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Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We conduct here a comprehensive study of these operators and their relevant system-theoretic properties. The general theory is then leveraged to delineate both known and new design methodologies for control, estimation, and model reduction. Several entirely new designs arise from this systematic categorization, including new recursive and low-gain design frameworks for observation of cascaded systems. The benefits of the results beyond the linear time-invariant setting are demonstrated through preliminary extensions for nonlinear systems, with an outlook towards the development of a similarly comprehensive nonlinear theory., Comment: 16 pages, 5 figures, submitted for publication

We propose a data-driven receding-horizon control method dealing with the chance-constrained output-tracking problem of unknown stochastic linear time-invariant (LTI) systems with partial state observation. The proposed method takes into account the statistics of the process noise, the measurement noise and the uncertain initial condition, following an analogous framework to Stochastic Model Predictive Control (SMPC), but does not rely on the use of a parametric system model. As such, our receding-horizon algorithm produces a sequence of closed-loop control policies for predicted time steps, as opposed to a sequence of open-loop control actions. Under certain conditions, we establish that our proposed data-driven control method produces identical control inputs as that produced by the associated model-based SMPC. Simulation results on a grid-connected power converter are provided to illustrate the performance benefits of our methodology., Comment: 20 pages, 4 figures. The extended version of a submission to IEEE Transactions on Automatic Control

Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to follow, and an online/closed-loop stage, tracking, that corrects for unmodeled dynamics and disturbances. Such an approach generally introduces conservativeness into the planning stage, which becomes difficult to overcome as the model complexity increases and real-time decisions need to be made in a changing environment. This work addresses these challenges for the class of differentially flat nonlinear systems by integrating planning and control into a cohesive closed-loop task. Precisely, we develop an optimization-based framework that aims to steer a differentially flat system to a trajectory implicitly defined via a constrained time-varying optimization problem. To that end, we generalize the notion of feedback linearization, which makes non-linear systems behave as linear systems, and develop controllers that effectively transform a differentially flat system into an optimization algorithm that seeks to find the optimal solution of a (possibly time-varying) optimization problem. Under sufficient regularity assumptions, we prove global asymptotic convergence for the optimization dynamics to the minimizer of the time-varying optimization problem. We illustrate the effectiveness of our method with two numerical examples: a multi-robot tracking problem and a robot obstacle avoidance problem.

Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be conservative. Here we consider a class of first-order algorithms for linearly constrained convex optimization problems, and provide a linear matrix inequality (LMI) analysis framework for certifying worst-case exponential convergence rates. Our approach builds on recent results for interpolation of convex functions and linear operators, and our LMI directly constructs a Lyapunov function certifying the guaranteed convergence rate. By comparing to rates established in the literature, we show that our approach can certify significantly faster convergence for this family of algorithms., Comment: 6 pages, 2 figures, to appear at IEEE Conference on Decision and Control 2023

To address the control challenges associated with the increasing share of inverter-connected renewable energy resources, this paper proposes a direct data-driven approach for fast frequency control in the bulk power system. The proposed control scheme partitions the power system into control areas, and leverages local dispatchable inverter-based resources to rapidly mitigate local power imbalances upon events. The controller design is based directly on historical measurement sequences, and does not require identification of a parametric power system model. Theoretical results are provided to support the approach. Simulation studies on a nonlinear three-area test system demonstrate that the controller provides fast and localized frequency control under several types of contingencies.

Current approaches to data-driven control are geared towards optimal performance, and often integrate aspects of machine learning and large-scale convex optimization, leading to complex implementations. In many applications, it may be preferable to sacrifice performance to obtain significantly simpler controller designs. We focus here on the problem of output regulation for linear systems, and revisit the so-called tuning regulator of E. J. Davison as a minimal-order data-driven design for tracking and disturbance rejection. Our proposed modification of the tuning regulator relies only on samples of the open-loop plant frequency response for design, is tuned online by adjusting a single scalar gain, and comes with a guaranteed margin of stability; this provides a faithful extension of tuning procedures for SISO integral controllers to MIMO systems with mixed constant and harmonic disturbances. The results are illustrated via application to a four-tank water control process., Comment: Submitted to IEEE Conference on Decision and Control 2023

Reactive power sharing and containment of voltages within limits for inverter-based resources (IBRs) are two important, yet coupled objectives in ac networks. In this article, we propose a distributed control technique to simultaneously achieve these objectives. Our controller consists of two components: a purely local nonlinear integral controller which adjusts the IBR voltage setpoint, and a distributed primal-dual optimizer that coordinates reactive power sharing between the IBRs. The controller prioritizes the voltage containment objective over reactive power sharing at all points in time; excluding the IBRs with saturated voltages, it provides reactive power sharing among all the IBRs. Considering the voltage saturation and the coupling between voltage and angle dynamics, a formal closed-loop stability analysis based on singular perturbation theory is provided, yielding practical tuning guidance for the overall control system. To validate the effectiveness of the proposed controller for different case studies, we apply it to a low-voltage microgrid and a microgrid adapted from the CIGRE medium-voltage network benchmark, both simulated in the MATLAB/Simulink environment., Comment: Summitted to IEEE TSG

This paper presents an algorithm that solves the AC power flow problem for balanced, three-phase transmission systems at steady state. The algorithm extends the "fixed-point power flow" algorithm in the literature to include transmission losses, phase-shifting transformers, and a distributed slack bus model. The algorithm is derived by vectorizing the component-wise AC power flow equations and manipulating them into a novel equivalent fixed-point form. Preliminary theoretical results guaranteeing convergence are reported for the case of a two-bus power system. We validate the algorithm through extensive simulations on test systems of various sizes under different loading levels, and compare its convergence behavior against those of classic power flow algorithms., Comment: Submitted to American Control Conference 2023

We consider the problem of designing a feedback controller which robustly regulates an LTI system to an optimal operating point in the presence of unmeasured disturbances. A general design framework based on so-called optimality models was previously put forward for this class of problems, effectively reducing the problem to that of stabilization of an associated nonlinear plant. This paper presents several simple and fully constructive stabilizer designs to accompany the optimality model designs from [1]. The designs are based on a low-gain integral control approach, which enforces time-scale separation between the exponentially stable plant and the controller. We provide explicit formulas for controllers and gains, along with LMI-based methods for the computation of robust/optimal gains. The results are illustrated via an academic example and an application to power system frequency control., Comment: 8 pages, to appear in IEEE CDC 2022

We consider the problem of data-driven predictive control for an unknown discrete-time linear time-periodic (LTP) system of known period. Our proposed strategy generalizes both Data-enabled Predictive Control (DeePC) and Subspace Predictive Control (SPC), which are established data-driven control techniques for linear time-invariant (LTI) systems. The approach is supported by an extensive theoretical development of behavioral systems theory for LTP systems, culminating in a generalization of the fundamental lemma. Our algorithm produces results identical to standard Model Predictive Control (MPC) for deterministic LTP systems. Robustness of the algorithm to noisy data is illustrated via simulation of a regularized version of the algorithm applied to a stochastic multi-input multi-output LTP system., Comment: 12 pages, 7 figures, the extended version of a CDC 2022 paper