This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based controller makes use of the hyperbolic controller canonical form that follows from a parametrization of the system's solutions. A backstepping design exploits the strict-feedback form of the system to recursively stabilize and transform the subsystems.
We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm com…
This paper studies a discrete-time stochastic control problem with linear quadratic criteria over an infinite-time horizon. We focus on a class of control systems whose system matrices are associated with random parameters involving unknown statistical properties. In particular, we design a distributed Q-learning algorithm to tackle the Riccati equation and derive the optimal controller stabilizing the system. The key technique is that we convert the problem of solving the Riccati equation into deriving the zero point of a matrix equation and devise a distributed stochastic approximation metho…
The rapidly increasing penetration of inverter-based resources into a power transmission network requires more sophisticated voltage control strategies considering their inherent output variabilities. In addition, faults and load variations affect the voltage profile over the power network. This paper proposes a Primal Dual Gradient Dynamics based optimal distributed voltage control approach that optimizes outputs of distributed reactive power sources to maintain an acceptable voltage profile while preserving operational limits. Case studies of this new approach on IEEE test systems have verif…
This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal feasibility of the iterates. Numerical results show that the proposed method can compete with the alternating direction method of multipliers in terms of communication requirements for a chain of masses example.
We address the multi-agent persistent monitoring problem defined on a set of nodes (targets) interconnected over a network topology. A measure of mean overall node state uncertainty evaluated over a finite period is to be minimized by controlling the motion of a cooperating team of agents. To address this problem, we propose an event-driven receding horizon control approach that is computationally efficient, distributed and on-line. The proposed controller differs from the existing on-line gradient-based parametric controllers and off-line greedy cycle search methods that often lead to either …
This work studies the potential vulnerability of distributed control schemes in smart grids. To this end, we consider an optimal inverter VAR control problem within a PV-integrated distribution network. First, we formulate the centralized optimization problem considering the reactive power priority and further reformulate the problem into a distributed framework by an accelerated proximal projection method. The inverter controller can curtail the PV output of each user by clamping the reactive power. To illustrate the studied distributed control scheme that may be vulnerable due to the two-hop…
This paper deals with a distributed implementation of minimax adaptive control algorithm for networked dynamical systems modeled by a finite set of linear models. To hedge against the uncertainty arising out of finite number of possible dynamics in each node in the network, it collects only the historical data of its neighboring nodes to decide its control action along its edges. This makes our proposed distributed approach scalable. Numerical simulations demonstrate that once each node has sufficiently estimated the uncertain parameters, the distributed minimax adaptive controller behaves lik…
Due to possible emergency faults and frequency regulation reserve shortage in the multi-infeed hybrid AC-DC (MIDC) system, the emergency frequency control (EFC) with LCC-HVDC systems participating is important for system frequency stability. Nevertheless, the existing decentralized EFC strategies cannot guarantee the transient stability constraints of lines and cannot meet the frequency restoration requirement. To fill this gap, this paper proposes a complementary distributed EFC strategy. By selecting the semi-distributed or fully-distributed control law according to the state of AC system co…
In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the con…
We propose a distributed control, in which many identical control agents are deployed for controlling a linear time-invariant plant that has multiple input-output channels. Each control agent can join or leave the control loop during the operation of stabilization without particular initialization over the whole networked agents. Once new control agents join the loop, they self-organize their control dynamics, which does not interfere the control by other active agents, which is achieved by local communication with the neighboring agents. The key idea enabling these features is the use of Bass…
Cyber-physical systems are becoming core of the most modern systems consisting control, data sharing and real-time monitoring. While centralized control technique has been implemented in the past, recent innovation in distributed control schemes makes it attractive due to various reasons. One of them is the use of state-of-the-art communication protocols that makes the system more robust toward extreme conditions and ensures observability. Thus, as an application of cyber-physical systems, distributed control architectures are prone to various cyber-vulnerability which makes cybersecurity rese…
In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require several (virtually, infinite) communication rounds between the subsystems to converge, which is a major drawback both computationally and from an energetic perspective (for wireless systems). Motivated by these challenges, we propose a suboptimal distributed MPC scheme in which the total communication burden is distributed also in time, by maintaining a run…
In this paper we propose an original distributed control framework for DC mcirogrids. We first formulate the (optimal) control objectives as an aggregative game suitable for the energy trading market. Then, based on the dual theory, we analyze the equivalent distributed optimal condition for the proposed aggregative game and design a distributed control scheme to solve it. By interconnecting the DC mcirogrid and the designed distributed control system in a power preserving way, we steer the DC microgrid's state to the desired optimal equilibrium, satisfying a predefined set of local and coupli…
