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At least 1,693 records · Page 94

Duty-Cycle Predictive Control of Quasi-Z-Source Modular Cascaded Converter Based Photovoltaic Power System

A duty-cycle predictive control is proposed for dc grid integration of front-end isolated quasi-Z-source modular cascaded converter (qZS-MCC) photovoltaic (PV) power system. The post-stage qZS half-bridge dc-dc converter deals with PV maximum power point tracking, dc grid integration, and dc-link voltage balance; whereas, the front-end isolation converters operate at a constant duty cycle of 50%. Thus, it saves control hardware resources while overcoming challenges from PV-panel voltage variations and dc-bus voltage limit. The proposed control uses the derived circuit model to predict the global active-state duty cycle for grid-connected current control and predict the shoot-through duty cycles for dc-link voltage balance, achieving a fast and accurate tracking target. The proposed control method has advantages of: i) eliminating weighting factors that exist in conventional model predictive control (MPC), ii) no sophisticated loop parameters design that exists in proportional-integral (PI) control, iii) operating at constant switching frequency that is different from the conventional MPC with variable switching frequency. Simulation and experimental tests are carried out to verify the effectiveness of the proposed control method and compare with the PI-based control system.

42 ENGINEERING↗

Direct Power Control of Back to Back Modular Multilevel Converter with Advanced Grid Support Functions for Grid Forming Application

Possibility of using back-to-back modular multilevel converter system with a direct power control architecture has been investigated in this paper. The rectifier side is controlled to be in grid following mode whereas the inverter side is controlled in grid forming mode. Both the sides’ local controllers use Lyapunov energy function based architecture to accomplish the objective of active and reactive power control as well as maintaining a fixed user defined voltage over the dc bus on the rectifier side. Therefore, the proposed direct power control architecture has embedded dc bus control architecture to maintain fixed user defined value of the capacitors. Similar architecture is implemented on the inverter side to accomplish either voltage control during grid forming or power control during grid following. Advanced grid support functionalities based on IEEE-1547-2018 is implemented and utilized to generate the reference values for either the rectifier or the inverter sides. The overall system is modeled based on MATLAB/Simulink and PLECS domain and various important case studies to verify the efficacy of the overall system has been presented.

direct power control (DPC)↗

Scalable Predictive Control and Optimization for Grid Integration of Large-Scale Distributed Energy Resources

Integrating a large number of distributed energy resources (DERs) into the power grid needs a scalable power balancing method. We formulate the power balancing problem as a look-ahead optimization problem to be solved sequentially by a power distribution system aggregator based on a model predictive control (MPC) framework. Solving large-scale look-ahead control problems requires proper configuration of the control steps. In this paper, to solve large-scale control problems, we propose a variable time granularity where control time steps nearby the current control step have finer resolutions. The aggregator objective includes maximization of power production revenue and minimization of power purchasing expense, renewable power curtailment, and mileage costs for energy storage and electric vehicle (EV) charging stations while satisfying system capacity and operational constraints. The control problem is formulated as a mixed-integer linear program (MILP) and solved using the XpressMP solver. We perform simulations considering a copper plate representation of a large distribution network consisting of 2507 devices (control-lable DERs), including curtailable photovoltaics (PVs), energy storage batteries, EV charging stations, and buildings with heating, ventilation, and air conditioning units (HVACs). We show the effectiveness of the proposed approach in managing DERs interactively for maximum energy trading profit and local supply-demand power balancing. Finally, we demonstrate that the proposed method outperforms other benchmark controllers regarding computation time without compromising operational performance.

