of urban logistics, we consider a vehicle routing problem with time-dependent travel times and time windows (VRPTW), and the goal is to minimize the total generalized costs including the transportation, waiting time, and fixed costs associated with each vehicle. We adopt a high-dimensional space–time network flow model to formulate an underlying vehicle routing problem (VRP) with a rich set of criteria and constraints. A difficult issue, when solving VRPs, is how to iteratively improve both the primal and dual solution quality in general and how to break the symmetry generated by many identical solutions, particularly with homogeneous vehicles. Along this line, many coupling constraints, such as the consensus constraints across different agents or decision makers, need to be carefully addressed to find high-quality optimal or close-to-optimal solutions under medium- or large-scale instances. Currently, the alternating direction method of multipliers (ADMM) is widely used in the field of convex optimization, as an integration of the augmented Lagrangian relaxation and block coordinate descent methods, for machine learning and large-scale continuous systems optimization and control. In this work, we introduce the use of ADMM to solve the multi-VRP, which is a special case of integer linear programming, and demonstrate a manner to reduce the quadratic penalty terms used in ADMM into simple linear functions. In a broader context, a computationally reliable decomposition framework is developed to iteratively improve both the primal and dual solution quality. Essentially, the least-cost path subproblem or other similar subproblems involving binary decisions can be embedded into a sequential solution scheme with an output of both lower bound estimates and upper bound feasible solutions. We examine the performance of the proposed approach using classical Solomon VRP benchmark instances. We also evaluate our approach on a real-world instance based on a problem-solving competition by Jingdong Logistics, a major E-commerce company.

Nonblocking Supervisory Control of State-Tree Structures With Conditional-Preemption Matrices

State-tree structure (STS) is a powerful tool for the modeling and control of large-scale discrete-event systems (DES) whose structure is organized in a top–down hierarchy. The notorious state-explosion problem can be managed effectively in the framework of STS. Priority is an important concept and exists in a wide range of DES, such as manufacturing systems, traffic systems, and logistic (service) systems. In this article, a conditional-preemption matrix is used to describe the preemption relations among events, which can represent the priority intuitively. In order to augment STS with priority, we propose a novel STS framework: STS with conditional-preemption matrices (STSM), which aims to solve different kinds of issues related to priority. The optimal nonblocking supervisory control is deployed in the framework of STSM. Symbolic synthesis algorithms are implemented and integrated in a software tool, STSLib, which exploits binary decision diagrams as a basis for efficient computation. The developed approach is demonstrated by (a) manufacturing systems using automatic guided vehicles and (b) real-time systems.

Adaptive fuzzy dynamic surface sliding mode control of large-scale power systems with prescribe output tracking performance

This paper focuses on an adaptive fuzzy based dynamic surface sliding mode control (ADSSMC) strategy for multi-machine power systems with SVC. The main characteristics of the proposed ADSSMC strategy are: (1) System robustness and the convergency speed of all surface error are enhanced by combining dynamic surface control with sliding mode, leading to the structural complexity of the controller in backstepping control scheme is eliminated; (2) By introducing an error performance conversion function, the errors of desired trajectory and system output are always within a predetermined range; (3) In the adaptive regulation laws, the number of estimated parameters of the control system is significantly reduced due to the utilization of the estimations of weight vector norm instead of the weight vectors itself. The stability analysis proves that the proposed ADSSMC control strategy can guarantee the boundaries of all signals in the closed-loop control system. Experimental results verify the effectiveness of the proposed ADSSMC scheme.

Time-optimal control of large-scale systems of systems usingcompositional optimization

Optimization of industrial processes such as manufacturing cells canhave great impact on their performance. Finding optimal solutions to theselarge-scale systems is, however, a complex problem. They typically include multiplesubsystems, and the search space generally grows exponentially with each subsystem.In previous work we proposed CompositionalOptimization as a method to solve these type of problems. Thisintegrates optimization with techniques from compositional supervisory control,dividing the optimization into separate sub-problems. The main purpose is tomitigate the state explosion problem, but a bonusis that the individual sub-problems can be solved using parallel computation, makingthe method even more scalable. This paper further improves on compositionaloptimization with a novel synchronization method, called partial time-weighted synchronization (PTWS), that is specificallydesigned for time-optimal control of asynchronous systems. The benefit is itsability to combine the behaviour of asynchronous subsystems without introducingadditional states or transitions. The method also reduces the search space furtherby integrating an optimization heuristic that removes many non-optimal or redundantsolutions already during synchronization. Results in this paper show thatcompositional optimization efficiently generates global optimal solutions tolarge-scale realistic optimization problems, too big to solve when based ontraditional monolithic models. It is also shown that the introduction of PTWSdrastically decreases the total search space of the optimization compared toprevious work.

