arXiv subjects

John W. Simpson-Porco

Publications and source records attributed to John W. Simpson-Porco.

At least 19 recordsLinked to original sources

arXiv2026

Closed-Loop Motion Planning for Differentially Flat Systems: A Time-Varying Optimization Framework

Motion planning and control are two core components of the robotic autonomy stack. The standard way to combine them uses an offline/open-loop stage, planning, which designs a feasible and safe trajectory, and an online/closed-loop stage, tracking, which corrects for unmodeled dynamics and disturbances. This separation introduces conservatism in planning that becomes difficult to overcome as model complexity increases and real-time decisions must be made in a changing environment. This work addresses these challenges for differentially flat nonlinear systems by integrating planning and control into a single closed-loop task. We develop an optimization-based framework that steers a flat system to a trajectory implicitly defined via a constrained time-varying optimization problem. Generalizing feedback linearization, our controllers effectively transform the flat system into an algorithm that seeks the optimal solution of the time-varying problem. Under sufficient regularity assumptions, we prove global asymptotic convergence to the time-varying minimizer. We illustrate the method on multi-robot tracking and robot obstacle avoidance problems.

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arXiv2026

A Lyapunov Characterization of Robust D-Stability with Application to Decentralized Integral Control of LTI Systems

The concept of matrix D-stability plays an important role in applications, ranging from economic and biological system models to decentralized control. Here we provide necessary and sufficient Lyapunov-type conditions for the robust (block) D-stability property. We leverage this characterization as part of a novel Lyapunov analysis of decentralized integral control for MIMO LTI systems, providing sufficient conditions guaranteeing stability under low-gain and under arbitrary connection and disconnection of individual control loops.

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arXiv2026

Frequency Nadir-Constrained Power System Restoration Planning with Energy Storage

Power system restoration following blackouts must ensure frequency stability throughout the recovery process. This paper proposes a frequency-constrained mixed-integer linear programming (MILP) framework for black-start restoration planning in transmission systems with synchronous machines and energy storage systems. To prevent excessive frequency deviations caused by restorative actions, a frequency nadir prediction method is developed for power systems with energy storage system (ESS) integration and incorporated into a multiperiod optimization framework. The formulation ensures that frequency deviations resulting from restorative actions remain within prescribed safe limits. Furthermore, the presented framework leverages ESSs to enhance frequency security and recovery speed. Case studies on a modified IEEE 9-bus system demonstrate that the computed restoration plan maintains frequency security, as validated through MATLAB and PSS/E simulations, while reducing restoration time through ESS coordination.

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arXiv2025

Stochastic Data-Driven Predictive Control with Equivalence to Stochastic MPC

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.

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arXiv2025

Removing Time-Scale Separation in Feedback-Based Optimization via Estimators

Feedback-based optimization (FBO) provides a simple control framework for regulating a stable dynamical system to the solution of a constrained optimization problem in the presence of exogenous disturbances, and does so without full knowledge of the plant dynamics. However, closed-loop stability requires the controller to operate on a sufficiently slower timescale than the plant, significantly constraining achievable closed-loop performance. Motivated by this trade-off, we propose an estimator-based modification of FBO which leverages dynamic plant model information to eliminate the time-scale separation requirement of traditional FBO. Under this design, the convergence rate of the closed-loop system is limited only by the dominant eigenvalue of the open-loop system. We extend the approach to the case of design based on only an approximate plant model when the original system is singularly perturbed. The results are illustrated via an application to fast power system frequency control using inverter-based resources.

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arXiv2025

Steady-State Cascade Operators and their Role in Linear Control, Estimation, and Model Reduction Problems

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 leveraged to delineate both known and new design methodologies for control and observation of cascades, and to characterize structural properties of reduced models. 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.

