Centralized Control Scheme Research Articles

Optimal control strategies for energy storage systems for HUB substation considering multiple distribution networks

With the global consensus to achieve carbon neutral goals, power systems are experiencing a rapid increase in renewable energy sources and energy storage systems (ESS). Especially, recent development of hub substations (HS/S) equipped with ESS, applicable for resolving site constraints if implemented as mobile transformers, is expanding the development of ESS-equipped facilities. However, these units require centralized control strategies considering variability within integrated networks. While studies on electric vehicle charging considering the variability of renewable energy or load are widely studied, ESS management scheme for individual substations requires further optimization, especially considering the state of distributed sources at lower levels and transmission system operators. Thus, in this study, an optimal control approach for ESS located at the connection point of transmission and distribution systems, including further consideration of the loss in distribution lines and the constraints of renewable energy sources is presented. This study attempts to derive proactive control strategies for ESS in HS/S to operate with various distribution networks. By establishing control priorities for each source through optimal operation strategy, a suitable capacity of ESS and its economic benefits for distribution network management can be examined. Validation of the current analysis results is performed by utilizing MATPOWER. By adapting the operational range of design scenarios, diverse distribution systems can be tested against multiple configurations of connected devices.

Centralized Finite State Machine Control to Increase the Production Rate in a Crusher Circuit

Crushing is a critical operation in mineral processing, and its efficient performance is vital for minimizing energy consumption, maximizing productivity, and maintaining product quality. However, due to variations in feed material characteristics and safety constraints, achieving the intended circuit performance can be challenging. In this study, a centralized control strategy based on a finite state machine (FSM) is developed to improve the operations of an iron ore crushing circuit. The aim is to increase productivity by manipulating the closed-side-setting (CSS) of cone crushers and the speed of an apron feeder while considering intermediate storage silo levels and cone crusher power limits, as well as product quality. A dynamic simulation was conducted to compare the proposed control strategy with the usual practice of setting CSS to a constant value. Four scenarios were analyzed based on variations in bond work index (BWI) and particle size distribution. The simulation results demonstrate that the proposed control strategy increased average productivity by 6.88% and 48.77% when compared to the operation with a constant CSS of 38 mm and 41 mm, respectively. The proposed strategy resulted in smoother oscillation without interlocking, and it maintained constant flow rates. This ultimately improved circuit reliability and predictability, leading to reduced maintenance costs.

An Enhanced Power Allocation Strategy for Microgrids Considering Frequency and Voltage Restoration

In a microgrid, load power should be properly shared among multiple distributed generation (DG) units, not only for fundamental power but also for negative sequence and harmonic power. In this paper, the operation of a microgrid under imbalance and nonlinear load conditions is studied, and a consensus algorithm-based distributed control strategy is proposed for the microgrid power allocation, frequency, and voltage restoration. First of all, the output current of DG unit is decomposed by second-order generalized integrator (SOGI) modules to obtain the fundamental power and harmonic power through the power calculation formula. Then, state values of DG units, such as local power, frequency, and voltage, are transmitted on a sparse communication network. Under the action of a consensus algorithm, the real power of DG units is allocated following the equal increment principle; the reactive power, imbalance, and harmonic power are allocated according to the capacities of DG units; and the frequency of the microgrid and the voltage at the point of common coupling (PCC) are rated. In the consensus-based strategy, DG units only communicate with their neighbor units; thus, the “plug and play” function is reserved. Compared with the centralized control strategy, the proposed strategy with a distributed consensus protocol can simplify the maintenance and possible expansions of the system, making the microgrid more flexible. Moreover, as the structure of the detailed network is not required, it is easy to apply in practice. Simulation and experiment results are presented to verify the proposed method.

