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1. Decentralized Stochastic Control of Distributed Energy Resources

   https://doi.org/10.1109/TPWRS.2017.2700472  

   Lin, Weixuan; Bitar, Eilyan (May 2017, IEEE Transactions on Power Systems)

   We consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and energy storage resources. For such systems, we investigate the problem of designing fully decentralized controllers that minimize the expected cost of balancing demand, while guaranteeing the satisfaction of individual resource and distribution system voltage constraints. Employing a linear approximation of the branch flow model, we formulate this problem as the design of a decentralized disturbance-feedback controller that minimizes the expected value of a convex quadratic cost function, subject to robust convex quadratic constraints on the system state and input. As such problems are, in general, computationally intractable, we derive a tractable inner approximation to this decentralized control problem, which enables the efficient computation of an affine control policy via the solution of a finite-dimensional conic program. As affine policies are, in general, suboptimal for the family of systems considered, we provide an efficient method to bound their suboptimality via the optimal solution of another finite-dimensional conic program. A case study of a 12 kV radial distribution system demonstrates that decentralized affine controllers can perform close to optimal. 

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2. Communication- and Control-aware Optimal Quantizer Selection for Multi-agent Control

   https://doi.org/10.1109/LCSYS.2024.3416858  

   Afshari, M; Maity, D; Tsiotras, P (June 2024, IEEE control systems letters)

   We consider a multi-agent linear quadratic optimal control problem. Due to communication constraints, the agents are required to quantize their local state measurements before communicating them to the rest of the team, thus resulting in a decentralized information structure. The optimal controllers are to be synthesized under this decentralized and quantized information structure. The agents are given a set of quantizers with varying quantization resolutions—higher resolution incurs higher communication cost and vice versa. The team must optimally select the quantizer to prioritize agents with ‘highquality’ information for optimizing the control performance under communication constraints. We show that there exist a sepatation between the optimal solution to the control problem and the choice of the optimal quantizer. We show that the optimal controllers are linear and the optimal selection of the quantizers can be determined by solving a linear program. 

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3. Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts

   https://doi.org/10.23919/ACC45564.2020.9147215  

   Lin, Weixuan; Bitar, Eilyan (July 2020, 2020 American Control Conference (ACC))

   null (Ed.)

   We consider the decentralized control of a discretetime, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. In this context, we investigate the design of decentralized controllers that are affinely parameterized in their measurement history. For problems with partially nested information structures, the optimization over such policy spaces is known to be convex. Convexity is not, however, guaranteed under more general (nonclassical) information structures in which the information available to one local controller can be affected by control actions that it cannot access or reconstruct. With the aim of alleviating the nonconvexity that arises in such problems, we propose an approach to decentralized control design where the information-coupling states are effectively treated as disturbances whose trajectories are constrained to take values in ellipsoidal contract sets whose location, scale, and orientation are jointly optimized with the underlying affine decentralized control policy. We establish a natural structural condition on the space of allowable contracts that facilitates the joint optimization over the control policy and the contract set via semidefinite programming. 

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4. A global algorithm for AC optimal power flow based on successive linear conic optimization

   https://doi.org/10.1109/PESGM.2017.8273957  

   Barati, Masoud; Kargarian, Amin (July 2017, 2017 IEEE Power & Energy Society General Meeting)

   Newly, there has been significant research interest in the exact solution of the AC optimal power flow (AC-OPF) problem. A semideflnite relaxation solves many OPF problems globally. However, the real problem exists in which the semidefinite relaxation fails to yield the global solution. The appropriation of relaxation for AC-OPF depends on the success or unfulflllment of the SDP relaxation. This paper demonstrates a quadratic AC-OPF problem with a single negative eigenvalue in objective function subject to linear and conic constraints. The proposed solution method for AC-OPF model covers the classical AC economic dispatch problem that is known to be NP-hard. In this paper, by combining successive linear conic optimization (SLCO), convex relaxation and line search technique, we present a global algorithm for AC-OPF which can locate a globally optimal solution to the underlying AC-OPF within given tolerance of global optimum solution via solving linear conic optimization problems. The proposed algorithm is examined on modified IEEE 6-bus test system. The promising numerical results are described. 

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5. Submodularity in Conic Quadratic Mixed 0–1 Optimization

   https://doi.org/10.1287/opre.2019.1888  

   Atamtürk, Alper; Gómez, Andrés (January 2020, Operations Research)

   We describe strong convex valid inequalities for conic quadratic mixed 0–1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0–1 relaxations. The inequalities exploit the submodularity of the binary restrictions and are based on the polymatroid inequalities over binaries for the diagonal case. We prove that the convex inequalities completely describe the convex hull of a single conic quadratic constraint as well as the rotated cone constraint over binary variables and unbounded continuous variables. We then generalize and strengthen the inequalities by incorporating additional constraints of the optimization problem. Computational experiments on mean-risk optimization with correlations, assortment optimization, and robust conic quadratic optimization indicate that the new inequalities strengthen the convex relaxations substantially and lead to significant performance improvements. 

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