This paper studies the distributed dual objective control problem of a heterogenous flywheel energy storage matrix system aiming at simultaneous reference power track-ing and state-of-energy balancing. We first prove that the solution to this problem exists by showing the existence of a common state-of-energy trajectory for all the flywheel systems on which the dual control objectives can be achieved simultaneously. Next, based on this common state-of-energy trajectory, the distributed dual objective control problem is converted into a double layer distributed tracking problem, which is then s…
This paper presents a distributed frequency control method for power grids with high penetration of inverter-connected resources under low and time-varying inertia due to renewable energy (RE). We provide a distributed virtual inertia (VI) allocation method using the distributed subgradient algorithm. We implement our distributed control strategy under full and sparse communication architectures. The distributed full and sparse communication controllers achieve comparable performance to a centralized controller and stabilize the test system within 6~s. We study the sensitivity of the controlle…
We consider the problem of designing distributed controllers to stabilize a class of networked systems, where each subsystem is dissipative and designs a reinforcement learning based local controller to maximize an individual cumulative reward function. We develop an approach that enforces dissipativity conditions on these local controllers at each subsystem to guarantee stability of the entire networked system. The proposed approach is illustrated on a DC microgrid example, where the objective is maintain voltage stability of the network using local distributed controllers at each generation …
This paper studies the state-of-charge (SoC) balancing and the total charging/discharging power tracking issues for battery energy storage systems (BESSs) with multiple distributed heterogeneous battery units. Different from the traditional cooperative control strategies based on the asymptotical or finite-time distributed observers, two distributed prespecified-time observers are proposed to estimate average battery units state and average desired power, respectively, which can be determined in advance and independent of initial states or control parameters. Finally, two simulation examples a…
In order to enhance the performance of cyber-physical systems, this paper proposes the integrated de-sign of distributed controllers for distributed plants andthe control of the communication network. Conventionaldesign methods use static interfaces between both enti-ties and therefore rely on worst-case estimations of com-munication delay, often leading to conservative behaviorof the overall system. By contrast, the present approachestablishes a robust distributed model-predictive controlscheme, in which the local subsystem controllers oper-ate under the assumption of a variable communication…
Distributed model predictive control methods for uncertain systems often suffer from considerable conservatism and can tolerate only small uncertainties due to the use of robust formulations that are amenable to distributed design and optimization methods. In this work, we propose a distributed stochastic model predictive control (DSMPC) scheme for dynamically coupled linear discrete-time systems subject to unbounded additive disturbances that are potentially correlated in time. An indirect feedback formulation ensures recursive feasibility of the DSMPC problem, and a data-driven, distributed …
This paper proposes a distributed design method of controllers having a glocal (global/local) information structure for large-scale network systems. Distributed design, independent design of all subcontrollers that constitute a structured controller, facilitates scalable controller synthesis. While existing distributed design methods confine attention to the decentralized or distributed information structures, this study addresses distributed design of glocal-structured controllers. Glocal control exploits the nature that network system's behavior can typically be represented as a superpositio…
The leader-follower formation control analysis for multiple quad-rotor systems is investigated in this paper. To achieve predefined formation in the three-dimensional air space ($x,y$ and $z$), a novel local tracking control law and a distributed observer are obtained. The local tracking control law starts with finding a bounded continuous yet greater-than-zero control in $z$, based on which following a feedback linearization controls derived for errors associated with $x$ and $y$. The distributed observer achieves position coordination among followers, though there are only partial followers …
In this paper, we propose a control law for camera-equipped drone networks to pursue a target rigid body with unknown motion based on distributed Gaussian process. First, we consider the situation where each drone has its own dataset, and learned the unknown target motion in a distributed manner. Second, we propose a control law using the distributed Gaussian processes, and show that the estimation and control errors are ultimately bounded. Furthermore, the effectiveness of the proposed method is verified by using simulations and experiments with actual drones.
Increasing penetration of Photovoltaic (PV) generation brings an opportunity, and sometimes necessity, for this new resource to provide ancillary services such as frequency support. Recent efforts toward this goal focused mainly on the large-scale PV plants with identical subsystems but cannot handle distributed PV systems with diversities. Therefore, directly applying them to distributed PV requires repetitive control design for each unit, and thus implies huge design efforts. In this paper, we propose a novel frequency support control scheme focusing on the distributed PV to overcome the abo…
Controlling large-scale systems sometimes requires decentralized computation. Communication among agents is crucial to achieving consensus and optimal global behavior. These negotiation mechanisms are sensitive to attacks on those exchanges. This paper proposes an algorithm based on Expectation Maximization to mitigate the effects of attacks in a resource allocation based distributed model predictive control. The performance is assessed through an academic example of the temperature control of multiple rooms under input power constraints.