Heterogeneous microgrids: Centralized control strategy with distributed grid-forming converters

Advanced microgrid (MG) is a likely model for reaching the goal of 100% renewable grid. A complete advanced MG control must steer the power flow in grid-connected mode; regulate voltage/frequency in islanded mode; and perform power sharing among distributed energy resources (DERs) in both modes. Power-based control (PBC) is a well-known centralized control capable of achieving these three targets. A serious disadvantage of usual MG structures using PBC approach is the existence of a single centralized grid-forming converter to form the islanded MG. Centralized grid-forming converter is a single point of failure, which reduces the capability of the MG expansion, and it is an expensive element for the MG. This paper proposes a MG control strategy using an improved centralized control together with a droop-based power-loop in distributed voltage-controlled mode (VCM) converters to allow the MG to operate in both modes, without a centralized grid-forming converter and critical islanding detection. Moreover, the new approach considers single- and three-phase DERs, controlled in VCM or current-controlled mode, and DERs with self-imposed limits, characterizing a heterogeneous MG. Real-time hardware-in-the-loop setup is used to test the proposed control strategy in several operating conditions considering ten heterogeneous DERs. Results show grid power flow control, power sharing, unbalance compensation, voltage/frequency restoration, and smooth transitioning between operating modes without critical islanding detection.

Increased Load Power With Centralized Control of Multiple Microgrid Resources

There are many rural areas on remote islands that cannot be reached by electricity sources from the utility grid. However, Indonesia is a country that has an abundant supply of renewable energy. One of the renewable energies that is obtained for free is solar energy sources. Renewable energy has great potential as a source of distributed electricity generation or microgrids. This article proposes a new method for providing large electrical power supplies for rural areas, namely multiple microgrids with a centralized control strategy. The purpose of this method is to provide stability of power supply to the load. In this method, each microgrid has solar panels (SP), batteries, and diesel generators (GD). Multiple microgrids provide power supply to DC loads and AC loads. The centralized controller uses an outseal programmable logic controller (PLC) which functions to regulate the power flow of microgrid 1 (MG1), microgrid 2 (MG2), and microgrid 3 (MG3) to the load alternately. Simulation test results show the performance of a centralized control which is able to provide power supply to the load according to demand or changes in load. Power regulation management for rural areas can be developed for large-scale microgrid systems.
 Keywords: multiple-microgrid; centralized control; solar panel

A low-complexity multi-channel active noise control system using local secondary path estimation and clustered control strategy for vehicle interior engine noise

Conventional multi-channel active noise control (ANC) system based on the adaptive notch filtered-x least mean square algorithm is typically used for active control of vehicle interior engine noise with prominent harmonic characteristics. However, due to the large estimated secondary path length and the centralized control strategy, the system has high computational complexity and fragile stability. To alleviate this problem, an efficient multi-channel ANC system using the local secondary path (LSP) estimation and clustered control strategy is proposed in this paper. Based on the modified LSP estimation method, the system may utilize a set of low-order but accurate LSP models to simplify the convolution operations of reference filtering. Besides, the proposed clustered control strategy combines the advantages of centralized and decentralized control strategies, and thus the system not only enjoys good noise attenuation performance and stability, but also its computational burden is further greatly reduced. Numerical simulations are performed to evaluate the noise attenuation performance and frequency mismatch effect of the proposed multi-channel ANC system. In addition, a series of real vehicle ANC experiments are conducted. The results show that, under stationary work conditions, the interior overall, 2nd order, 4th order, 6th order engine noises may be attenuated by 12.91 dB(A), 32.98 dB(A), 15.34 dB(A) and 8.74 dB(A), respectively, and under nonstationary work conditions, the maximum overall noise reductions at the four error microphones may reach 6.40 dB(A), 6.14 dB(A), 12.48 dB(A) and 11.07 dB(A), respectively. This fully confirms the effectiveness of the proposed multi-channel ANC system in real-world applications.

Decentralized self-stabilizing primary control of microgrids

The usage of distributed generation sources and the segmentation of power systems into microgrids brings several advantageous features, such as energy independence, lower transmission losses, and improved energy management flexibility. Still, the expected steady abolition of traditional centralized networks and their centralized control schemes introduces several operational difficulties, that can compromise (micro)grid’s stability and reliability. Consequently, several approaches to how microgrids should be operated have been proposed, albeit with several salient deficiencies. Precise power exchange, control of frequency and voltage excursions, applicability on different grid topologies, and the possibility to integrate grid codes, which are very important control aspects, are not jointly enabled in a general case. This paper proposes a novel approach, based on a specific goal function and corresponding decentralized control that addresses the mentioned problems and guarantees the microgrid’s stability by constraining the frequency and node voltage deviations, simultaneously supporting the desired active power exchange between prosumers. Unlike droop-based and droop-derived control schemes, the proposed approach aims to inherently preserve the frequency and voltage levels within the limits defined by the grid operator or future microgrid codes, thus preventing the generation unit’s unwanted disconnection during transients and disturbances. In addition, the control algorithm is independent of network topology, can be applied in both islanded and non-islanded microgrids, and secures system scalability. To confirm the effectiveness of the proposed control strategy, a number of simulation results are presented and thoroughly discussed.

