Performance guarantees for greedy maximization of non-submodular controllability metrics

A key problem in emerging complex cyber-physical networks is the design of information and control topologies, including sensor and actuator selection and communication network design. These problems can be posed as combinatorial set function optimization problems to maximize a dynamic performance metric for the network. Some systems and control metrics feature a property called submodularity, which allows simple greedy algorithms to obtain provably near-optimal topology designs. However, many important metrics lack submodularity and therefore lack provable guarantees for using a greedy optimization approach. Here we show that performance guarantees can be obtained for greedy maximization of certain non-submodular functions of the controllability and observability Gramians. Our results are based on two key quantities: the submodularity ratio, which quantifies how far a set function is from being submodular, and the curvature, which quantifies how far a set function is from being supermodular

Structured Neural-PI Control with End-to-End Stability and Output Tracking Guarantees

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$\beta$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.Comment: arXiv admin note: text overlap with arXiv:2206.0026

LUNES: Agent-based Simulation of P2P Systems (Extended Version)

We present LUNES, an agent-based Large Unstructured NEtwork Simulator, which allows to simulate complex networks composed of a high number of nodes. LUNES is modular, since it splits the three phases of network topology creation, protocol simulation and performance evaluation. This permits to easily integrate external software tools into the main software architecture. The simulation of the interaction protocols among network nodes is performed via a simulation middleware that supports both the sequential and the parallel/distributed simulation approaches. In the latter case, a specific mechanism for the communication overhead-reduction is used; this guarantees high levels of performance and scalability. To demonstrate the efficiency of LUNES, we test the simulator with gossip protocols executed on top of networks (representing peer-to-peer overlays), generated with different topologies. Results demonstrate the effectiveness of the proposed approach.Comment: Proceedings of the International Workshop on Modeling and Simulation of Peer-to-Peer Architectures and Systems (MOSPAS 2011). As part of the 2011 International Conference on High Performance Computing and Simulation (HPCS 2011

Experimental implementation of a real-time token-based network protocol on a microcontroller

The real-time token-based RTnet network protocol has been implemented on a standard Ethernet network to investigate the possibility to use cheap components with strict resource limitations while preserving Quality of Service guarantees. It will be shown that the proposed implementation is feasible on a small network. For larger networks a different approach is necessary, using delegation by means of proxies. A delegation proposal will be discussed. For small networks it is possible to use a PIC microcontroller in combination with a standard Ethernet controller to run the RTnet network protocol. As more systems are added to the network the performance of this combination becomes insufficient. When this happens it is necessary for the microcontroller to delegate some tasks to a more powerful master and to organize a low-level communication protocol between master and slave

Distributed Online Modified Greedy Algorithm for Networked Storage Operation under Uncertainty

The integration of intermittent and stochastic renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of storage networks in stochastic environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems on continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or provably near-optimal performance for this problem. This paper provides an efficient algorithm to solve this problem with performance guarantees. We study the operation of storage networks, i.e., a storage system interconnected via a power network. An online algorithm, termed Online Modified Greedy algorithm, is developed for the corresponding constrained stochastic control problem. A sub-optimality bound for the algorithm is derived, and a semidefinite program is constructed to minimize the bound. In many cases, the bound approaches zero so that the algorithm is near-optimal. A task-based distributed implementation of the online algorithm relying only on local information and neighbor communication is then developed based on the alternating direction method of multipliers. Numerical examples verify the established theoretical performance bounds, and demonstrate the scalability of the algorithm.Comment: arXiv admin note: text overlap with arXiv:1405.778