The linear-quadratic controller is one of the fundamental problems in control theory. The optimal solution is a linear controller that requires access to the state of the entire system at any given time. When considering a network system, this renders the optimal controller a centralized one. The interconnected nature of a network system often demands a distributed controller, where different components of the system are controlled based only on local information. Unlike the classical centralized case, obtaining the optimal distributed controller is usually an intractable problem. Thus, we ado…
This paper considers the use of fully homomorphic encryption for the realisation of distributed formation control of multi-agent systems via edge computer. In our proposed framework, the distributed control computation in the edge computer uses only the encrypted data without the need for a reset mechanism that is commonly required to avoid error accumulation. Simulation results show that, despite the use of encrypted data on the controller and errors introduced by the quantization process prior to the encryption, the formation is able to converge to the desired shape. The proposed architectur…
This paper studies the distributed L2-gain control problem for continuous-time large-scale systems under Round-Robin communication protocol. In this protocol, each sub-controller obtains its own subsystem's state information continuously, while communicating with neighbors at discrete-time instants periodically. Distributed controllers are designed such that the closed-loop system is exponentially stable and that the prescribed L2-gain is satisfied. The design condition is obtained based on a time-delay approach and given in terms of linear matrix inequalities. Finally, three numerical example…
This paper considers the optimal distributed control problem for a linear stochastic multi-agent system (MAS). Due to the distributed nature of MAS network, the information available to an individual agent is limited to its vicinity. From the entire MAS aspect, this imposes the structural constraint on the control law, making the optimal control law computationally intractable. This paper attempts to relax such a structural constraint by expanding the neighboring information for each agent to the entire MAS, enabled by the distributed estimation algorithm embedded in each agent. By exploiting …
When designing large-scale distributed controllers, the information-sharing constraints between sub-controllers, as defined by a communication topology interconnecting them, are as important as the controller itself. Controllers implemented using dense topologies typically outperform those implemented using sparse topologies, but it is also desirable to minimize the cost of controller deployment. Motivated by the above, we introduce a compact but expressive graph recurrent neural network (GRNN) parameterization of distributed controllers that is well suited for distributed controller and commu…
Various efforts have been devoted to developing stabilizing distributed Model Predictive Control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this pap…
In this paper it is established that any jointly controllable, jointly observable, multi-channel, discrete or continuous time linear system with a strongly connected neighbor (communication) graph can be exponentially stabilized with any pre-specified convergence rate using a time-invariant distributed linear control. As an illustration of how this finding can be used to deal with certain distributed tracking problems, a solution is given to a distributed set-point control problem for a continuous-time, multi-channel linear system in which each and every agent with access to the system is able…
The modular open-source framework GRAMPC-D for model predictive control of distributed systems is presented in this paper. The modular concept allows to solve optimal control problems (OCP) in a centralized and distributed fashion using the same problem description. It is tailored to computational efficiency with the focus on embedded hardware. The distributed solution is based on the Alternating Direction Method of Multipliers (ADMM) and uses the concept of neighbor approximation to enhance convergence speed. The presented framework can be accessed through Cpp and Python and also supports plu…
Fully Distributed Secondary Voltage Control in Inverter-Based Microgrids
Lane Department of Computer Science and Electrical Engineering, West Virginia University（西弗吉尼亚大学计算机科学与电气工程学院）；Advanced Power & Electricity Research Group (APERC)（先进电力与能源研究小组 (APERC)）；Wireless Sensor Actuator Networks (WSAN) Research Group（无线传感器执行器网络研究小组）
This paper investigates a distributed formation tracking control law for large-scale networks of mechanical systems. In particular, the formation network is represented by a directed communication graph with leaders and followers, where each agent is described as a port-Hamiltonian system with a constant mass matrix. Moreover, we adopt a distributed parameter approach to prove the scalable asymptotic stability of the network formation, i.e., the scalability with respect to the network size and the specific formation preservation. A simulation case illustrates the effectiveness of the proposed …
This paper proposes a fuel-economical distributed model predictive control design (Eco-DMPC) for a homogenous heavy-duty truck platoon. The proposed control strategy integrates a fuel-optimal control strategy for the leader truck with a distributed formation control for the following trucks in the heavy-duty truck platoon. The fuel-optimal control strategy is implemented by a nonlinear model predictive control (NMPC) design with an instantaneous fuel consumption model. The proposed fuel-optimal control strategy utilizes the preview information of the preceding traffic to achieve the fuel-econo…