Consensus-based Distributed Bus Voltage Control of in DC Microgrid Clusters

This paper proposes a consensus-based voltage control strategy for the bus of a DC microgrid cluster. Firstly, the closed-loop dynamics of a DC microgrid cluster bus voltage control system based on the consensus distributed control architecture is described, taking into full account the information exchange delay among the microgrid subsystems. Secondly, by constructing the Lyapunov-Krasovskii functional, the voltage control system asymptotic stability criteria under parameter uncertainties are rigorously derived, and the corresponding controller design criteria are obtained. Simulation results show that compared with the centralized control schemes, the proposed consensus distributed control method can reduce the average settling time by 24.39% and the average integral of absolute error of aggregate deviations by 23.92%.

Integrating Vehicle-to-Home Unit with Smart Home Energy Management Systems: A Unified Energy Management Framework

The increasing acceptance of electric vehicles (EVs) and renewable energy sources (RES) has led to the need for a unified energy management framework that can integrate multiple energy systems, including Vehicle-to-Home (V2H) units, Smart Home Energy Management Systems (SHEMS), Solar PV systems, and the grid. The framework uses a centralized control strategy that makes decisions based on real-time integration of a Vehicle-to-Home (V2H) unit with a Smart Home Energy Management System (SHEMS), which can provide a solution to these challenges by enabling bidirectional power flow between the EV battery and the home. We proposed a unified energy management framework that integrates a Ve- hicle-to-Home (V2H) unit with a SHEMS using a Perturb and Observe (P-&-O) algorithm. The proposed framework allows for the optimization of energy usage in the home by utilizing the battery of an EV, which can be charged during off-peak hours and discharged during peak hours. The P&O algorithm is a well-known algorithm used in photovoltaic systems to track the Maximum Power Point (MPP) of a solar panel. The algorithm is also applicable to EV charging and discharging systems. The algorithm uses a per- turbation signal to change the charging rate of the EV battery and observes the resulting change in the bat- tery voltage. The simulation results can also provide benefits to EV owners, such as reduced electricity costs and increased flexibility in managing their EV charging, helping to achieve efficient and sustainable energy management in residential areas. Keywords: Solar panel, Electric Vehicle Battery, Vehicle-to-Home (V2H), Smart Home Energy Manage- ment Systems (SHEMS), Demand side management.

Integrating Demand Response for Enhanced Load Frequency Control in Micro-Grids with Heating, Ventilation and Air-Conditioning Systems

Heating, ventilation and air-conditioning (HVAC) systems constitute the majority of the demands in modern power systems for aggregated buildings. However, HVAC integrated with renewable energy sources (RES) face notable issues, such as uneven demand–supply balance, frequency oscillation and significant drop in system inertia owing to sudden disturbances in nearby generation for a longer period. To overcome these challenges, load frequency control (LFC) is implemented to regulate the frequency, maintain zero steady-state error between the generation and demand, reduce frequency deviations and balance the active power flow with neighboring control areas at a specified value. In view of this, the present paper investigates LFC with a proposed centralized single control strategy for a micro-grid (µG) system consisting of RESs and critical load of a HVAC system. The proposed control strategy includes a newly developed cascaded two-degree-of-freedom (2-DOF) proportional integral (PI) and proportional derivative filter (PDF) controller optimized with a very recent meta-heuristic algorithm—a modified crow search algorithm (mCSA)—after experimenting with the number of performance indices (PICs). The superiority of both the proposed optimization algorithm and the proposed controller is arrived at after comparison with similar other algorithms and similar controllers, respectively. Compared to conventional control schemes, the proposed scheme significantly reduces the frequency deviations, improving by 27.22% from the initial value and reducing the performance index criteria (ƞISE) control error to 0.000057. Furthermore, the demand response (DR) is implemented by an energy storage device (ESD), which validates the suitability of the proposed control strategy for the µG system and helps overcome the challenges associated with variable RESs inputs and load demand. Additionally, the improved robustness of the proposed controller for this application is demonstrated through sensitivity analysis with ±20% μG coefficient variation.

