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At least 127 records · Page 7

Interactive Power to Frequency Dynamics Between Grid-Forming Inverters and Synchronous Generators in Power Electronics-Dominated Power Systems

With increased attention on grid-forming inverters as a power system stabilizing device during high shares of inverter-based resource operations, there is a present need for a transparent and methodical investigation of the inverted and direct power to frequency control capabilities and impacts of these devices on emerging power systems. Here, analysis of the frequency dynamics of the droop-controlled grid-forming inverter and the synchronous generator illuminates the inverted active power-frequency relationship and the frequency response order reduction, forming the basis for novel, nonlinear frequency control approaches. Device-level electromagnetic transient domain simulations corroborate the order-reduction findings, establish that a properly designed dc-side system has a negligible impact on power transfer and will not impede frequency regulation, and confirm the primary frequency response improvement with nonlinear control. Simulations of the 9- and 39-bus test systems validate the order reduction and associated decoupling of the nadir and rate of change of frequency in larger networks. Oscillatory mode analysis confirms the grid-forming benefit of increased damping; decreased damping is observed at shares above 80%, but not at 100%. Finally, simulations on a validated Maui power system model with a 96% of inverter-based resources model yield a trend toward a first-order response.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Cyber-Resilient Frequency Control of Power Grids with Energy Storage Systems

The integration of synchronous generators and energy storage systems operated through communication networks introduces new challenges and vulnerabilities to the electric grid, where cyber attacks can corrupt sensor measurements or control inputs and interrupt functions such as frequency regulation. This paper proposes a defense methodology for the design of resilient operating constraints imposed on each generation and storage unit in order to prevent any attack sequence from driving the system's frequency to unsafe conditions. The resilient operating constraints are found by using ellipsoidal approximations of the reachable set of the power system, leading to a convex optimization problem with linear matrix inequalities. Numerical results in a single-area power system with synchronous generation and energy storage demonstrate how the resilient constraints provide security guarantees against any type of attack affecting frequency measurements or controller setpoints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Frequency Restoration of Grid-Forming Inverters in Pulse Load and Plug-in Events

This article presents a restoration technique using grid-forming inverters in an islanded microgrid during pulse load and plug-in events. In a microgrid powered by droop-controlled inverters, frequency is the variable that is accessible to all inverters for adjusting their power contributions. The problem is that the microgrid frequency deviates from its nominal value after a load change. The presented method enables the inverters to restore the frequency to the nominal value and regulate their bus voltage amplitudes. The frequency and voltage restorations are performed without communication while achieving the desired power-sharing between grid-forming inverters. The restoration is activated after detecting any active or reactive power changes. In this article, the dynamic model of an inverter equipped with enabled restoration paths is developed to verify the stability of the inverter controller under various conditions. The frequency and voltage restorations are examined during pulse load and plug-in events. Furthermore, this study is performed using a laboratory-scale islanded microgrid powered by two 208 V, 60 Hz, 5 kVA inverters.

24 POWER TRANSMISSION AND DISTRIBUTION↗

River Dynamics Control Transit Time Distributions and Biogeochemical Reactions in a Dam-Regulated River Corridor

Residence Time Distributions (RTDs) exert an important control on biogeochemical translation in the hydrological systems. Previous tracer studies have revealed that RTDs often followed time-invariant exponential, lognormal, or heavy-tailed RTDs that have power-law behavior for long tails in headwater or low-order streams. However, there is a recognition that RTDs can be more complicated and time-variable in response to dynamic hydrological forcing. Here, we use particle tracking to estimate RTDs along the Hanford Reach of the Columbia River and to quantify the influences of river stage fluctuations. Particle tracking is conducted using the velocity field from high-resolution 3D groundwater flow simulations. The effects of hydrological forcing on the residence time distribution were evaluated by varying river flow boundary conditions and releasing particles in different time windows. Our results revealed that dynamic stage fluctuations created rapidly changing losing-gaining conditions in the river and led to highly transient RTDs, which contributes to multiple modes of RTDs. Dam-induced high-frequency (sub-daily) flow variation contributes to the short-time (sub-daily) component of the RTDs. Deviation of the reactant consumption under the single-mode assumption compared to the multimodal RTDs is relatively small (~5%) and appears when the Damköhler number was close to one.More specifically, high-frequency (daily) dam-induced stage variations have higher impacts on biogeochemical reactions with faster reaction rate, and can potentially increase the reactant consumption by 26.68%. Based on these findings, we suggest that current river basin models could be improved by including bank storage and more complex RTDs influenced by both short and long term river stage fluctuations.