Decentralized Fault-tolerant Resilient Control for Fractional-order Interconnected Systems with Input Saturation

This paper investigates the problem of robust decentralized fault-tolerant resilient control for fractional-order large-scale interconnected uncertain system, and the problem considered here is subject to mixed H∞ and passivity performance constraint, external disturbances, controller perturbations and control input saturation. Based on the Lyapunov approach, the sufficient conditions are derived in terms of linear matrix inequalities to ensure the asymptotic stabilization of the fractional-order large-scale system with a prespecified mixed H∞ and passivity performance index. The main objective of this work is to design a robust decentralized fault-tolerant resilient controller which compensates both actuator fault and input saturation in its design for obtaining the required result. Finally, a numerical example is included to illustrate the effectiveness of the designed control law. The simulation results reveal that our proposed controller not only can effectively deal with actuator faults, but also has very good robustness for input saturation and external disturbances.

Noise-induced limitations to the scalability of distributed integral control

We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise’s impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this may in practice imply that very large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.

Proximal Algorithms for Large-Scale Statistical Modeling and Sensor/Actuator Selection

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework.

Improved decentralized prescribed performance control for non-affine large-scale systems with uncertain actuator nonlinearity

This work considers a decentralized control problem for non-affine large-scale systems with non-affine functions possibly being discontinuous. A semi-bounded condition for non-affine functions is presented to guarantee the controllability, and the non-affine system is transformed to an equivalent pseudo-affine one based on the mild condition. Different from conventional control schemes on specific actuator nonlinearity, the controller proposed in this paper can deal with a series of actuator nonlinearities such as backlash and deadzone nonlinearity. A time-varying stable manifold involving the tracking error and its high-order derivatives is utilized to handle the high-order dynamics of each subsystem. Besides an improved prescribed performance controller independent of the initial condition is constructed to ensure the finite-time convergence of the error manifold to a predefined region. The boundedness and convergence of the closed-loop system are proved by Lyapunov theory and the counter-evidence method. Two examples are performed to verify the theoretical findings.

Distributed L 2-gain control of large-scale systems under gossip communication protocol

This paper studies the distributed controller design problem for linear discrete-time large-scale systems under gossip communication protocol. In this communication protocol, each sub-controller transmits the subsystem's state information to only one randomly chosen neighbour at transmission instants. Distributed controllers are designed such that the closed-loop system is exponentially mean-square stable and that the prescribed -gain performance is satisfied in the mean-square sense. The design condition is obtained based on Lyapunov stability theory and given in terms of linear matrix inequalities. Finally, two numerical examples are presented to illustrate the advantages of the proposed scheme.

Event-triggered distributed dynamic output-feedback dissipative control of multi-weighted and multi-delayed large-scale systems

This paper considers multi-weighted and multi-delayed large-scale interconnected systems, which have multiple coupling links between neighboring subsystems and all links have different coupling weights and delays. It describes an event-triggered distributed dynamic output-feedback control approach for dissipative stabilization of the concerned systems under quantization, packet dropouts and stochastic deception attacks. An event-triggered distributed dynamic output feedback controller (DOFC) is constructed and sufficient conditions are calculated for the exponential mean square stability along with a strict ( Q, S, R)-dissipative performance of the considered large-scale systems. The control gains for the subsystem controllers are determined by solving a nonlinear minimization problem using the cone complementarity linearization (CCL) algorithm. Finally, the obtained results are verified through a numerical example consisting of a continuous stirred tank reactor (CSTR) system.

Economic model predictive control for achieving offset-free operation performance of industrial constrained systems

The optimization and control of large-scale industrial systems are typically based on hierarchical structures. The real-time optimizer (RTO) solves a steady-state setpoint optimal problem in long time-scale, based on a rigorous nonlinear model. The down-layer advanced controller is designed to achieve setpoint tracking based on a linear model to get efficient computation. This paradigm on the one hand lacks consideration about dynamic economic performance, on the other hand leads to the unreachable and inconsistent issues, which cause feasibility problem in the controller and the deviation of the plant operating point, i.e., offset. In this work, a linear offset-free economic model predictive controller (EMPC) is proposed for systems in the presence of model mismatch. The method constituted by a dynamic target optimization (DTO) stage and the following EMPC stage. These two stages work in a bidirectional way. The DTO stage uses the dynamic augmented model to derive a feasible trajectory with the terminal target attainable for down-layer EMPC. The EMPC optimizes the dynamic economic performance in the presence of a contractive energy-like constraint related to the feasible trajectory. Recursive feasibility, input-to-state stability (ISS) and offset-free property are guaranteed. The proposed method is applied to a fluid catalytic cracking (FCC) process. The numerical results demonstrate the effectiveness of the proposed offset-free EMPC for improving the overall economic performance and achieving stability and offset-free property in process control.