Heat pumps and thermal energy storages centralised management in a Renewable Energy Community.

This paper examines a Renewable Energy Community (REC) made up of 10 dwellings that collectively self-consume energy produced by a photovoltaic field connected to a water purifier. Each dwelling heat demand is satisfied by means of Heat Pump (HP) coupled with Thermal Energy Storage (TES), which can be managed to perform load shifting and increase collective-self-consumption (CSC). Techno-economic analyses are performed accounting for HPs' COP variation with temperature and part load operations, as well as TES heat dispersion. A new centralised control strategy for HPs is proposed and a sensitivity analysis is performed to assess the impact of varying TES system capacity. The results show that the centralised strategy can increase the CSC by 12-30%, with TES sizes of 100-1000 litres respectively. But the electricity consumption of HPs increases by 2-5% due to higher storage system temperatures causing worse average COPs by 2.3-0.6% and higher thermal losses by 29-58%. As a result, REC's energy independence rise, as does the amount of CSC incentives, but electricity bills also increase. Comparing these trends shows that CSC incentives should be adjusted according to energy prices to ensure cost-effective outcomes for all stakeholders and encourage the adoption of similar centralised control strategies.

Design and control of a multi-mobile-robot cooperative transport system based on a novel six degree-of-freedom connector

Multi-robot cooperative object transport on uneven roads is challenging. The key barrier is dealing with nonholonomic and rigid-formation motion constraints. In this study, to alleviate the influence of these constraints on a multi-robot cooperative transport system (MRCTS), a six degree-of-freedom connector capable of sensing three-axial displacements, three-axial forces, and three-axial angular displacements is designed and employed. Based on the local displacements derived from each connector, we develop a position calibration method to calculate the relative position of each robot and achieve a centralized control strategy. Based on the forces sensed by each connector, we design a decentralized control strategy to accomplish cooperative transport in which a leader robot guides the follower robots toward a destination by applying forces, instead of centralized information broadcasting. The experimental results show that the MRCTS works well on an uneven surface, and the tracking errors are within the design stroke of the connectors, demonstrating the effectiveness of the design and control methods of the MRCTS.

Frequency Control Strategy for Grid-tied Virtual Power Plant Using SSA-tuned Fractional Order PID Controller

This paper investigates the frequency control strategy of the Virtual Power Plant (VPP), with the structure of an independent control area that includes diverse Distributed Energy Resources. The proposed VPP system comprises generating units such as Solar PV, Archimedes Wave Energy Conversion, Biodiesel driven Generator, and Plug-in Hybrid Electric Vehicle, which are interconnected to conventional thermal power plant. Centralized control strategy is adopted for frequency control studies, by considering the communication time delays. Fractional order Proportional Integral Derivative (FOPID), Proportional Integral Derivative (PID), and Proportional Integral (PI) controllers are employed to perform the control action on generating units to perform the frequency control. Tuning of the controllers is done using optimization algorithms such as Particle Swarm Optimization, Firefly Algorithm, Grasshopper Optimization Algorithm, Ant Lion Optimizer, Sine Cosine Algorithm, and Salp Swarm Algorithm (SSA). By comparative analysis, SSA algorithm is proved to outperform the other algorithms in terms of minimizing the objective function of Integral of Squared Error of the deviations in system frequencies and tie-line power. The system is also investigated under various scenarios of generation and load disturbances to study the comparative performance of the FOPID controller over PID and PI controllers. Results prove the superiority of SSA-tuned FOPID controller over PID and PI controllers in terms of providing better system responses. Sensitivity test has been conducted on the system without resetting nominal controller gain values and the proposed SSA-tuned FOPID controller is proved to be robust against the uncertainties in the load and parameters of our system.