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arXiv2024

Data-driven harmonic output regulation of a class of nonlinear systems

The paper deals with the data-based design of state-feedback controllers that solve the output regulation problem for a class of nonlinear systems. Inspired by recent developments in model-based output regulation design techniques and in data-driven control design for nonlinear systems, we derive a data-dependent semidefinite program that, when solved, directly returns a controller that steers the regulation error to a periodic signal whose Fourier series has identically zero coefficients up to a certain order set by the controller. When specialized to the case of linear systems, the result appears to improve upon existing work. Numerical results illustrate the findings

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arXiv2024

Distributionally Robust Stochastic Data-Driven Predictive Control with Optimized Feedback Gain

We consider the problem of direct data-driven predictive control for unknown stochastic linear time-invariant (LTI) systems with partial state observation. Building upon our previous research on data-driven stochastic control, this paper (i) relaxes the assumption of Gaussian process and measurement noise, and (ii) enables optimization of the gain matrix within the affine feedback policy. Output safety constraints are modelled using conditional value-at-risk, and enforced in a distributionally robust sense. Under idealized assumptions, we prove that our proposed data-driven control method yields control inputs identical to those produced by an equivalent model-based stochastic predictive controller. A simulation study illustrates the enhanced performance of our approach over previous designs.

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arXiv2024

A Multi-Area Architecture for Real-Time Feedback-Based Optimization of Distribution Grids

A challenge in transmission-distribution coordination is how to quickly and reliably coordinate Distributed Energy Resources (DERs) across large multi-stakeholder Distribution Networks (DNs) to support the Transmission Network (TN), while ensuring operational constraints continue to be met within the DN. Here we propose a hierarchical feedback-based control architecture for coordination of DERs in DNs, enabling the DN to quickly respond to power set-point requests from the Transmission System Operator (TSO) while maintaining local DN constraints. Our scheme allows for multiple independently-managed areas within the DN to optimize their local resources while coordinating to support the TN, and while maintaining data privacy; the only required inter-area communication is between physically adjacent areas within the DN control hierarchy. We conduct a rigorous stability analysis, establishing intuitive conditions for closed-loop stability, and provide detailed tuning recommendations. The proposal is validated via case studies on multiple feeders, including IEEE-123 and IEEE-8500, using a custom MATLAB-based application which integrates with OpenDSS. The simulation results show that the proposed structure is highly scalable and can quickly coordinate DERs in response to TSO commands, while responding to local disturbances within the DN and maintaining DN operational limits.

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arXiv2023

Automated Lyapunov Analysis of Primal-Dual Optimization Algorithms: An Interpolation Approach

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.

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arXiv2023

Data-Driven Fast Frequency Control using Inverter-Based Resources

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.

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arXiv2023

Data-Driven Output Regulation using Single-Gain Tuning Regulators

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.

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arXiv2023

Distributed Optimization for Reactive Power Sharing and Stability of Inverter-Based Resources Under Voltage Limits

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.

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arXiv2022

A Fixed-Point Algorithm for the AC Power Flow Problem

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.

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arXiv2022

Data-Driven Model Predictive Control for Linear Time-Periodic Systems

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.

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arXiv2022

Low-Gain Stabilizers for Linear-Convex Optimal Steady-State Control

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.

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arXiv2021

Diagonal Stability of Systems with Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems

We study a class of matrices with a rank-1 interconnection structure, and derive a simple necessary and sufficient condition for diagonal stability. The underlying Lyapunov function is used to provide sufficient conditions for diagonal stability of approximately rank-1 interconnections. The main result is then leveraged as a key step in a larger stability analysis problem arising in power systems control. Specifically, we provide the first theoretical stability analysis of automatic generation control (AGC) in an interconnected nonlinear power system. Our analysis is based on singular perturbation theory, and provides theoretical justification for the conventional wisdom that AGC is stabilizing under the typical time-scales of operation. We illustrate how our main analysis results can be leveraged to provide further insight into the tuning and dynamic performance of AGC.

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arXiv2021

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forward-backward splitting algorithm to act as an integral controller which ensures that the input constraints are met at each time step. We establish a low-gain stability result for the closed-loop system when the plant is exponentially stable, generalizing previously known results for integral control of discrete-time systems. Specifically, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is strongly monotone, then the closed-loop system is exponentially stable for all sufficiently small integral gains. The method is illustrated via application to a four-tank process.

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