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.

Coverage control for mobile sensing networks

An attack graph is a succinct representation of all paths through a system that end in a state where an intruder has successfully achieved his goal. Today Red Teams determine the vulnerability of networked systems by drawing gigantic attack graphs by hand. Constructing attack graphs by hand is tedious, error-prone, and impractical for large systems. By viewing an attack as a violation of a safety property, we can use off-the-shelf model checking technology to produce attack graphs automatically: a successful path from the intruder's viewpoint is a counterexample produced by the model checker In this paper we present an algorithm for generating attack graphs using model checking as a subroutine. Security analysts use attack graphs for detection, defense and forensics. In this paper we present a minimization analysis technique that allows analysts to decide which minimal set of security measures would guarantee the safety of the system. We provide a formal characterization of this problem: we prove that it is polynomially equivalent to the minimum hitting set problem and we present a greedy algorithm with provable bounds. We also present a reliability analysis technique that allows analysts to perform a simple cost-benefit trade-off depending on the likelihoods of attacks. By interpreting attack graphs as Markov Decision Processes we can use the value iteration algorithm to compute the probabilities of intruder success for each attack the graph.

Two Formal Analyses of Attack Graphs

The authors present a new method to solve the problem of economic power dispatch with piecewise quadratic cost function using the Hopfield neural network. Traditionally one convex cost function for each generator is assumed. However, it is more realistic to represent the cost function as a piecewise quadratic function rather than one convex function. In this study, multiple intersecting cost functions are used for each unit. Through case studies, the possibility of the application of the Hopfield neural network to the economic load dispatch problem with general nonconvex cost functions was shown. The proposed approach is much simpler and the results are very close to those of the numerical method. >

/pdf/economic-load-dispatch-for-piecewise-quadratic-cost-function-3h7yetcxg8.pdf

Economic load dispatch for piecewise quadratic cost function using Hopfield neural network

A Systems and Control Perspective of CPS Security

Cyber-security on smart grid: Threats and potential solutions

Due to the global reliance on the power grid, coordinated cyber-physical attacks on its critical infrastructure can lead to disastrous human and economic losses. In this paper, a stochastic game-theoretic approach is proposed to analyze the optimal strategies that a power grid defender can adopt to protect the grid against coordinated attacks. First, an optimal load shedding technique is devised to quantify the physical impacts of coordinated attacks. Taking these quantified impacts as input parameters, the interactions between a malicious attacker and the defender are modeled using a resource allocation stochastic game. The game is shown to admit a Nash equilibrium and a novel learning algorithm is introduced to enable the two players to reach their equilibrium strategies while maximizing their respective minimum rewards in a sequence of stages. The convergence of the proposed algorithm to a Nash equilibrium point is proved and its properties are studied. Simulation results of the stochastic game model on the WSCC 9-bus system and the IEEE 118-bus system are contrasted with those of static games, and show that different defense resources owned lead to different defense strategies.

Stochastic Games for Power Grid Protection Against Coordinated Cyber-Physical Attacks

This paper is concerned with the development of a control system for tracking of a desired temperature-time profile for accelerated cooling processes in hot rolling of steel. Control of temperature during cooling is essential for achieving desired mechanical and metallurgical properties of steel. The cooling process is represented by the heat equation in Lagrangian coordinates which is approximated by a set of ordinary differential equations. The control variable is the velocity of coolant water flow. Motivated by the fact that in many steel industries water flow is adjusted to some fixed velocity based on experience and heuristics, we assume that the control variable, water jet velocity, be a constant time invariant parameter. Gamkrelidze minimum principle is used to determine the optimal jet velocity for the desired temperature tracking. The results are illustrated by simulation examples.

http://www.math.yorku.ca/~hhuang/math6937-06/temp-control1.pdf

Optimal temperature tracking for accelerated cooling processes in hot rolling of steel

We consider the problem of rigorous modelling of flexible spacecraft and their stabilization. It is shown that the dynamics of the flexible spacecraft can be described by a coupled system of ordinary differential equations and partial differential equations (hybrid system). Lyapunov's approach is used to prove the stabilizability of the system. Simple feedback controls are suggested for stabilization of flexible spacecraft.

Stabilization of a class of hybrid systems arising in flexible spacecraft

The cyber-physical nature of the smart grid has rendered it vulnerable to a multitude of attacks that can occur at its communication, networking, and physical entry points. Such cyber-physical attacks can have detrimental effects on the operation of the grid as exemplified by the recent attack which caused a blackout of the Ukranian power grid. Thus, to properly secure the smart grid, it is of utmost importance to: a) understand its underlying vulnerabilities and associated threats, b) quantify their effects, and c) devise appropriate security solutions. In this paper, the key threats targeting the smart grid are first exposed while assessing their effects on the operation and stability of the grid. Then, the challenges involved in understanding these attacks and devising defense strategies against them are identified. Potential solution approaches that can help mitigate these threats are then discussed. Last, a number of mathematical tools that can help in analyzing and implementing security solutions are introduced. As such, this paper will provide the first comprehensive overview on smart grid security.

Smart Grid Security: Threats, Challenges, and Solutions

In this paper, we consider the problem of associating estimated direction-of-arrival (DOA) angles of multiple targets using two uniform linear arrays (ULAs) of sensors. It is categorized as a multisource information aggregation problem, in which we devise our algorithm in the following two steps: (1) Estimate two sets of DOA angles from two ULAs, respectively, and (2) associate estimated DOA angles with the targets. Note, however, that the primary focus of this paper is the second step, i.e., association of DOA angles with the corresponding targets, whereas for the first step, we use the well-known improved polynomial rooting method. Generally speaking, if there are q targets, we have q! possible association pairs, among which, there is only one set corresponding to the correct association. Since target signals must be correlated in the observations of two ULAs, we can determine how to associate the DOA angles computed from step 1 by evaluating the covariance matrix of the data received at the two ULAs. The algorithm is effective, robust, and accurate in classifying the DOA angles into the correct association.

Saroj Biswas

Papers

Stochastic Games for Power Grid Protection Against Coordinated Cyber-Physical Attacks

Optimal temperature tracking for accelerated cooling processes in hot rolling of steel

Stabilization of a class of hybrid systems arising in flexible spacecraft

Smart Grid Security: Threats, Challenges, and Solutions

Association of DOA Estimation From Two ULAs