Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

Reis, Matheus F.; Aguiar, A. Pedro; Tabuada, Paulo

doi:10.1109/lcsys.2020.3004797

Cited by 49 publications

(33 citation statements)

References 22 publications

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“…In reference [59], Hosseinzadeh et al introduced the Explicit Reference Governor scheme for continuous-time systems, which guaranteed that the system states were constrained in a specified range. Other approaches refer to the control barrier functions (CBFs), which has been significantly applied, above all, in the context of safety and critical control conditions [60] or to the safety preserving control algorithm, where the system was forced to remain within the constraint invariant set [61].…”

Section: Overview In Mpc Methods For Greenhouse Efficiencymentioning

confidence: 99%

Model Predictive Control versus Traditional Relay Control in a High Energy Efficiency Greenhouse

et al. 2021

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The sustainable agriculture cultivation in greenhouses is constantly evolving thanks to new technologies and methodologies able to improve the crop yield and to solve the common concerns which occur in protected environments. In this paper, an MPC-based control system has been realized in order to control the indoor air temperature in a high efficiency greenhouse. The main objective is to determine the optimal control signals related to the water mass flow rate supplied by a heat pump. The MPC model allows a predefined temperature profile to be tracked with an energy saving approach. The MPC has been implemented as a multiobjective optimization model that takes into account the dynamic behavior of the greenhouse in terms of energy and mass balances. The energy supply is provided by a ground coupled heat pump (GCHP) and by the solar radiation while the energy losses related to heat transfers across the glazed envelope. The proposed MPC method was applied in a smart innovative greenhouse located in Italy, and its performances were compared with a traditional reactive control method in terms of deviation of the indoor temperature in respect to the desired one and in terms of electric power consumption. The results demonstrated that, for a time horizon of 20 h, in a greenhouse with dimensions 15.3 and 9.9 m and an average height of 4.5 m, the proposed MPC approach saved about 30% in electric power compared with a relay control, guaranteeing a consistent and reliable temperature profile in respect to the predefined tracked one.

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Section: Overview In Mpc Methods For Greenhouse Efficiencymentioning

confidence: 99%

Model Predictive Control versus Traditional Relay Control in a High Energy Efficiency Greenhouse

et al. 2021

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“…Hence, backstepping generates a safety-filter with explicit tuning variables that dictate the exponential approach to the barrier. Worth remembering is that, in safety-filter design, the goals of ensuring safety and allowing the system to evolve according to a desired nominal trajectory can be conflicting: it was shown in [30] that quadratic program (QP)-based methods for safety design may come at the cost of asymptotic convergence to undesirable equilibria. (This does not occur when applying time-varying backstepping for regulation to an equilibrium at the barrier over a finite time interval.…”

Section: A Hi-rel-deg Cbfsmentioning

confidence: 99%

Prescribed-Time Safety Design for a Chain of Integrators

Abel¹,

Steeves²,

Krstić³

et al. 2022

Preprint

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Safety in dynamical systems is commonly pursued using control barrier functions (CBFs) which enforce safetyconstraints over the entire duration of a system's evolution. We propose a prescribed-time safety (PTSf) design which enforces safety only for a finite time of interest to the user. While traditional CBF designs would keep the system farther from the barrier than necessary, and longer than necessary, our PTSf design lets the system reach the barrier by the prescribed time and obey the operator's intent thereafter. To emphasize the capability of our design for safety constraints with high relative degrees, we focus our exposition on a chain of integrators where the safety condition is defined for the state furthest from the control input. In contrast to existing CBF-based methods for high-relative degree constraints, our approach involves choosing explicitly specified gains (instead of class K functions), and, with the aid of backstepping, operates in the entirety of the original safe set with no additional restriction on the initial conditions. With QP being employed in the design, in addition to backstepping and CBFs with a PTSf property, we refer to our design as a QP-backstepping PT-CBF design. For illustration, we include a simulation for the double-integrator system.

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“…However, new developments show that the quadratic program methods may produce undesirable local equilibria [21], [22] because of confliction between the CLF and CBF, which may lead to control failure. For example, when the vehicle tracks a reference trajectory in an obstacle field, undesirable equilibria may cause extreme variation in vehicle velocity, which may deteriorate obstacle avoidance performance.…”

Section: A Objectivesmentioning

confidence: 99%

Exponential Barrier Functions for Safe Steering of Nonholonomic Vehicles With Actuator Time-Delay

Ghaffari

Desai

2022

IEEE Access

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This work provides a provably safe feedback control for nonholonomic vehicles that autonomously operate in an obstacle field. A barrier function with a tunable, exponential decay rate is used to obtain a safe steering envelope for the vehicle. The safe steering envelope adapts, in real-time, to the vehicle's velocity and its distance to the static obstacles. The safety control corrects steering commands provided by a nominal tracking control and prevents collisions between the vehicle and the obstacles. The safety and stability of the algorithm are proved analytically and verified via multiple experiments. The resulting safety control is modular and can work well with obstacles of different footprints. Since quick steering control is essential for successful vehicle navigation, a two-layer predictor is proposed to compensate for the time-delay in the vehicle dynamics. The two-layer predictor improves the control response time by as much as a factor of four. The safety and tracking control act on the vehicle kinematics, and the two-layer predictor improves the vehicle's dynamic performance. The proposed control structure has a closed-form with eight tunable parameters, which facilitates control calibration and tuning in large systems of vehicles. Extensive experiments are carried out on a nonholonomic vehicle to verify the effectiveness of the proposed algorithm.INDEX TERMS Collision avoidance, vehicle safety, unmanned autonomous vehicles.

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Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

Cited by 49 publications

References 22 publications

Model Predictive Control versus Traditional Relay Control in a High Energy Efficiency Greenhouse

Model Predictive Control versus Traditional Relay Control in a High Energy Efficiency Greenhouse

Prescribed-Time Safety Design for a Chain of Integrators

Exponential Barrier Functions for Safe Steering of Nonholonomic Vehicles With Actuator Time-Delay

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