Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints

Abstract

In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples.

Reinforcement Learning-Based Decentralized Safety Control for Constrained Interconnected Nonlinear Safety-Critical Systems

“…Over the past few decades, safety has received increasing attention in autonomous driving [ 1 ], intelligent robots [ 2 ], robotic arms [ 3 ], adaptive cruise control [ 4 ], etc. The design of these systems and controllers require that the system state trajectories evolve within a set called the safe set, reflecting the inherent properties of the system [ 5 ].…”

“… Nonlinear interconnected safety-critical systems with asymmetric input constraints and safety constraints are converted to equivalent systems that satisfy user-defined safety constraints using barrier functions. Unlike the nonlinear safety-critical systems [ 3 , 9 , 10 , 13 ], this paper solves the security constraint problem of the interconnection term through the potential barrier function, which ensures the interconnected nonlinear safety-critical system satisfies the security constraint. The asymmetric input constraints are solved by utilizing a single CNN architecture for online approximation of the performance function.…”