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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. Decentralized control of distributed energy resources in radial distribution systems

   https://doi.org/10.1109/SmartGridComm.2016.7778777  

   Lin, Weixuan; Bitar, Eilyan (November 2016, 2016 IEEE International Conference on Smart Grid Communications (SmartGridComm))

   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. 

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3. Bridging Transient and Steady-State Performance in Voltage Control: A Reinforcement Learning Approach With Safe Gradient Flow

   https://doi.org/10.1109/LCSYS.2023.3289435  

   Feng, Jie; Cui, Wenqi; Cortés, Jorge; Shi, Yuanyuan (June 2023, IEEE Control Systems Letters)

   Deep reinforcement learning approaches are becoming appealing for the design of nonlinear controllers for voltage control problems, but the lack of stability guarantees hinders their real-world deployment. This letter constructs a decentralized RL-based controller for inverter-based real-time voltage control in distribution systems. It features two components: a transient control policy and a steady-state performance optimizer. The transient policy is parameterized as a neural network, and the steady-state optimizer represents the gradient of the long-term operating cost function. The two parts are synthesized through a safe gradient flow framework, which prevents the violation of reactive power capacity constraints. We prove that if the output of the transient controller is bounded and monotonically decreasing with respect to its input, then the closed-loop system is asymptotically stable and converges to the optimal steady-state solution. We demonstrate the effectiveness of our method by conducting experiments with IEEE 13-bus and 123-bus distribution system test feeders. 

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4. Event-Triggered Robust Stabilization of Nonlinear Input-Constrained Systems Using Single Network Adaptive Critic Designs

   https://doi.org/10.1109/TSMC.2018.2853089  

   Xiong Yang, Haibo He (January 2018, IEEE transactions on systems, man, and cybernetics. Systems)

   In this paper, we study the event-triggered robust stabilization problem of nonlinear systems subject to mismatched perturbations and input constraints. First, with the introduction of an infinite-horizon cost function for the auxiliary system, we transform the robust stabilization problem into a constrained optimal control problem. Then, we prove that the solution of the event-triggered Hamilton–Jacobi–Bellman (ETHJB) equation, which arises in the constrained optimal control problem, guarantees original system states to be uniformly ultimately bounded (UUB). To solve the ETHJB equation, we present a single network adaptive critic design (SN-ACD). The critic network used in the SN-ACD is tuned through the gradient descent method. By using Lyapunov method, we demonstrate that all the signals in the closed-loop auxiliary system are UUB. Finally, we provide two examples, including the pendulum system, to validate the proposed event-triggered control strategy. 

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5. Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

   https://doi.org/10.1109/TRO.2019.2923880  

   Abraham, Ian; Murphey, Todd D. (July 2019, IEEE Transactions on Robotics)

   This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free-fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems. 

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