54 ENVIRONMENTAL SCIENCES↗

Bulk Grid Frequency Support Using Electrolyzers

Increasing renewable penetration in the bulk power systems has resulted in declining inertial response of the generation during system disturbances. This results in larger frequency deviations and oscillations during such events. This paper proposes a strategy for controlled dispatch of electrolyzers as loads to improve the system’s frequency response. A droop based controller with constraints based on electrolyzer operating limits has been developed to regulate its load. Consecutively, a localized frequency based control strategy has been developed to support the bulk system during disturbances. The impact of the electrolyzer support has been demonstrated using the 23-bus SAVNW system, and the 240-bus WECC system for baseline, 25% and 50% renewable penetration. The impact of changing droop settings and the available controllable electrolyzer capacities on the system’s frequency response has also been presented. Overall, the dispatchable electrolyzers helps improve (reduce) both the maximum frequency deviation and the settling times during common disturbances like loss of load/generation, and line faults. Systems with lower inertia were seen to benefit more from the controlled electrolyzer dispatch.

39 EE - Hydrogen and Fuel Cell Technologies (EE-3F↗

Value Gradient Learning Approach in Power and Frequency Regulation of Grid-Connected Synchronverters

In this paper, a neural network adaptive critic design (ACD) method based on value gradient learning (VGL) is used to optimally control a grid-connected synchronverter. The main drawback of the traditional synchronverters is their infeasibility to face non-inductive grids. To be able to implement a synchronverter technique in any impedance angle, a neural network-based adaptive controller is used. The advantage of adaptive dynamic programing is its ability to adjust itself when it faces changes and uncertainties in the power system. The proposed VGL consists of two subnetworks: the critic network and the action network. The action network is trained during the operation, and the critic network can be pretrained offline or can be simultaneously trained with the action network. To compare the effectiveness of the traditional synchronverter to the VGL-based synchronverter, the simulation results are provided.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Unified Universal Control and Coordination of Inverter-Based Resources, and Validation for a PV + Battery Hybrid Plant

As renewable energy deployment grows, hybrid power plants (HPPs) combining photovoltaic (PV) and battery systems must evolve to offer both energy and grid stability services. These systems typically include a mix of grid-following (GFL) and grid-forming (GFM) inverters, presenting unique coordination and control challenges. This Department of Energy–funded project developed and validated a Unified Universal Control and Coordination (UUCC) framework for such PV + battery hybrid plants, enabling seamless and stable operation, including ultrafast black start, autonomous synchronization, and robust frequency and voltage regulation, under different grid conditions. The project significantly advanced the understanding of inverter-based resource (IBR) control by developing and validating three complementary system-level approaches for hybrid GFL/GFM operation: 1. A combined Virtual Resistance (VR)-based GFL and Virtual Oscillator Control (VOC)-based GFM method, where each inverter type is governed by a specialized control strategy. Together, these achieve stable, fast-response coordination, eliminating inrush current and enabling smooth black start and grid synchronization across a wide range of grid strengths. 2. A Deadbeat-based UUCC strategy, which uses discrete-time, switching-cycle-level control for both GFL and GFM inverters. This approach replaces traditional PI/PLL control with a control parameter-free, high-bandwidth framework that supports stable LVRT and instantaneous synchronization under all conditions. 3. A benchmark comparison with Siemens’ commercial GFM microgrid controller, which provided a fast baseline platform. The commercial approach decoupled v & f control was implemented on a commercial microgrid controller.The baseline commercial benchmark helped highlight superior transient response and black start performance offered by the deadbeat and VOC approaches. These technical contributions offer substantial improvements over conventional inverter control schemes, which often rely on slow phase-locked loop (PLL)-based synchronization, require careful control parameters tuning, and prone to unstable in weak grids with GFL inverters and in stiff grid with GFM inverters therefore challenging for hybrid GFL+GFM under all grid conditions. The deadbeat-based UUCC framework enables simpler, faster, and more robust operation of hybrid IBR systems using wide-bandgap (WBG) devices such as SiC power semiconductors. The rapid expansion of hybrid distributed energy resources (DERs), including residential and commercial PV-BESS installations such as Tesla Powerwall, PV with vehicle-to-grid (V2G) capability, and other integrated configurations, presents complex operational challenges for medium-voltage radial distribution feeders. These networks are subject to frequent disturbances such as faults, switching operations, rapid reclosing sequences, and feeder reconfigurations, all of which introduce dynamic stress on IBRs. In addition, planned feeder segmentation and deliberate islanding for resilience will require DERs that can autonomously perform blackstart, establish voltage and frequency references, and resynchronize with the main grid. The advanced deadbeat-based UUCC control and blackstart functionalities developed in this project directly address these requirements, enabling decentralized and autonomous operation of inverter-dominated DERs in distribution systems under a wide range of fault and reconfiguration scenarios. From a public benefit perspective, these innovations enable more reliable and cost-effective integration of renewable energy into distribution networks. The ability to autonomously black start and stabilize grids under varying grid conditions support accelerates recovery from outages and support decentralized resilient energy systems. By reducing system complexity and improving performance, this project lays critical groundwork for future inverter-dominated power grids that are clean, reliable, and accessible to all.