DER↗

Network-Wide Traffic Signal Control Using Bilinear System Modeling and Adaptive Optimization

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

42 ENGINEERING↗

Sparse Control Synthesis for Uncertain Responsive Loads With Stochastic Stability Guarantees

In this report, recent studies have demonstrated the potential of flexible loads in providing frequency response services, predominantly due to their availability and cost-effectiveness. However, uncertainty and variability in various weather-related and end-use behavioral factors often impact the reliability of demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive in the power system dynamics. Recently developed mean square exponential stability (MSES) results for continuous-time linear stochastic systems are applied to pose the control synthesis problem which results in an LMI-based optimization problem. Additional costs and constraints are added to the LMI-based controller synthesis to ensure MSES, improve closed-loop transient performance, maximize tolerable uncertainties, and promote sparsity in the controller. Additionally, the fundamental limitations between the tolerable uncertainties and control efforts while ensuring MSES are discussed. Further, the control synthesis problem for the case of the full-state measurement is generalized to the case of partial-state measurements. The proposed control synthesis is illustrated on an IEEE 39 bus system with rigorous studies to demonstrate the role of sparsity, closed-loop transient performance, tolerable uncertainties, and control efforts while ensuring MSES and achieving frequency response.

42 ENGINEERING↗

Enabling Grid-Forming Control with Fault Ride-Through in Unbalanced Distribution Networks

Distribution networks are often unbalanced, causing oscillatory responses in inverter control designed for balanced conditions. Here, to address this problem, this paper proposes a novel time-domain transformation appropriate for inverter control and enables the decomposition of three-phase unbalanced signals into constant positive and negative components. Relations useful for calculating unbalanced active and reactive power are derived from first principle, providing insight into vector products of unbalanced three-phase signals. Furthermore, a grid-forming control effective under unbalanced conditions is developed, which delivers superior performance while meeting UNIFI1 specifications for grid-forming control under unbalanced conditions. specifications applicable to category 4 inverter-based resource, like setting and regulating frequency/voltage, providing voltage support, sharing active power, injecting negative sequence current, and riding through faults. A current limiter is proposed for safe fault ride-through and integrates with the grid-forming control featuring frequency/voltage droop controllers and current and voltage control loops. The transformation of interconnected inverters is formulated and stability of the proposed control analyzed to support robust parameter selections. The effectiveness of the proposed transformation and grid-forming control is demonstrated through analytical results and real-time simulation of a IEEE 123 distribution network on the Real-Time Digital Simulator. Comparison with existing methods shows that the proposed strategy satisfies the UNIFI specifications with a much better performance.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Control of airborne infectious disease in buildings: Evidence and research priorities

The evolution of SARS-CoV-2 virus has resulted in variants likely to be more readily transmitted through respiratory aerosols, underscoring the increased potential for indoor environmental controls to mitigate risk. Use of tight-fitting face masks to trap infectious aerosol in exhaled breath and reduce inhalation exposure to contaminated air is of critical importance for disease control. Administrative controls including the regulation of occupancy and interpersonal spacing are also important, while presenting social and economic challenges. Indoor engineering controls including ventilation, exhaust, air flow control, filtration, and disinfection by germicidal ultraviolet irradiation can reduce reliance on stringent occupancy restrictions. However, the effects of controls-individually and in combination-on reducing infectious aerosol transfer indoors remain to be clearly characterized to the extent needed to support widespread implementation by building operators. We review aerobiologic and epidemiologic evidence of indoor environmental controls against transmission and present a quantitative aerosol transfer scenario illustrating relative differences in exposure at close-interactive, room, and building scales. We identify an overarching need for investment to implement building controls and evaluate their effectiveness on infection in well-characterized and real-world settings, supported by specific, methodological advances. Finally, improved understanding of engineering control effectiveness guides implementation at scale while considering occupant comfort, operational challenges, and energy costs.

