Georgios Darivianakis

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Darivianakis

First Name

Georgios

ORCID

0000-0003-3101-8572

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Publications 1 - 9 of 9

Distributed Model Predictive Control for Linear Systems With Adaptive Terminal Sets
Darivianakis, Georgios; Eichler, Annika; Lygeros, John (2020)
IEEE Transactions on Automatic Control
We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples.
Scalability through decentralization: A robust control approach for the energy management of a building community
Darivianakis, Georgios; Georghiou, Angelos; Eichler, Annika; et al. (2017)
IFAC-PapersOnLine ~ 20th IFAC World Congress. Proceedings
Recent studies in the literature have shown that cooperative energy management of Abstract: Recent studies in the literature have shown that cooperative energy management of an aggregation of buildings may lead to substantial energy savings. These approaches typically assume the existence of a central operator that is capable of formulating and solving, within a reasonable amount of time, a centralized optimization problem. However, this requirement may be unrealizable in cases of large scale districts, and it also fails to address privacy concerns of the building occupants. In this paper, we deal with these issues by proposing a decentralized control scheme which only requires the individual buildings to communicate bounds on their energy demands. The proposed method partly alleviates concerns on privacy since this limited communication scheme does not reveal the exact characteristics of the energy usage within each building. In addition, it enables a distributed computation of the solution, making our method highly scalable. We demonstrate through a numerical study the efficacy of the proposed approach, which leads to solutions that closely approximate those obtained by the centralized formulation only at a fraction of the computational effort.
The REPOP toolbox: tackling polynomial optimization using relative entropy relaxations
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.
A convex relaxation approach for the optimized pulse pattern problem
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.
A stochastic optimization approach to cooperative building energy management via an energy hub
Darivianakis, Georgios; Georghiou, Angelos; Smith, Roy; et al. (2015)
2015 IEEE 54th Annual Conference on Decision and Control (CDC)
Building energy management is an active field or research since the potential in energy savings can be substantial. Nevertheless, the opportunities for large saving of individual buildings can be limited by the flexibility of the installed climate control devices and the individual construction characteristics. The energy hub concept allows one to manage a collection of buildings in a cooperative manner, by providing opportunities for load shifting between buildings and the sharing of expensive but energy efficient equipment housed in the hub, such as heat pumps, boilers, batteries. Typically, control design for the buildings and the energy hub are done separately, underutilizing the potential flexibility provided by the interconnected system. To address these issues, we propose a unified framework for controlling the operation of the energy hub and the buildings it connects to. By modeling all exogenous disturbance parameters as stochastic processes, and by using state-space representation of the building dynamics, we formulate a multistage stochastic optimization problem to minimize the total energy consumption of the system in a cooperative manner. We solve the resulting infinite dimensional optimization problem using a decision rule approximation, and we benchmark its performance on a numerical study, comparing it with established solution techniques.
High-Performance Cooperative Distributed Model Predictive Control for Linear Systems
Darivianakis, Georgios; Fattahi, Salar; Lygeros, John; et al. (2018)
2018 American Control Conference (ACC)
Approximate Explicit Model Predictive Controller using Gaussian Processes
Binder, Matthias; Darivianakis, Georgios; Eichler, Annika; et al. (2020)
2019 IEEE 58th Conference on Decision and Control (CDC)
A Robust Optimization Approach to Network Control Using Local Information Exchange
Darivianakis, Georgios; Georghiou, Angelos; Shafiee, Soroosh; et al. (2024)
Operations Research
Designing policies for a network of agents is typically done by formulating an optimization problem where each agent has access to state measurements of all the other agents in the network. Such policy designs with centralized information exchange result in optimization problems that are typically hard to solve, require establishing substantial communication links, and do not promote privacy since all information is shared among the agents. Designing policies based on arbitrary communication structures can lead to nonconvex optimization problems that are typically NP-hard. In this work, we propose an optimization framework for decentralized policy designs. In contrast to the centralized information exchange, our approach requires only local communication exchange among the neighboring agents matching the physical coupling of the network. Thus, each agent only requires information from its direct neighbors, minimizing the need for excessive communication and promoting privacy amongst the agents. Using robust optimization techniques, we formulate a convex optimization problem with a loosely coupled structure that can be solved efficiently. We numerically demonstrate the efficacy of the proposed approach in energy management and supply chain applications. We show that the proposed approach leads to solutions that closely approximate those obtained by the centralized formulation only at a fraction of the computational effort.
Data-Driven Decentralized Decision Making under Uncertainty in Energy Systems
Darivianakis, Georgios (2018)

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Georgios Darivianakis

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