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Register a new userA Distributed Optimization Scheme for State Estimation of Nonlinear Networks with Norm-bounded Uncertainties
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This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach, the estimation problem is reformulated as an optimization problem, solving for a solution in a distributed way by utilizing a decoupling technique. Then, based on this solution, a class of estimators is designed to handle the system dynamics and constraints. A novel feature of this design lies in the unified modeling of uncertainties and nonlinearities, the decoupling of nodes, and the construction of recursive approximate covariance matrices for the optimization problem. Furthermore, the feasibility of the proposed estimators and the boundedness of the mean-square errors are ensured under a developed criterion, which is easier to check than some typical estimation strategies including the linear matrix inequalities-based and the variance-constrained ones. Finally, the effectiveness of the theoretical results is verified by a numerical simulation.
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In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.
This paper proposes a joint input and state dynamic estimation scheme for power networks in microgrids and active distribution systems with unknown inputs. The conventional dynamic state estimation of power networks in the transmission system relies on the forecasting methods to obtain the state-transition model of state variables. However, under highly dynamic conditions in the operation of microgrids and active distribution networks, this approach may become ineffective as the forecasting accuracy is not guaranteed. To overcome such drawbacks, this paper employs the power networks model derived from the physical equations of branch currents. Specifically, the power network model is a linear state-space model, in which the state vector consists of branch currents, and the input vector consists of bus voltages. To estimate both state and input variables, we propose linear Kalman-based dynamic filtering algorithms in batch-mode regression form, considering the cross-correlation between states and inputs. For the scalability of the proposed scheme, the distributed implementation is also presented. Complementarily, the predicted state and input vectors are leveraged for bad data detection. Results carried out on a 13-bus microgrid system in real-time Opal-RT platform demonstrate the effectiveness of the proposed method in comparison with the traditional weighted least square and tracking state estimation methods.
Although state estimation in networked control systems is a fundamental problem, few efforts have been made to study distributed state estimation via multiple access channels (MACs). In this article, we give a characterization of the zero-error capacity region of an M-input, single-output MAC at any finite block-length. To this end, nonstochastic information-theoretic tools are used to derive the converse and achievability proofs. Next, a tight condition to be able to achieve uniformly bounded state estimation errors over such a MAC is provided. The obtained condition establishes a connection between the intrinsic topological entropies of the linear systems and the zero-error capacity region of the MAC.
We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals. Leveraging affine abstraction methods and the existence of nonlinear decomposition functions, as well as applying our previously developed data-driven function over-approximation/abstraction approach to over-estimate the unknown dynamic model, our proposed observer recursively computes the maximal and minimal elements of the estimate intervals that are proven to contain the true augmented states. Then, using observed output/measurement signals, the observer iteratively shrinks the intervals by eliminating estimates that are not compatible with the measurements. Finally, given new interval estimates, the observer updates the over-approximation of the unknown model dynamics. Moreover, we provide sufficient conditions for uniform boundedness of the sequence of estimate interval widths, i.e., stability of the designed observer, in the form of tractable (mixed-)integer programs with finitely countable feasible sets.
Demand flexibility is increasingly important for power grids, in light of growing penetration of renewable generation. Careful coordination of thermostatically controlled loads (TCLs) can potentially modulate energy demand, decrease operating costs, and increase grid resiliency. However, it is challenging to control a heterogeneous population of TCLs: the control problem has a large state action space; each TCL has unique and complex dynamics; and multiple system-level objectives need to be optimized simultaneously. To address these challenges, we propose a distributed control solution, which consists of a central load aggregator that optimizes system-level objectives and building-level controllers that track the load profiles planned by the aggregator. To optimize our agents policies, we draw inspirations from both reinforcement learning (RL) and model predictive control. Specifically, the aggregator is updated with an evolutionary strategy, which was recently demonstrated to be a competitive and scalable alternative to more sophisticated RL algorithms and enables policy updates independent of the building-level controllers. We evaluate our proposed approach across four climate zones in four nine-building clusters, using the newly-introduced CityLearn simulation environment. Our approach achieved an average reduction of 16.8% in the environment cost compared to the benchmark rule-based controller.
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