The Viability of a Grid of Autonomous Ground-Tethered UAV Platforms in Agricultural Pest Bird Control

Pest birds are a salient problem in agriculture all around the world due to the damage they can cause to commercial or high-value crops. Recent advancements in Unmanned Aerial Vehicles (UAVs) have motivated the use of drones in pest bird deterrence, with promising success already being demonstrated over traditional bird control techniques. This paper presents a novel bird deterrence solution in the form of tethered UAVs, which are attached and arranged in a grid-like fashion across a vineyard property. This strategy aims to bypass the power and endurance limitations of untethered drones while still utilising their dynamism and scaring potential. A simulation model has been designed and developed to assess the feasibility of different UAV arrangements, configurations, and strategies against expected behavioural responses of incoming bird flocks, despite operational and spatial constraints imposed by a tether. Attempts at quantifying bird persistence and relative effort following UAV-induced deterrence are also introduced through a novel bird energy expenditure model. This aims to serve as a proxy for selecting control techniques that reduce future foraging missions. The simulation model successfully isolated candidate configurations, which were able to deter both single and multiple incoming bird flocks using a centralised multi-UAV control strategy. Overall, this study indicates that a grid of autonomous ground-tethered UAV platforms is viable as a bird deterrence solution in agriculture, a novel solution not seen nor dealt with elsewhere to the authors’ knowledge.

A Distributed Control Strategy for Unbalanced Voltage Compensation in Islanded AC Microgrids Without Continuous Communication

Due to the unbalanced load connection in the sensitive load bus (SLB), the ac microgrid may suffer from voltage unbalance in the system. To overcome this issue, this article presents a new distributed control scheme to achieve the unbalanced voltage compensation for islanded ac microgrid with limited noncontinuous communication among the distributed generation (DG) units. In this article, a two-layer control framework, including the cyber layer and the primary control layer, is employed. The proposed control strategy that is applied in the cyber layer implements an event-triggered communication to effectively compensate for the unbalanced voltage in the SLB. In contrast with the centralized control strategy, the proposed control strategy is fully distributed, and the information exchange among the DG units at only the event-triggered times. As a result, the communication burdens can be measurably reduced while the control performance is not affected. The stability is analyzed with the Lyapunov function in this article. Finally, several experimental case studies are provided to verify the effectiveness of the proposed scheme.

Multi-agent deep reinforcement learning based distributed control architecture for interconnected multi-energy microgrid energy management and optimization

Environmental and climate change concerns are pushing the rapid development of new energy resources (DERs). The Energy Internet (EI), with the power-sharing functionality introduced by energy routers (ERs), offers an appealing alternative for DER systems. However, previous centralized control schemes for EI systems that follow a top-down architecture are unreliable for future power systems. This study proposes a distributed control scheme for bottom-up EI architecture. Second, model-based distributed control methods are not sufficiently flexible to deal with the complex uncertainties associated with multi-energy demands and DERs. A novel model-free/data-driven multiagent deep reinforcement learning (MADRL) method is proposed to learn the optimal operation strategy for the bottom-layer microgrid (MG) cluster. Unlike existing single-agent deep reinforcement learning methods that rely on homogeneous MG settings, the proposed MADRL adopts a form of decentralized execution, in which agents operate independently to meet local customized energy demands while preserving privacy. Third, an attention mechanism is added to the centralized critic, which can effectively accelerate the learning speed. Considering the bottom-layer power exchange request and the predicted electricity price, model predictive control of the upper layer determines the optimal power dispatching between the ERs and main grid. Simulations with other alternatives demonstrate the effectiveness of the proposed control scheme.

Distributed Active Noise Control Based on an Augmented Diffusion FxLMS Algorithm

Multichannel active noise control (ANC) systems have been widely investigated for low-frequency noise attenuation over a spatial region. Using a conventional centralized control strategy based on the multichannel filtered- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> least mean square (F <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> LMS) algorithm has been demonstrated to be effective for multichannel ANC systems, but the high computational burden restricts its practical applications. Meanwhile, a decentralized control strategy suffers from stability problems although it has been successful in reducing the computational load. Recently, distributed control strategies, such as the multitask diffusion adaptation scheme, have been introduced to ANC systems and shown to mitigate the stability problems in decentralized systems. However, distributed ANC systems using the diffusion F <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> LMS algorithm require strong symmetry of acoustic paths because of the dependence on node-based adaptation and neighborhood-based combination. To overcome this limitation, this paper proposes an Augmented Diffusion F <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> LMS algorithm with neighborhood-based adaptation and node-based combination. A theoretical formulation and convergence analysis are presented and simulations are performed to compare the proposed algorithm with existing ones under different system configurations for tonal, multi-tonal, narrowband and broadband signals. Simulation results demonstrate that the proposed algorithm has the same noise reduction performance as centralized method even if the acoustic paths are strongly asymmetrical, which is superior over existing distributed multitask diffusion strategy.

