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1. Optimal Steady-State Control for Linear Time-Invariant Systems

   https://doi.org/10.1109/CDC.2018.8619812  

   Lawrence, Liam S.; Nelson, Zachary E.; Mallada, Enrique; Simpson-Porco, John W. (December 2018, 2018 IEEE Conference on Decision and Control (CDC))

   We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations. 

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2. An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systems

   https://doi.org/10.23919/ACC.2018.8431231  

   Nelson, Zachary E.; Mallada, Enrique (June 2018, 2018 Annual American Control Conference (ACC))

   Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. We logically divide the proposed solution into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component calculates an input to the LTI system that aims to drive the system toward the optimal steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using Integral Quadratic Constraints (IQCs), the proposed framework can translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed-loop system. We illustrate several resulting controller designs using a numerical example. 

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3. Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs

   https://doi.org/10.1109/TAC.2018.2884650  

   Weitenberg, Erik; Jiang, Yan; Zhao, Changhong; Mallada, Enrique; De Persis, Claudio; Dorfler, Florian (December 2018, IEEE Transactions on Automatic Control)

   Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of the energy transition, technological advances, and the scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently that rely on communication amongst local controllers. In this paper, we propose a fully decentralized leaky integral controller for frequency restoration that is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable trade-off between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its DC gain and time constant. We compare our findings to conventional decentralized integral control and distributed- averaging-based integral control in theory and simulations. 

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4. 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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5. On Abstraction-Based Controller Design With Output Feedback

   https://doi.org/10.1145/3365365.3382219  

   Majumdar, Rupak; Ozay, Necmiye; Schmuck, Anne-Kathrin (January 2020, Proc. Hybrid Systems Computation and Control (HSCC) 2020.)

   null (Ed.)

   We consider abstraction-based design of output-feedback controllers for dynamical systemswith a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original systemand its abstractionwhich characterizes the soundness and completeness conditions for an abstract state-feedback controller to be refined to a concrete output-feedback controller for the original system, and (II) we provide an algorithm to compute a sound finite-state abstraction fulfilling this relation. Our relation generalizes feedback-refinement relations fromABCD with state-feedback. Our algorithm for constructing sound finitestate abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis. We lift their idea to the computation of an observation-equivalent system and show how sound abstractions can be obtained by stopping this algorithm at any point. Additionally, our new algorithm produces a realization of the topological closure of the input/output behavior of the original system if it is finite state realizable. 

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