There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

/pdf/information-flow-and-cooperative-control-of-vehicle-4ws61wioze.pdf

Information flow and cooperative control of vehicle formations

In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

/pdf/event-triggered-real-time-scheduling-of-stabilizing-control-t1gebqsndp.pdf

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

In Hybrid Electricle Vehicles (HEV), performing online energy management is an important task to be achieved to reduce emissions, fuel consumption and increase vehicle performance. For this task, estimating the State of Charge (SOC) is needed since it serves as a measure of energy that is left inside an electrochemical battery. A variety of methods to solve this estimation problem have been proposed in the literature. However, most of these methods either assume equivalent circuit models for the battery and thus lose their validity under some discharge conditions or depend heavily on the choice of parameters in the algorithm. In this paper, we use behavioral framework to avoid postulation of a specific model for a battery and develop a new and simple SOC estimation algorithm. Once the problem is formulated as the computation of a specific free response of the battery, algorithm computes this response using only terminal current and terminal voltage measurements. We demonstrate the effectiveness of the algorithm with different discharge profiles using both simulated and real data.

https://www.mdpi.com/2032-6653/5/2/412/pdf

A Behavioral Algorithm for State of Charge Estimation

Claudio De Persis and Nima Monshizadeh have recently brought to our attention a mistake in the proof of [1, Theor. 2]. The purpose of this note is to explain this mistake and to correct the statement of [1, Theor. 2]. We refer the reader to [1] for notation and all of the symbols employed in this paper.

Correction to “Compositional Transient Stability Analysis of Multimachine Power Networks”

Submodularity is a pivotal property of functions defined on lattices, as it permits their exact minimization and approximate maximization in polynomial time. In this work, we examine submodular function minimization defined on continuous and discrete lattices simultaneously. We identify a class of these mixed optimization problems that can be exactly solved by applying a combination of submodular and convex optimization routines. The utility of this approach is demonstrated via several examples from the proposed class of optimization problems.

Why not both? Exact continuous and discrete optimization with submodularity

We consider the optimal control of linear timeinvariant (LTI) systems via self-triggered sparse optimal control (SSOC) laws. Our control objective is to design an optimal control law which stabilizes the LTI system for all initial conditions, requires less sensing, minimizes communication requirements between the subsystems, minimizes the number of active actuators, and provides guaranteed closed-loop performance bounds. To achieve such control objectives, we formulate a sequence of ?o-regularized linear-quadratic optimal control problems, wherein the objective is to optimize a cost function which involves three penalizing terms: one for maximizing the inter-execution time, another one for minimizing the number of nonzero elements of the state feedback gain, and the last one for minimizing the number of active actuators. Deriving a lower bound on inter-execution times, we propose a scheme to solve this problem. First, the relaxation is utilized to cast the problem as a semi-definite program (SDP) to compute a feedback gain while the inter-execution time is kept fixed. Second, a nonlinear equation is solved to determine the inter-execution time while the feedback gain is kept fixed. The proposed SSOC law is feasible and results in a stabilizing sequence of sparse optimal controllers. Additionally, the performance of the resulting closed-loop system does not exceed a prespecified performance bound. By numerical simulations, sparsity in time/space is improved compared to periodic time-triggered LQR design. Moreover, a tradeoff between prespecified performance bound and sparsity in time/space is observed. Finally, the paper is concluded by drawing some future directions.

Improving sparsity in time and space via self-triggered sparse optimal controllers

Control algorithms, like model predictive control, can be computationally expensive and may benefit from being executed over the cloud. This is especially the case for nodes at the edge of a network since they tend to have reduced computational capabilities. However, control over the cloud requires transmission of sensitive data (e.g., system dynamics, measurements) which undermines privacy of these nodes. When choosing a method to protect the privacy of these data, efficiency must be considered to the same extent as privacy guarantees to ensure adequate control performance. In this paper, we review a transformation-based method for protecting privacy, previously introduced by the authors, and quantify the level of privacy it provides. Moreover, we also consider the case of adversaries with side knowledge and quantify how much privacy is lost as a function of the side knowledge of the adversary.

/pdf/symmetries-and-privacy-in-control-over-the-cloud-uncertainty-23qphzhmqd.pdf

Paulo Tabuada

Papers

A Behavioral Algorithm for State of Charge Estimation

Correction to “Compositional Transient Stability Analysis of Multimachine Power Networks”

Why not both? Exact continuous and discrete optimization with submodularity

Improving sparsity in time and space via self-triggered sparse optimal controllers

Symmetries and privacy in control over the cloud: uncertainty sets and side knowledge *