An official website of the United States government
In this paper, we investigate the problem of actuator selection for linear dynamical systems. We develop a framework to design a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using deterministic polynomial-time and randomized approximately linear-time algorithms. First, we introduce systemic controllability metrics for linear dynamical systems that are monotone and homogeneous with respect to the controllability Gramian. We show that several popular and widely used optimization criteria in the literature belong to this class of controllability metrics. Our main result is to provide a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time step, independent of the dimension, to furnish a guaranteed approximation of the controllability metrics in comparison to when all actuators are in use. Our results naturally apply to the dual problem of sensor selection, in which we provide a guaranteed approximation to the observability Gramian. We illustrate the effectiveness of our theoretical findings via several numerical simulations using benchmark examples.
more »
« less
Learning-based Sensor Selection with Guaranteed Performance Bounds
In this paper, we consider the problem of sensor selection for discrete-time linear dynamical networks. We develop a framework to design a sparse sensor schedule for a given large-scale linear system with guaranteed performance bounds using a learning-based algorithm. To sparsify the sensors in both time and space, we build our combinatorial optimization problems based on the notion of systemic controllability/observability metrics for linear dynamical networks with three properties: monotonicity, convexity, and homogeneity with respect to the controllability/observability Gramian matrix of the network. These combinatorial optimizations are inherently intractable and NP-hard. However, solving a continuous relaxation for each optimization is considered best practice. This is achievable since we constructed the objective based on the systemic metrics, which are convex. Furthermore, by leveraging recent advances in sparsification literature and regret minimization, we then round the fractional solution obtained by the continuous optimization to achieve a (1+epsilon) approximation sparse schedule that chooses on average a constant number of sensors at each time, to approximate all types of systemic metrics.
more »
« less
- PAR ID:
- 10352496
- Date Published:
- Journal Name:
- 2022 American Control Conference (ACC)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This study addresses the challenge of selecting sensors for linear time-varying (LTV) systems dynamically. We present a framework that designs an online sparse sensor schedule with performance guarantees using randomized algorithms for large-scale LTV systems. Our approach calculates each sensor’s contribution at each time in real-time and immediately decides whether to keep or discard the sensor in the schedule, with no possibility of reversal. Additionally, we provide new performance guarantees that approximate the fully-sensed LTV system with a multiplicative approximation factor and an additive one by using a constant average number of active sensors at each time. We demonstrate the validity of our findings through several numerical examples.more » « less
-
We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume partial observability, where the state evolution of only a subset of nodes comprising the network is observed. We propose a new feature-based paradigm: to each pair of nodes, we compute a feature vector from the observed time series. We prove that these features are linearly separable, i.e., there exists a hyperplane that separates the cluster of features associated with connected pairs of nodes from those of disconnected pairs. This renders the features amenable to train a variety of classifiers to perform causal inference. In particular, we use these features to train Convolutional Neural Networks (CNNs). The resulting causal inference mechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity. The trained CNNs generalize well over structurally distinct networks (dense or sparse) and noise-level profiles. Remarkably, they also generalize well to real-world networks while trained over a synthetic network -- namely, a particular realization of a random graph.more » « less
-
Benton, J; Lipovetzky, Nir; Onaindia, Eva; Smith, David E; Srivastava, Siddharth (Ed.)Controllability for Simple Temporal Networks with Uncertainty (STNUs) has thus far been limited to three levels: strong, dynamic, and weak. Because of this, there is currently no systematic way for an agent to assess just how far from being controllable an uncontrollable STNU is. We use a new geometric interpretation of STNUs to introduce the degrees of strong and dynamic controllability – continuous metrics that measure how far a network is from being controllable. We utilize these metrics to approximate the probabilities that an STNU can be dispatched successfully offline and online respectively. We introduce new methods for predicting the degrees of strong and dynamic controllability for uncontrollable networks. In addition, we show empirically that both metrics are good predictors of the actual dispatch success rate.more » « less
-
A linear mechanical oscillator is non-linearly coupled with an electromagnet and its driving circuit through a magnetic field. The resulting non-linear dynamics are investigated using magnetic circuit approximations without major loss of accuracy and in the interest of brevity. Different computational approaches to simulate the setup in terms of dynamical system response and design parameters optimization are pursued. A current source operating in baseband without modulation directly feeds the electromagnet, which consists commonly of a solenoid and a horseshoe-shaped core. The electromagnet is then magnetically coupled to a mass made of soft magnetic material and attached to a spring with damping. The non-linear system is described by a linearized steady-space representation while is examined for controllability and observability. A controller using a pole placement approach is built to stabilize the element. Drawing upon the fact that coupling works both ways, enabling estimation of the mass position and velocity (state variables) by processing the induced voltage across the electromagnet, a state observer is constructed. Accurate and fast tracking of the state variables, along with the possibility of driving more than one module from the same source using modulation, proves the applicability of the electro-magneto-mechanical transducer for sensor applications. Next, a three-layer feed-forward artificial neural network (ANN) system equivalent was trained using the non-linear plant-linear controller-linear observer configuration. Simulations to investigate the robustness of the system with respect to different equilibrium points and input currents were carried out. The ANN proved robust with respect to position accuracy.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867174