14 SOLAR ENERGY↗

Grid-Forming Frequency Shaping Control for Low-Inertia Power Systems

As power systems transit to a state of high renewable penetration, little or no presence of synchronous generators makes the prerequisite of well-regulated frequency for grid-following inverters unrealistic. As such, there is a trend to resort to grid-forming inverters which set frequency directly. We propose a novel grid-forming frequency shaping control that is able to shape the aggregate system frequency dynamics into a first-order one with the desired steady-state frequency deviation and Rate of Change of Frequency (RoCoF) after a sudden power imbalance. The no overshoot property resulting from the first-order dynamics allows the system frequency to monotonically move towards its new steady-state without experiencing frequency Nadir, which largely improves frequency security. We prove that our grid-forming frequency-shaping control renders the system internally stable under mild assumptions. The performance of the proposed control is verified via numerical simulations on a modified Icelandic Power Network test case.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Grid Integration of Offshore Wind Power: Standards, Control, Power Quality and Transmission

Offshore wind is expected to be a major player in the global efforts toward decarbonization, leading to exceptional changes in modern power systems. Understanding the impacts and capabilities of the relatively new and uniquely positioned assets in grids with high integration levels of inverter-based resources, however, is lacking, raising concerns about grid reliability, stability, power quality, and resilience, with the absence of updated grid codes to guide the massive deployment of offshore wind. To help fill the gap, this paper presents an overview of the state-of-the-art technologies of offshore wind power grid integration. First, the paper investigates the most current grid requirements for wind power plant integration, based on a harmonized European Network of Transmission System Operators (ENTSO-E) framework and notable international standards, and it illuminates future directions. The paper discusses the wind turbine and wind power plant control strategies, and new control approaches, such as grid-forming control, are presented in detail. The paper reviews recent research on the ancillary services that offshore wind power plants can potentially provide, which, when harmonized, will not only comply with regulations but also improve the value of the asset. The paper explores topics of wind power plant harmonics, reviewing the latest standards in detail and outlining mitigation methods. The paper also presents stability analysis methods for wind power plants, with discussions centered on validity and computational efficiency. Finally, the paper discusses wind power plant transmission solutions, with a focus on high-voltage direct-current topologies and controls.

17 WIND ENERGY↗

Grid-Forming Frequency Shaping Control for Low-Inertia Power Systems

As power systems transit to a state of high renewable penetration, little or no presence of synchronous generators makes the prerequisite of well-regulated frequency for grid-following inverters unrealistic. Thus, there is a trend to resort to grid-forming inverters which set frequency directly. We propose a novel grid-forming frequency shaping control that is able to shape the aggregate system frequency dynamics into a first-order one with the desired steady-state frequency deviation and Rate of Change of Frequency (RoCoF) after a sudden power imbalance. The no overshoot property resulting from the first-order dynamics allows the system frequency to monotonically move towards its new steady-state without experiencing frequency Nadir, which largely improves frequency security. We prove that our grid-forming frequency-shaping control renders the system internally stable under mild assumptions. The performance of the proposed control is verified via numerical simulations on a modified Icelandic Power Network test case.