60 APPLIED LIFE SCIENCES↗

HIL Testbed and Motion Control Strategy for the Hybrid Hydraulic-Electric Architecture (HHEA)

The Hybrid Hydraulic-Electric Architecture (HHEA) was proposed in recent years to increase system efficiency of high power mobile machines and to reap the benefits of electrification without the need for large electric machines. It uses a set of common pressure rails to provide the majority of power hydraulically and small electric motors to modulate that power for precise control. This paper presents the development of a Hardware-in-the-loop (HIL) test-bed for testing motion control strategies for the HHEA. Precise motion control is important for off-road vehicles whose utility requires the machine being dexterous and performing tasks exactly as commanded. Motion control for the HHEA is challenging due to its intrinsic use of discrete pressure rail switches to minimize system efficiency or to keep the system within the torque capabilities of the electric motor. The motion control strategy utilizes two different controllers: a nominal passivity based back-stepping controller used in between pressure rail switches and a transition controller used to handle the event of a pressure rail switch. In this paper, the performance of the nominal control under various nominal and rail switching scenarios is experimentally evaluated on the HIL testbed.

33 ADVANCED PROPULSION SYSTEMS↗

Integrated Dynamic Facade Control with an Agent-based Architecture for Commercial Buildings

Dynamic façades have significant technical potential to minimize heating, cooling, and lighting energy use and peak electric demand in the perimeter zone of commercial buildings, but the performance of these systems is reliant on being able to balance complex trade-offs between solar control, daylight admission, comfort, and view over the life of the installation. As the context for controllable energy-efficiency technologies grows more complex with the increased use of intermittent renewable energy resources on the grid, it has become increasingly important to look ahead towards more advanced approaches to integrated systems control in order to achieve optimum life-cycle performance at a lower cost. This study examines the feasibility of a model predictive control system for low-cost autonomous dynamic façades. A system architecture designed around lightweight, simple agents is proposed. The architecture accommodates whole building and grid level demands through its modular, hierarchical approach. Automatically-generated models for computing window heat gains, daylight illuminance, and discomfort glare are described. The open source Modelica and JModelica software tools were used to determine the optimum state of control given inputs of window heat gains and lighting loads for a 24-hour optimization horizon. Penalty functions for glare and view/ daylight quality were implemented as constraints. The control system was tested on a low-power controller (1.4 GHz single core with 2 GB of RAM) to evaluate feasibility. The target platform is a low-cost ($35/unit) embedded controller with 1.2 GHz dual-core cpu and 1 GB of RAM. Configuration and commissioning of the curtainwall unit was designed to be largely plug and play with minimal inputs required by the manufacturer through a web-based user interface. An example application was used to demonstrate optimal control of a three-zone electrochromic window for a south-facing zone. The overall approach was deemed to be promising. Further engineering is required to enable scalable, turnkey solutions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Active Aerodynamic Load Control for Wind Turbines

The goal of this project was to develop and demonstrate an advanced dielectric barrier discharge (DBD) plasma actuator technology. We set out to demonstrate the efficacy and impact of the new actuator technology as a key component of an active load control system for wind turbines. A DBD plasma actuator consists of a thin layer of dielectric material separating a pair of offset electrodes. One of those electrodes is embedded between the dielectric layer and a non-conductive substrate, while the other is exposed to air. When driven by an appropriate high voltage waveform, the device ionizes the air near the surface of the dielectric and adjacent to the exposed electrode. Collisions between the ions in the plasma and neutral air molecules result in a wall-jet – a region of induced air velocity that can be used to modify the flow around a lifting body. Use of the device near the trailing edge of a wind turbine blade, designed in such a way as to amplify the effects of the flow-modifying device, can result in large changes to the global forces experienced by the blade. Because of the fast response time of the device, it can allow the turbine to react in real time to changes in the wind associated with turbulence, wind shear, gusts, and the like, when paired with appropriate sensors and control algorithms. The goal of this project was to increase the capacity of the device to induce velocity on its surface at the levels required by large, utility-scale wind turbines. The first technical goal was to increase the induced velocity from the current industry-best of about 4 m/s to 10 m/s by modifying the electrical waveform used to drive the device and by introducing a semi-conductive surface coating to control electrostatic charge build-up on the surface. The second goal was to use the device to modify the lift on a representative airfoil in a wind tunnel, demonstrating a reduction in lift coefficient of 0.2 or better. The third goal was to produce an actuator-induced velocity of 20 m/s. Alongside our partners at the University of Texas at Dallas, we also applied modern, advanced design methods to optimize the impact of the technology on the design of wind turbines. We also had planned to install a segmented, active load control system on a test turbine to demonstrate the ability to reduce unsteady aerodynamic forces on the turbine associated with changes in the wind. The highest induced velocity achieved during this research was 11 m/s. However, practical design constraints limited the change in lift coefficient to about 0.12 for a representative airfoil in the wind tunnel at a Reynolds number of 400,000. The primary conclusion is that the plasma actuator control authority remains insufficient for practical purposes when extrapolated to Reynolds numbers over 1 million. The potential impact of the active lift control concept was evaluated through detailed simulations for three wind turbine sizes: a 3.4MW onshore turbine, a 10MW offshore turbine, and a 15MW offshore turbine. A feedback control system was designed for each turbine within two scenarios: one where the active lift control is used as a retrofit capability on the baseline design, and the other where the designers were permitted to “upscale” the turbines in order increase annual energy production. The levelized cost of energy was then evaluated for the range of turbine sizes and design configuration. It was found that the LCOE reduction associated with active lift control fell in the range of 0.7% to 7.2%, with the highest reduction associated with upscaling the 3.4MW turbine.

