Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function

Zeng, Jun; Zhang, Bike; Sreenath, Koushil

doi:10.23919/acc50511.2021.9483029

Cited by 173 publications

(82 citation statements)

References 20 publications

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“…Combining MPC control design with control Lyapunov or control barrier functions has also been proposed in [20], [21], [22], where the idea is to impose an explicit barrier function constraint on each predicted system state, which provides guarantees in terms of constraint satisfaction. While there also exists a soft-constrained formulation using control Lyapunov functions [23], the main limitation of these approaches is that each predicted state must be contained in the domain of the control barrier/control Lyapunov function.…”

Section: B Related Workmentioning

confidence: 99%

Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

Wabersich¹,

Zeilinger²

2021

Preprint

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While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety filters, which assess if a proposed learning-based control input can lead to constraint violations and modifies it if necessary to ensure safety for all future time steps. The theoretical guarantees of such predictive safety filters rely on the model assumptions and minor deviations can lead to failure of the filter putting the system at risk. This paper introduces an auxiliary softconstrained predictive control problem that is always feasible at each time step and asymptotically stabilizes the feasible set of the original safety filter, thereby providing a recovery mechanism in safety-critical situations. This is achieved by a simple constraint tightening in combination with a terminal control barrier function. By extending discrete-time control barrier function theory, we establish that the proposed auxiliary problem provides a 'predictive' control barrier function. The resulting algorithm is demonstrated using numerical examples.

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Section: B Related Workmentioning

confidence: 99%

Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

Wabersich¹,

Zeilinger²

2021

Preprint

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“…Some researchers formulate this problem using control barrier functions under the continuous dynamics of the system [1], [2], where the optimal performance is achieved by the control Lyapunov functions and safety criteria is guaranteed through control barrier functions. Recently, this methodology is also introduced in the discrete-time domain and the optimal control problem can be formulated to calculate the current optimal input [3] or a sequence of ones in the fashion of model predictive control [4]. However, feasibility and safety are still the main challenges for these formulations using discrete-time control barrier functions.…”

Section: A Motivationmentioning

confidence: 99%

“…The model predictive control with control Lyapunov functions (CLF-NMPC) is proposed to ensure stability in [15], where CLF constraints are considered under nonlinear model predictive control (NMPC). A control design (MPC-CBF) for safety-critical tasks is firstly presented in [4], where the safety-critical constraints are enforced by discrete-time control barrier functions. This approach could also be applied to a multi-layer control framework [16], [17], where the safety-critical control with discrete-time CBF serves as a mid-level controller or planner.…”

Section: B Related Workmentioning

confidence: 99%

“…The infeasibility issues come from the potential empty intersection between the reachable set and the safe region confined by CBF constraints at each time step. Moreover, there exists a tradeoff between safety performance and feasibility and they cannot be enhanced at the same time, discussed in [4]. In other words, reducing decay rates of CBF constraints increases the system safety, but comes at the possibility of infeasibility.…”

Section: B Related Workmentioning

confidence: 99%

“…2) MPC-CBF [4]: Inspired by the previous work of model predictive control and control barrier functions, DCLF-DCBF can be improved by taking future state prediction into account, yielding the form of MPC-CBF firstly introduced in [4] and shown as follows, MPC-CBF:…”

Section: B Existing Approaches Revisitedmentioning

confidence: 99%

See 2 more Smart Citations

Enhancing Feasibility and Safety of Nonlinear Model Predictive Control with Discrete-Time Control Barrier Functions

Zeng¹,

Li²,

Sreenath³

2021

Preprint

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Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system are formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the optimization feasibility and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Relaxing variables are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.

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Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure

Tang

Liu

2021

Intl J Robust & Nonlinear

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This article puts forward an adaptive neural network fault-tolerant control scheme under the state constraints for the flexible manipulator system with uncertain terms. The dynamic model of the system is described by partial differential equations. The tangent barrier Lyapunov functions are chosen in the design process for the sake of ensuring that all states in the system satisfy the constrained conditions. The uncertainties resulted from load mass, hub inertia, and bending stiffness in the system are approximated by using the universal approximation property of neural networks. The adaptive method is used to counteract the influence of joint motor actuator failure. At the same time, combining with the backstepping design framework to design effective controllers to assure that all signals in the closed-loop system are bounded. Lyapunov stability analysis method is used to prove the stability of the system. Finally, the simulation results prove the availability of the raised control method.

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Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function

Cited by 173 publications

References 20 publications

Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

Enhancing Feasibility and Safety of Nonlinear Model Predictive Control with Discrete-Time Control Barrier Functions

Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure

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