control systems↗

Valuing Resilience for Microgrids: Challenges, Innovative Approaches, and State Needs

The United States depends on the delivery of reliable, affordable, clean, and safe electricity. Electric utilities invest billions of dollars each year in generation, transmission, and distribution assets to meet this need. However, experiences with recent natural disasters of increasing frequency and duration demonstrate the shortcomings of this approach in the face of modern threats. Further, as customers rely on electricity for a broader range of important needs, such as transportation, as well as critical life-saving services and mission critical facilities such as water treatment, medical care, shelters, telecommunications, and more, the need to minimize the likelihood and impacts of outages grows. Against this backdrop, resilience has emerged as a key consideration to guide electricity spending, whether from utilities, customers, or taxpayers. Although reliability has been defined and measured for decades with broadly accepted metrics that measure how many customers lose power and at what frequency and duration, resilience considers the electricity system’s response to a disruption and its subsequent impacts on customers. Developing tools and methods to accurately assess the costs and benefits of resilience investments is a critical step toward the goal of mitigating the impacts of outages on customers and society. Today, electric system resilience is largely treated as an externality due to challenges estimating the costs of long-duration outages, impacts of outages on society, and increasing reliance on electricity for a growing set of interdependent services. These interdependencies include the water, wastewater, telecommunications, natural gas, and health sectors. Without knowing how much a given resilience investment will benefit customers or society more broadly, investors, policymakers, and regulators are less likely to make or approve such investments, and less able to prioritize those investments. State Energy Offices and public utility commissions (PUCs) lead the development of state-level energy policy and utility regulation, respectively, and each has interests in encouraging appropriate public and private investments in resilience. To this end, the National Association of State Energy Officials (NASEO) and National Association of Regulatory Utility Commissioners (NARUC), with the support of the U.S. Department of Energy (DOE) Office of Electricity (OE), formed a joint Microgrids State Working Group to explore the costs and benefits of microgrids, barriers to broader deployment of microgrids to meet resilience and other objectives, and policy and regulatory strategies to optimize investments in resilience, including but not limited to microgrids. Although no universally accepted valuation tool for resilience exists, National Laboratories, utilities, researchers, and state and federal agencies have collaborated to develop, apply, and improve a number of approaches to quantify resilience, several of which are still in progress at the time this report is published. This report seeks to share these important advances by discussing current definitions of resilience (Section 1), how microgrids are defined and used to meet resilience objectives (Section 2), new approaches to valuing resilience (Section 3), steps State Energy Offices and PUCs have taken to further resilience valuation efforts (Section 4), and finally, considerations and suggested next steps for State Energy Offices and PUCs (Section 5). Relevant examples of specific microgrid projects and resilience valuation efforts are included throughout the report. While this report is written specifically for NASEO and NARUC members, it may be useful for utilities, local governments, and individual customers interested in improving the way public and private dollars are spent to achieve resilience outcomes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Pore confinement enhances but surface adhesion reduces bacterial cell-to-cell conjugation

As the habitats of bacteria, soil pore network and surface properties control the distribution, adhesion, and motility of bacteria in soils. These physical processes in turn influence bacterial accesses to nutrients and bacterial interactions. Our understanding on the pore- and surface-mediated bacterial interactions is currently limited. In this research, we evaluated the effects of soil pore confinement and surface adhesion on conjugation-based bacterial interactions. The interaction was measured by plasmid transfer between donor and recipient cells within the population of soil bacterium Pseudomonas putida. We found that the presence of porous sand media led to a net increase in conjugation frequency compared to sand-free liquid control. The increase is attributed to the facilitated effect of pore confinement on the collision of bacteria within pores. In contrast, bacterial adhesion to sand surfaces under elevated ionic strength conditions decreased the conjugation frequency as a result of mobility reduction on the surface. Such collision and adhesion mechanisms jointly drive the conjugation as a function of pore and surface properties of porous media. Finally, these results provide valuable insights into the roles of soil pores and surfaces in regulating horizontal gene transfer, an essential cell-to-cell interaction sustaining key processes of soil ecology and health.