17 WIND ENERGY↗

Enabling a Physical Twin for Control Methods Evaluation

Advanced nuclear reactors play an important role in the energy future of the United States and the rest of the world. They are designed and operated based on a different model than that of the current operating fleet, thus enabling deployment in remote locations and allowing for safe semi-autonomous or autonomous operations. Such characteristics require the development of a new reactor control paradigm. A significant factor in the development of control technologies and methods is integration of the various technologies and methods with each other and with hardware (both reactor system hardware and control hardware). A recent workshop on control of advanced reactors identified the lack of a flexible, expandable software/hardware infrastructure to enable such integration as a key gap. A previous phase of the current effort involved developing and demonstrating the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND) platform, which is capable of integrating autonomous-control-enabling technologies and methods, without the constraints imposed by existing software solutions. This platform will enable advanced reactor developers to deploy and test any developed technologies and methods by employing a common framework, and to couple them with their own models and hardware. The present phase of this effort entails using the Microreactor Automated Control System (MACS) platform, which was developed by the U.S. Department of Energy (DOE) Microreactor Program, to serve as a control method testbed. MACS can be used by advanced reactor developers to integrate their control related research activities with any reactor system. For the present effort, MACS was customized to mirror Idaho National Laboratory (INL)’s Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor, and COMMAND was leveraged to enable MACS to emulate the physics of MARVEL, thus positioning MACS as a physical twin of MARVEL.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Hardware-Based Demonstration of Temperature Control Functions for Reactor Systems

Establishing autonomy in reactor control systems has become essential for the expansion of nuclear technologies. Thermal regulation in particular remains crucial for maintaining stable operation and ensuring the integrity of fuel. To alleviate public skepticism of the safety of nuclear reactors, demonstrating control over this key factor is pivotal. Utilizing electric heat pads to simulate the heat released in a reactor core, thermocouples for temperature monitoring, and an Arduino micro programmable logic controller (PLC) for control, a hardware-based demonstration of a reactor heating system validates the efficacy of reactor control over this key parameter. To improve precision, a proportional-integral-derivative (PID) algorithm was implemented in the heating control loop to ensure meticulous control of reactor functions. In addition, the integration of this physical system with a digital simulator tool such as RELAP5-3D establishes a foundation for a comprehensive testing environment. This allows for a refinement of temperature control under various simulated reactor conditions, bringing another layer of reliability to the operation of the system. By facilitating a physical demonstration of reactor thermal management and control strategies, this project provides a foundation for expanded testing and educational outreach. Ultimately, this system advances the broader goal of demonstrating the safety and viability of autonomous reactor operations, contributing to public trust and future reactor deployment.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Employing MACS/ViBRANT as a Surrogate MARVEL Reactor for Startup Reactivity Tuning and Supervisory Control Processes

