Orçun Karaca


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Karaca

First Name

Orçun

ORCID

0000-0002-6584-3709

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Publications1 - 10 of 17
  • Actuator Placement under Structural Controllability using Forward and Reverse Greedy Algorithms
    Item type: Journal Article
    Guo, Baiwei; Karaca, Orçun; Summers, Tyler H.; et al. (2021)
    IEEE Transactions on Automatic Control
    Actuator placement is an active field of research, which has received significant attention for its applications in complex dynamical networks. In this article, we study the problem of finding a set of actuator placements minimizing the metric that measures the average energy consumed for state transfer by the controller, while satisfying a structural controllability requirement and a cardinality constraint on the number of actuators allowed. As no computationally efficient methods are known to solve such combinatorial set function optimization problems, two greedy algorithms, forward and reverse, are proposed to obtain approximate solutions. We first show that the constraint sets these algorithms explore can be characterized by matroids. We then obtain performance guarantees for the forward and reverse greedy algorithms applied to the general class of matroid optimization problems by exploiting properties of the objective function such as the submodularity ratio and the curvature. Finally, we propose feasibility check methods for both algorithms based on maximum flow problems on certain auxiliary graphs originating from the network graph. Our results are verified with case studies over large networks.
  • Designing Coalition-Proof Reverse Auctions over Continuous Goods
    Item type: Journal Article
    Karaca, Orçun; Sessa, Pier Giuseppe; Walton, Neil; et al. (2019)
    IEEE Transactions on Automatic Control
  • The REPOP toolbox: tackling polynomial optimization using relative entropy relaxations
    Item type: Conference Paper
    Karaca, Orçun; Darivianakis, Georgios; Beuchat, Paul N.; et al. (2017)
    IFAC-PapersOnLine ~ 20th IFAC World Congress. Proceedings
    Polynomial optimization is an active field of research which can be used in a broad range of applications including the synthesis of control policies for non-linear systems, and solution methods such as approximate dynamic programming. Finding the optimal solution of a generic polynomial optimization problem remains a computationally intractable problem. Several studies in the literature resort to hierarchical schemes that converge to the optimal solution, by employing appropriate convex relaxations of the original problem. In this direction, sum of squares methods have shown to be effective in addressing problems of low degree and dimension, with numerous MATLAB toolboxes allowing for efficient implementation. An alternative solution method is to cast the problem as a signomial optimization and solve it using a hierarchy of relative entropy relaxations. In contrast to sum of squares, this method can tackle problems involving high degree and dimension polynomials. In this paper, we develop the publicly available REPOP toolbox to address polynomial optimization problems using relative entropy relaxations. The toolbox is equipped with appropriate pre-processing routines that considerably reduce the size of the resulting optimization problem. In addition, we propose a convergent hierarchy which combines aspects from sum of squares and relative entropy relaxations. The proposed method offers computational advantages over both methods.
  • Performance guarantees of forward and reverse greedy algorithms for minimizing nonsupermodular nonsubmodular functions on a matroid
    Item type: Working Paper
    Karaca, Orçun; Tihanyi, Dániel; Kamgarpour, Maryam (2021)
    This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied problems including video summarization, actuator and sensor placement problems in control theory, multi-robot task allocation problems, and many others. We study two greedy heuristics, namely, the forward and the reverse greedy algorithms. We provide two novel performance guarantees for the approximate solutions obtained by these heuristics depending on both the submodularity ratio and the curvature.
  • A convex relaxation approach for the optimized pulse pattern problem
    Item type: Conference Paper
    Wachter, Lukas; Karaca, Orçun; Darivianakis, Georgios; et al. (2021)
    2021 European Control Conference (ECC)
    Optimized Pulse Patterns (OPPs) are gaining increasing popularity in the power electronics community over the well-studied pulse width modulation due to their inherent ability to provide the switching instances that optimize current harmonic distortions. In particular, the OPP problem minimizes current harmonic distortions under a cardinality constraint on the number of switching instances per fundamental wave period. The OPP problem is, however, non-convex involving both polynomials and trigonometric functions. In the existing literature, the OPP problem is solved using off-the-shelf solvers with local convergence guarantees. To obtain guarantees of global optimality, we employ and extend techniques from polynomial optimization literature and provide a solution with a global convergence guarantee. Specifically, we propose a polynomial approximation to the OPP problem to then utilize well-studied globally convergent convex relaxation hierarchies, namely, semi-definite programming and relative entropy relaxations. The resulting hierarchy is proven to converge to the global optimal solution. Our method exhibits a strong performance for OPP problems up to 50 switching instances per quarter wave.
  • Exploiting Weak Supermodularity for Coalition-Proof Mechanisms
    Item type: Conference Paper
    Karaca, Orçun; Kamgarpour, Maryam (2018)
    2018 IEEE Conference on Decision and Control (CDC)
  • A comment on performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid
    Item type: Journal Article
    Karaca, Orçun; Guo, Baiwei; Kamgarpour, Maryam (2021)
    European Journal of Operational Research
    We provide a counterexample to the performance guarantee obtained in the paper “Il’ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid”, which was published in Volume 171 of the European Journal of Operational Research. We point out where this error originates from in the proof of the main theorem.
  • Designing Coalition-Proof Reverse Auctions over Continuous Goods
    Item type: Working Paper
    Karaca, Orçun; Sessa, Pier Giuseppe; Walton, Neil; et al. (2018)
  • Core-Selecting Mechanisms in Electricity Markets
    Item type: Journal Article
    Karaca, Orçun; Kamgarpour, Maryam (2020)
    IEEE Transactions on Smart Grid
  • Game Theoretic Analysis of Electricity Market Auction Mechanisms
    Item type: Conference Paper
    Karaca, Orçun; Kamgarpour, Maryam (2017)
    2017 IEEE 56th Annual Conference on Decision and Control (CDC)
    We consider two prominent mechanisms for the electricity market; the pay-as-bid mechanism, currently applied in certain control reserve markets, and the proposed Vickrey- Clarke-Groves mechanism, an established auction mechanism used in advertising and spectrum auctions, for example. Bringing in tools from game theory and auction theory, we compare the Nash equilibria of these two mechanisms in terms of social efficiency and strategic behavior of the players. Furthermore, by formulating a coalitional game corresponding to the electricity market, we propose alternative mechanisms that incentivize truthful bidding while ensuring shill bidding is not profitable. Finally, we analyze the proposed mechanisms in a case study based on electricity market data.
Publications1 - 10 of 17