Weixuan Lin

Performance bounds for robust decentralized control

We consider the decentralized output feedback control of stochastic linear systems, subject to robust linear constraints on both the state and input trajectories. For problems with partially nested information structures, we establish an upper bound on the minimum achievable cost by computing the optimal affine decentralized control policy as a solution to a finite-dimensional conic program. For problems with general (possibly nonclassical) information structures, we construct another finite-dimensional conic program whose optimal value stands as a lower bound on the minimum achievable cost. With this lower bound in hand, one can bound the suboptimality incurred by any feasible decentralized control policy. A study of a partially nested system reveals that affine policies can be close to optimal, even in the presence state/input constraints and non-Gaussian disturbances.

Decentralized control of distributed energy resources in radial distribution systems

We consider the decentralized control of radial distribution systems with controllable photovoltaic inverters and storage devices. For such systems, we consider the problem of designing controllers that minimize the expected cost of meeting demand, while respecting distribution system and resource 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 convex quadratic constraints on the state and input. As such problems are, in general, computationally intractable, we derive an inner approximation to this decentralized control problem, which enables the efficient computation of an affine control policy via the solution of a conic program. As affine policies are, in general, suboptimal for the systems considered, we provide an efficient method to bound their suboptimality via the solution of another conic program. A case study of a 12 kV radial distribution feeder demonstrates that decentralized affine controllers can perform close to optimal.

Networked Cournot Competition in Platform Markets: Access Control and Efficiency Loss

This paper studies network design and efficiency loss in online platforms using the model of networked Cournot competition. We consider two styles of platforms: open access platforms and discriminatory access platforms. In open access platforms, every firm can connect to every market, while discriminatory access platforms limit connections between firms and markets in order to improve social welfare. Our results provide tight bounds on the efficiency loss of both open access and discriminatory access platforms. For open access platforms, we show that the efficiency loss at a Nash equilibrium is upper bounded by 3/2. In the case of discriminatory access platforms, we prove that, under an assumption on the linearity of cost functions, a greedy algorithm for optimizing network connections can guarantee the efficiency loss at a Nash equilibrium is upper bounded by 4/3.