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Register a new userCommunication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control
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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 communication topology co-design. Our proposed parameterization enjoys a local and distributed architecture, similar to previous Graph Neural Network (GNN)-based parameterizations, while further naturally allowing for joint optimization of the distributed controller and communication topology needed to implement it. We show that the distributed controller/communication topology co-design task can be posed as an $ell_1$-regularized empirical risk minimization problem that can be efficiently solved using stochastic gradient methods. We run extensive simulations to study the performance of GRNN-based distributed controllers and show that (a) they achieve performance comparable to GNN-based controllers while having fewer free parameters, and (b) our method allows for performance/communication density tradeoff curves to be efficiently approximated.
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Wide Area Cyber-Physical Systems (WA-CPSs) are a class of control systems that integrate low-powered sensors, heterogeneous actuators and computer controllers into large infrastructure that span multi-kilometre distances. Current wireless communication technologies are incapable of meeting the communication requirements of range and bounded delays needed for the control of WA-CPSs. To solve this problem, we use a Control-Communication Co-design approach for WA-CPSs, that we refer to as the $C^3$ approach, to design a novel Low-Power Wide Area (LPWA) MAC protocol called textit{Ctrl-MAC} and its associated event-triggered controller that can guarantee the closed-loop stability of a WA-CPS. This is the first paper to show that LPWA wireless communication technologies can support the control of WA-CPSs. LPWA technologies are designed to support one-way communication for monitoring and are not appropriate for control. We present this work using an example of a water distribution network application which we evaluate both through a co-simulator (modelling both physical and cyber subsystems) and testbed deployments. Our evaluation demonstrates full control stability, with up to $50$% better packet delivery ratios and $80$% less average end-to-end delays when compared to a state of the art LPWA technology. We also evaluate our scheme against an idealised, wired, centralised, control architecture and show that the controller maintains stability and the overshoots remain within bounds.
We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal Temporal Logic (STL) formulae. RNNs can store information of a system over time, thus, enable us to determine satisfaction of the dynamic temporal requirements specified in STL formulae. Given a STL formula, a dataset of satisfying system executions and corresponding control policies, we can use RNNs to predict a control policy at each time based on the current and previous states of system. We use Control Barrier Functions (CBFs) to guarantee the safety of the predicted control policy. We validate our theoretical formulation and demonstrate its performance in an optimal control problem subject to partially unknown safety constraints through simulations.
We propose a policy search approach to learn controllers from specifications given as Signal Temporal Logic (STL) formulae. The system model is unknown, and it is learned together with the control policy. The model is implemented as a feedforward neural network (FNN). To capture the history dependency of the STL specification, we use a recurrent neural network (RNN) to implement the control policy. In contrast to prevalent model-free methods, the learning approach proposed here takes advantage of the learned model and is more efficient. We use control barrier functions (CBFs) with the learned model to improve the safety of the system. We validate our algorithm via simulations. The results show that our approach can satisfy the given specification within very few system runs, and therefore it has the potential to be used for on-line control.
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 adopt a graph neural network (GNN) as a parametrization of distributed controllers. GNNs are naturally local and have distributed architectures, making them well suited for learning nonlinear distributed controllers. By casting the linear-quadratic problem as a self-supervised learning problem, we are able to find the best GNN-based distributed controller. We also derive sufficient conditions for the resulting closed-loop system to be stable. We run extensive simulations to study the performance of GNN-based distributed controllers and showcase that they are a computationally efficient parametrization with scalability and transferability capabilities.
Controlling network systems has become a problem of paramount importance. Optimally controlling a network system with linear dynamics and minimizing a quadratic cost is a particular case of the well-studied linear-quadratic problem. When the specific topology of the network system is ignored, the optimal controller is readily available. However, this results in a emph{centralized} controller, facing limitations in terms of implementation and scalability. Finding the optimal emph{distributed} controller, on the other hand, is intractable in the general case. In this paper, we propose the use of graph neural networks (GNNs) to parametrize and design a distributed controller. GNNs exhibit many desirable properties, such as being naturally distributed and scalable. We cast the distributed linear-quadratic problem as a self-supervised learning problem, which is then used to train the GNN-based controllers. We also obtain sufficient conditions for the resulting closed-loop system to be input-state stable, and derive an upper bound on the trajectory deviation when the system is not accurately known. We run extensive simulations to study the performance of GNN-based distributed controllers and show that they are computationally efficient and scalable.
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