Advanced nuclear reactors are a key part of the future of nuclear energy both in the United States and globally. They offer unique benefits for various energy-demanding applications, including use in remote locations, compact size, modular manufacturing, remote monitoring, low and/or variable power rating operation, and reliance on novel technologies to enhance operational safety. To achieve economic feasibility, advanced reactors must significantly reduce their workforces in comparison with the current fleet. Achieving this reduction will occur through reducing staff workloads using technology to achieve autonomous or semi-autonomous operations, demonstrated by comprehensive testing and validation activities. These operations will require both software and hardware platforms during the design and testing phases. While simulations are useful during the design phase, their performance can significantly deviate during actual deployment on hardware. This report presents the outcomes of a collaborative technical initiative between the U.S. Department of Energy (DOE) Microreactor Program (MRP) and Advanced Sensors and Instrumentation (ASI) Program. The collaboration utilized the Microreactor Automated Control System (MACS) hardware platform to bridge the gap between theoretical reactor design and actual startup and control operations. Two key use cases were investigated: facilitating the startup testing period and demonstrating supervisory control. The first use case details the key Microreactor Applications Research Validation and Evaluation (MARVEL) reactor startup physics testing activities conducted using the MACS platform. These activities included drum worth measurements, shutdown margin assessment, temperature feedback analysis, and scram time evaluation, as well as unique testing that would apply to the MARVEL reactor to demonstrate the testing methodologies in a low-risk environment. The MACS platform, serving as a surrogate representation of the MARVEL reactor, proved instrumental in performing these tests. The exercise revealed aspects that led to optimized processes, refined hardware design, and enhanced base software capabilities. By maturing methods and technologies in this manner, the initiative promises to reduce wasted time in the actual on-site reactor deployment effort, thereby saving significant time and resources. The second use case focuses on the development and implementation of supervisory control methods aimed at managing core tilt, which can result from asymmetrical operations or manufacturing imperfections in fuel rods or reactivity control devices. A key objective was to assess and compare the use of artificial intelligence (AI) for supervisory control. The effort aimed to define the role of supervisory control to enhance performance without risking control instability. This effort explored three distinct approaches: rules-based (RB) methods, optimization techniques, and reinforcement learning (RL) algorithms. Each approach was evaluated for its ease of implementation, its usability, and its effectiveness in responding to asymmetries in neutron flux. Comparative analysis of these approaches provided valuable insights into their applicability and effectiveness, offering a robust framework for advanced reactor operations. Together, these two use cases highlight the potential of hardware test beds to help streamline the design, operation, and control of advanced nuclear reactors. This collaborative effort underscores the importance of continued innovation and experimentation in achieving the next generation of safe, reliable, and economically viable nuclear energy solutions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Controller Requirements for Managing Community Microgrids

Microgrid control systems are central to the functioning of a microgrid. They are responsible for managing distributed energy resources (DER) in both grid-connected and islanded modes of operation. Although microgrids are being developed and deployed by many utilities, several questions are being raised about the control system that manages them. This document provides the detailed list of requirements for a feeder-level microgrid controller to manage various islanded and grid-connected use cases. Functionally, the use cases include control scenarios that require the controller to maintain energy balance, prevent constraint violations, manage switching equipment, manage grid-forming (GFM) and grid-following (GFL) DER, manage critical/non-critical loads, and coordinate with peer systems to operate joined island areas. In addition to detailed requirements, the document includes interface and performance metrics for functional evaluation. These requirements can be applied to utility-managed microgrid controllers that exclusively manage utility-owned equipment; requirements also apply to third-party managed microgrid controllers that coordinate with the utility- and customer-owned equipment. The document can also be used by technology developers and project developers in industry to specify desired control strategies and performance characteristics for community microgrid controllers.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Tracking and Rejection of Biased Sinusoidal Signals Using Generalized Predictive Controller

