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We propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify an optimal sparse control architecture and optimize the closed-loop performance while stabilizing the system in the mean-square sense. Our approach approximates the nonconvex combinatorial optimization problem by minimizing various matrix norms subject to the linear matrix inequality (LMI) stability condition. We present two design problems to reduce the number of actuators and the number of sensors via a low-dimensional output. A regularized linear quadratic regulator with multiplicative (LQRm) noise optimal control problem and its convex relaxation are presented to demonstrate the tradeoff between the suboptimal closed-loop performance and the sparsity degree of control structure. Case studies on power grids for wide-area frequency control show that the proposed sparsity-promoting control can considerably reduce the number of sensors and actuators without significant loss in system performance. The sparse control architecture is robust to substantial system-level disturbances while achieving mean-square stability.

In this article, we propose an optimal joint optimization–estimation architecture for distribution networks, which jointly solves the optimal power flow (OPF) problem and static state estimation (SE) problem through an online gradient-based feedback algorithm. The main objective is to enable a fast and timely interaction between the OPF decisions and state estimators with limited sensor measurements. First, convergence and optimality of the proposed algorithm are analytically established. Then, the proposed gradient-based algorithm is modified by introducing statistical information of the inherent estimation and linearization errors for an improved and robust performance of the online OPF decisions. Overall, the proposed method eliminates the traditional separation of operation and monitoring, where optimization and estimation usually operate at distinct layers and different time scales. Hence, it enables a computationally affordable, efficient, and robust online operational framework for distribution networks under time-varying settings.

In this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy “pseudomeasurements.” We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

In this article, we propose a data-based methodology to solve a multiperiod stochastic optimal water flow (OWF) problem for water distribution networks (WDNs). The framework explicitly considers the pump schedule and water network head level with limited information of demand forecast errors for an extended period simulation. The objective is to determine the optimal feedback decisions of network-connected components, such as nominal pump schedules and tank head levels and reserve policies, which specify device reactions to forecast errors for accommodation of fluctuating water demand. Instead of assuming that the uncertainties across the water network are generated by a prescribed certain distribution, we consider ambiguity sets of distributions centered at an empirical distribution, which is based directly on a finite training dataset. We use a distance-based ambiguity set with the Wasserstein metric to quantify the distance between the real unknown data-generating distribution and the empirical distribution. This allows our multiperiod OWF framework to trade off system performance and inherent sampling errors in the training dataset. Case studies on a three-tank WDN systematically illustrate the tradeoff between pump operational cost, risks of constraint violation, and out-of-sample performance.