59 BASIC BIOLOGICAL SCIENCES↗

Demonstration of Grid Services Using Mixed Grid-Forming and Grid-Following Technologies at the Wheatridge Renewable Energy Facility (Final Technical Report)

This Final Technical Report summarizes the analytical, modeling, and engineering work performed to evaluate grid-forming (GFM) inverter capabilities within a large hybrid renewable energy facility. The project focused on assessing the ability of advanced inverter-based resources to provide essential reliability services through coordinated operation of grid-forming (GFM) and grid-following (GFL) technologies. During Budget Period 1, the project developed a comprehensive framework of GFM performance metrics, including angle support, voltage regulation, frequency response, damping behavior, and current-limiting performance. Extensive electromagnetic transient (EMT) studies and hardware-in-the-loop (HIL) testing were conducted to validate GFM behavior under a range of operating conditions, including weak-grid scenarios, voltage disturbances, and multi-resource interactions. The project also established validated modeling approaches, plant-level control integration strategies, commissioning frameworks, and high-speed measurement infrastructure to support future field demonstration. Although the project concluded prior to field demonstration, the results provide a utility-scale foundation for evaluating, modeling, and deploying grid-forming technologies. The methodologies and tools developed contribute to industry understanding of inverter-based resource behavior and support future power system reliability under increasing renewable penetration.

14 SOLAR ENERGY↗

Empirical Evaluation of GPS Clock Accuracy for Isochronous Droop-Based Inverters: Preprint

Grid-forming inverters rely upon an internal reference to regulate the grid’s voltage and frequency. Without a reliable reference, issues such as loss of synchronism, frequency instability, and unequal power sharing can occur. One proposed internal phase reference for grid-forming inverters is generated by the controller’s clock, but this is affected by nonidealities in the crystal oscillator leading to time drift in the phase reference. To improve the controller’s clock accuracy, the Global Positioning System (GPS) can be used to calibrate the internal clock. Previously, GPS-based clock calibration was explored theoretically and various methods were developed for mitigating frequency/phase drift at the power system level. This paper experimentally validates the direct performance of GPS time-calibration at the controller level and justifies its use in maintaining an accurate phase reference for droop-based grid-forming inverters.

clock drift↗

Empirical Evaluation of GPS Clock Accuracy for Isochronous Droop-based Inverters

Grid-forming inverters rely upon an internal reference to regulate the grid 's voltage and frequency. Without a reliable reference, issues such as loss of synchronism, frequency instability, and unequal power sharing can occur. One proposed internal phase reference for grid-forming inverters is generated by the controller's clock, but this is affected by nonidealities in the crystal oscillator leading to time drift in the phase reference. To improve the controller's clock accuracy, the Global Positioning System (GPS) can be used to calibrate the internal clock. Previously, GPS-based clock calibration was explored theoretically and various methods were developed for mitigating frequency/phase drift at the power system level. This paper experimentally validates the direct performance of GPS time-calibration at the controller level and justifies its use in maintaining an accurate phase reference for droop-based grid-forming inverters.

clock drift↗

Black hole and galaxy co-evolution in radio-loud active galactic nuclei at z ~ 0.3–4

The relation between the mass of the supermassive black hole (SMBH) in the center of galaxies and their bulge mass or central velocity dispersion is well known. This suggests a coevolution between the SMBHs and their galaxy hosts. Our aim is to study this relation, specifically, for radio loud galaxies, and as a function of redshift z. We selected a sample of 42 radio galaxies and active galactic nuclei (AGN) with broad emission lines and spectroscopic redshifts between z = 0.3 - 4 by cross-matching the low radio frequency sources from Very Large Array (VLA) FIRST with spectroscopically confirmed galaxies from wide-field surveys, including Sloan Digital Sky Survey (SDSS) DR14 ugriz and Dark Energy Survey (DES) DR2 grzY in the optical, Wield Infrared Survey Explorer (WISE), and the Galaxy And Mass Assembly (GAMA) spectroscopic survey. We characterized the stellar mass (M $\star$ ), star formation, and black hole properties (mass of the central SMBH, Eddington ratio η, and jet power, Q jet ). The relation between SMBH mass, M $\star$ , η, and z is placed into context by comparing them with scaling relations (M BH –M $\star$ , M BH /M $\star$ –z, M BH –Q jet , and Q jet –η) from the literature. On the basis of a multiwavelength spectral energy distribution modeling, our radio sources are broadly consistent with being on the star-forming main sequence. They have sub-Eddington accretion rates, η ≃ 1% on average, as typically found in type I AGN, while higher accretion rates favor more powerful jets to be launched by the central engine. We find overmassive SMBHs in (17 ± 5)% of our radio sources, similarly to previous studies on nearby early-type galaxies. Altogether, an evolutionary scenario in which radio-mode AGN feedback regulates the accretion onto the SMBHs and the stellar mass assembly of the radio sources is discussed, which may explain the observed phenomenology. This pilot study represents a benchmark for future studies using wide-field surveys such as those with Euclid and the Vera Rubin Observatory.