Some novel applications require the tracking/rejection of biased sinusoidal reference/distur-bances. According to the internal model principle (IMP), a controller must embed the model of a biased sinusoidal signal to track references and also reject perturbations modeled through the aforementioned signal. However, the design of that kind of controller is not straightforward, especially when they are implemented in digital processors. This paper presents a controller, based on generalized predictive control (GPC), designed for tracking/rejection of biased sinusoidal signals. In general, GPC is based on the prediction of the plant responses through an augmented prediction model. The proposed approach develops an augmented model that predicts the future errors. The prediction model and the control law used in the proposed approach embed the discrete-time model of a biased sinusoidal signal. Thus, the proposed controller can track/reject biased sinusoidal references/disturbances. The predicted errors and the future inputs of the proposed augmented model are used to define the cost function that measures the control performance. An optimization technique was applied to obtain the solution of the cost function, which is the optimal sequence of future model inputs that allows defining the control law. Experimental tests prove that the proposed controller can asymptotically track and reject biased sinusoidal signals.

42 ENGINEERING↗

Optimal Traffic Signal Control Using Priority Metric Based on Real-Time Measured Traffic Information

Optimizing traffic control systems at traffic intersections can reduce network-wide fuel consumption as well as improve traffic flow. While traffic signals have conventionally been controlled based on predetermined schedules, various adaptive control systems have been developed recently using advanced sensors such as cameras, radars, and LiDARs. By utilizing rich traffic information enabled by the advanced sensors, more efficient or optimal traffic signal control is possible in response to varying traffic conditions. This paper proposes an optimal traffic signal control method to minimize network-wide fuel consumption utilizing real-time traffic information provided by advanced sensors. This new method employs a priority metric calculated by a weighted sum of various factors, including the total number of vehicles, total vehicle speed, vehicle waiting time, and road preference. Genetic Algorithm (GA) is used as a global optimization method to determine the optimal weights in the priority metric. In order to evaluate the effectiveness of the proposed method, a traffic simulation model is developed in a high-fidelity traffic simulation environment called SUMO, based on a real-world traffic network. The traffic flow within this model is simulated using actual measured traffic data from the traffic network, enabling a comprehensive assessment of the novel optimal traffic signal control method in realistic conditions. The simulation results show that the proposed priority metric-based real-time traffic signal control algorithm can significantly reduce network-wide fuel consumption compared to the conventional fixed-time control and coordinated actuated control methods that are currently used in the modeled network. Additionally, incorporating truck priority in the priority metric leads to further improvements in fuel consumption reduction.

47 OTHER INSTRUMENTATION↗

Integrated Aeropropulsion Control System Design

%T Integrated Aeropropulsion Control System Design%A C-F. Lin%A Francis X. Hurley%A Jie Huang%A F. Y. Hadaegh%J International Conference on Control and Information(psi)995%C Hong Kong%D June 1995%K aeropropulsion, control, system%U http://jpltrs.jpl.nasa.gov/1995/95-0658.pdfAn integrated intelligent control approach is proposed to design a high performance control system for aeropropulsion systems based on advanced sensor processing, nonlinear control and neural fuzzy control integration. Our approach features the following innovations:??e complexity and uncertainty issues are addressed via the distributed parallel processing, learning, and online reoptimization properties of neural networks.??e nonlinear dynamics and the severe coupling can be naturally incorporated into the design framework.??e knowledge base and decision making logic furnished by fuzzy systems leads to a human intelligence enhanced control scheme.In addition, fault tolerance, health monitoring and reconfigurable control strategies will be accommodated by this approach to ensure stability, graceful degradation and reoptimization in the case of failures, malfunctions and damage.!.

aeropropulsion control systems↗

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

feed - forward↗