Join us for talks with our Grassi & MOR fellows for 2019.

Caleb Bugg — Theory and Applications for Sample Average Approximation (SAA)

Abstract: Sample Average Approximation (SAA) (often known within the controls community as scenario-based optimization) is commonly used to approximately solve stochastic optimization problems, and it often works better in practice than existing theoretical bounds suggest for the number of samples needed to ensure the SAA minimum value is close to the true minimum value. In this talk, we will show new theoretical bounds for SAA that, for certain types of stochastic optimization problems, are logarithmic in problem dimension, whereas existing bounds are polynomial in dimension. Our approach characterizes the stability of random instances of the optimization problem using stochastic process theory, and then uses this characterization to construct confidence intervals using concentration of measure techniques. Lastly, we will show another application area for SAA, chance-constrained optimization, and describe a weighted gradient method for producing a Pareto front of solutions, effectively making our solver global, whereas most multiobjective methods assure convergence only to a single point on the Pareto front.

Bio: Caleb Bugg is currently a PhD student in the Industrial Engineering and Operations Research (IEOR) department. His interests in Operations Research combine sociological and economic perspectives in the development of incentive models for food-and-water based neighborhood self-sufficiency. He quantifies and motivates government policies and programs that incentivize traditionally underserved populations towards healthful food sufficiency, which increases population health and neighborhood viability, while simultaneously reducing burdens on the national health insurance infrastructure, thus helping to, in the long-run, alleviate portions of the national budget endowed towards this end. He received his B.S. in Mathematics from the Morehouse College in 2017, and his M.S. in IEOR from UC Berkeley in 2018.

Pedro Hespanhol — Sensor Switching Control Under Attacks Detectable by Finite Sample Dynamic Watermarking Tests

Abstract:  Control system security is enhanced by the ability to detect malicious attacks on sensor measurements. Dynamic watermarking can detect such attacks on linear time-invariant (LTI) systems. However, existing theory focuses on attack detection and not on the use of watermarking in conjunction with attack mitigation strategies. In this paper, we study the problem of switching between two sets of sensors:  One set of sensors has high accuracy but is vulnerable to attack, while the second set of sensors has low accuracy but cannot be attacked. The  problem is to design a sensor switching strategy based on attack detection by dynamic watermarking. This requires new theory because existing results are not adequate to control or bound the behavior of sensor switching strategies that use finite data. To overcome this, we develop new finite sample hypothesis tests for dynamic watermarking in the case of bounded disturbances, using the modern theory of concentration of measure for random matrices. Our resulting switching strategy is validated with a simulation analysis in an autonomous driving setting, which demonstrates the strong performance of our proposed policy.

Bio:  Pedro Hespanhol is a PhD candidate in the in Industrial Engineering and Operations Research (IEOR) department at UC Berkeley working with Professor Anil Aswani. His research is focused on developing safe and efficient algorithms for autonomous systems. He has developed active defense mechanisms for cyber-physical systems and real-time optimal control algorithms for hybrid systems. He received his B.S. in Industrial Engineering from Pontifical Catholic University of Rio de Janeiro in 2014 and his M.S. in IEOR from UC Berkeley in 2016.

SangWoo Park — Towards a more reliable operation of power systems

Abstract: In this talk, I will summarize some of the works that I have been doing over the past few years. The first project proposes a new technique for robust state estimation in the presence of a small number of topological errors for power systems modeled by AC power flow equations. We first study the properties of the solution obtained by the “nonlinear absolute value (NLAV)” estimator and argue that, under mild conditions, this solution identifies a small subgraph of the network that can be used to find topological errors in the modeling of the state estimation problem. In the second project, we establish conditions for the uniqueness of power flow solutions in an AC power system via the monotonic relationship between real power flow and the phase angle difference. More specifically, we prove that strict monotonicity holds if the angle difference is bounded by the steady-state stability limit in a power system with a series-parallel topology, or if transmission losses are sufficiently low. Finally in the third project, we find theoretical guarantees to ensure that the “contingency optimal power flow (contingency-OPF)” problem will converge to its global minimum under certain conditions. We show that this convergence is dependent on the geometry of the homotopy path, and lay out some new groundwork for the characterization of such paths.

Bio:  SangWoo Park is a PhD candidate at the department of Industrial Engineering and Operations Research (IEOR), UC Berkeley. He is being advised by Professor Javad Lavaei and his research focuses on designing and analyzing algorithms for complex and large scale optimization problems, mainly related to electric power systems. He received his B.S. degree from Johns Hopkins Whiting School of Engineering in 2016 and M.S. degree from UC Berkeley IEOR in 2017.