79 ASTRONOMY AND ASTROPHYSICS↗

Overcoming the Technical Challenges of Coordinating Distributed Load Resources at Scale (Final Report)

Significant recent research has investigated the potential for loads to provide balancing services to the grid. However, this research has not addressed key issues that may arise when such schemes are applied at scale including: 1. Distribution Network Issues. Coordination of large numbers of loads could result in power flows that violate distribution network constraints; 2. Stability Issues. Certain strategies to control loads can exhibit nonlinearity in the form of period-adding bifurcations and chaos. Other control strategies can potentially synchronize the behavior of large numbers of loads. In both cases, the outcome can be power oscillations and instability; 3. Communication Network Issues. Bidirectional low-latency communication channels between a central controller (or several distributed controllers) and each resource are expensive and likely not necessary for effective coordination. Our research questions were: What network, stability, and communication issues might arise in practice when we coordinate large aggregations of loads? How can we coordinate loads to achieve performance objectives in a cost effective manner while avoiding these issues? The ultimate technical goal of the project was the development of network-aware, communication-constrained, non-disruptive load control strategies with stability guarantees that achieve the performance requirements of typical balancing services at a sufficiently low cost to enable the load aggregator and customer to profit. The overall goal was to establish credibility for load control at scale and contribute to U.S. energy security and environmental goals. The team succeeded in answering these research questions and developing these control strategies. The overall approach was based on the development of three testing environments: a simulation testbed, an experimental testbed (20 physical model houses with window-box air conditioners) coupled with the simulation testbed, and a field testbed (100 actual homes in Austin, TX) coupled with the simulation testbed, which enabled controller testing, identification of issues, controller development, and controller validation. The resulting controller was used to demonstrate fast timescale grid balancing (frequency regulation) by aggregations of physical and virtual air conditioners, with sufficient quality to participate in the electricity market. Cost benefit analysis showed overall benefits to the participating households, load aggregators, and the grid, especially if the control technology was integrated directly into existing programmable communicating thermostats. The project provides a variety of wider benefits. Our technology transfer and outreach activities lead us to choose an open-source licensing commercialization pathway, enabling the project results to be available to researchers, industry, and the public. Furthermore, new grid balancing technologies will increase grid flexibility and will enable higher penetrations of intermittent renewable energy resources, such as wind and solar, to be connected to the grid, reducing its environmental impact, and mitigating climate change to the benefit of society.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Stability-Constrained Learning for Frequency Regulation in Power Grids With Variable Inertia

The increasing penetration of converter-based renewable generation has resulted in faster frequency dynamics, and low and variable inertia. As a result, there is a need for frequency control methods that are able to stabilize a disturbance in the power system at timescales comparable to the fast converter dynamics. This paper proposes a combined linear and neural network controller for inverter-based primary frequency control that is stable at time-varying levels of inertia. We model the time-variance in inertia via a switched affine hybrid system model. We derive stability certificates for the proposed controller via a quadratic candidate Lyapunov function. We test the proposed control on a 12-bus 3-area test network, and compare its performance with a base case linear controller, optimized linear controller, and finite-horizon Linear Quadratic Regulator (LQR). Our proposed controller achieves faster mean settling time and over 50% reduction in average control cost across 100 inertia scenarios compared to the optimized linear controller. Unlike LQR which requires complete knowledge of the inertia trajectories and system dynamics over the entire control time horizon, our proposed controller is real-time tractable, and achieves comparable performance to LQR.

data-driven control↗