Two-Stage Optimal Active-Reactive Power Coordination for Microgrids with High Renewable Sources Penetration and Electrical Vehicles Based on Improved Sine−Cosine Algorithm

As current global trends aim at the large-scale insertion of electric vehicles as a replacement for conventional vehicles, new challenges occur in terms of the stable operation of electric distribution networks. Microgrids have become reliable solutions for integrating renewable energy sources, such as solar and wind, and are considered a suitable alternative for accommodating the growing fleet of electrical vehicles. However, efficient management of all equipment within a microgrid requires complex solving algorithms. In this article, a novel two-stage scheme is proposed for the optimal coordination of both active and reactive power flows in a microgrid, considering the high penetration of renewable energy sources, energy storage systems, and electric mobility. An improved sine-cosine algorithm is introduced to ensure the day-ahead optimal planning of the microgrid’s components aiming at minimizing the total active energy losses of the system. In this regard, both local and centralized control strategies are investigated for multiple generations and consumption scenarios. The latter proved itself a promising control scheme for the microgrid operation, as important energy loss reduction is encountered when applied.

COOR-PLT: A hierarchical control model for coordinating adaptive platoons of connected and autonomous vehicles at signal-free intersections based on deep reinforcement learning

Platooning and coordination are two implementation strategies that are frequently proposed for traffic control of connected and autonomous vehicles (CAVs) at signal-free intersections instead of using conventional traffic signals. However, few studies have attempted to integrate both strategies to better facilitate the CAV control at signal-free intersections. To this end, this study proposes a hierarchical control model, named COOR-PLT, to coordinate adaptive CAV platoons at a signal-free intersection based on deep reinforcement learning (DRL). COOR-PLT has a two-layer framework. The first layer uses a centralized control strategy to form adaptive platoons. The optimal size of each platoon is determined by considering multiple objectives (i.e., efficiency, fairness and energy saving). The second layer employs a decentralized control strategy to coordinate multiple platoons passing through the intersection. Each platoon is labeled with coordinated status or independent status, upon which its passing priority is determined. As an efficient DRL algorithm, Deep Q-network (DQN) is adopted to determine platoon sizes and passing priorities respectively in the two layers. The model is validated and examined on the simulator Simulation of Urban Mobility (SUMO). The simulation results demonstrate that the model is able to: (1) achieve satisfactory convergence performances; (2) adaptively determine platoon size in response to varying traffic conditions; and (3) completely avoid deadlocks at the intersection. By comparison with other control methods, the model manifests its superiority of adopting adaptive platooning and DRL-based coordination strategies. Also, the model outperforms several state-of-the-art methods on reducing travel time and fuel consumption in different traffic conditions.

A distributed simplex architecture for multi-agent systems

We present the Distributed Simplex Architecture (DSA), a new runtime assurance technique that provides safety guarantees for multi-agent systems (MASs). DSA is inspired by the Simplex control architecture of Sha et al., but with some significant differences. The traditional Simplex approach is limited to single-agent systems or a MAS with a centralized control scheme. DSA addresses this limitation by extending the scope of Simplex to include MASs under distributed control. In DSA, each agent runs a local instance of traditional Simplex such that the preservation of safety in the local instances implies safety for the entire MAS. Control Barrier Functions (CBFs) play a critical role. They are used to define DSA’s core components – the baseline controller and the decision module’s logic for switching between advanced and baseline control – and they provide the basis for the proof of safety. We present a general proof of safety for DSA, provided the CBF-related optimization problem solved by the baseline controller is feasible (has a solution) at each time step for which the baseline controller is in control. We also propose a novel extension to the switching logic designed to avoid states in which this optimization problem is infeasible. Finally, we present experimental results for several case studies, including flocking with collision avoidance, safe navigation of ground rovers through way-points, and safe operation of a microgrid.