No Arabic abstract
In this paper, we propose a new control barrier function based quadratic program for general nonlinear control-affine systems, which, without any assumptions other than those taken in the original program, simultaneously guarantees forward invariance of the safety set, complete elimination of undesired equilibrium points inside it, and local asymptotic stability of the origin. To better appreciate this result, we first characterize the equilibrium points of the closed-loop system with the original quadratic program formulation. We then provide analytical results on how a certain parameter in the original quadratic program should be chosen to remove the undesired equilibrium points or to confine them in a small neighborhood of the origin. The new formulation then follows from these analytical results. Numerical examples are given alongside the theoretical discussions.
Under voltage load shedding has been considered as a standard and effective measure to recover the voltage stability of the electric power grid under emergency and severe conditions. However, this scheme usually trips a massive amount of load which can be unnecessary and harmful to customers. Recently, deep reinforcement learning (RL) has been regarded and adopted as a promising approach that can significantly reduce the amount of load shedding. However, like most existing machine learning (ML)-based control techniques, RL control usually cannot guarantee the safety of the systems under control. In this paper, we introduce a novel safe RL method for emergency load shedding of power systems, that can enhance the safe voltage recovery of the electric power grid after experiencing faults. Unlike the standard RL method, the safe RL method has a reward function consisting of a Barrier function that goes to minus infinity when the system state goes to the safety bounds. Consequently, the optimal control policy can render the power system to avoid the safety bounds. This method is general and can be applied to other safety-critical control problems. Numerical simulations on the 39-bus IEEE benchmark is performed to demonstrate the effectiveness of the proposed safe RL emergency control, as well as its adaptive capability to faults not seen in the training.
We introduce High-Relative Degree Stochastic Control Lyapunov functions and Barrier Functions as a means to ensure asymptotic stability of the system and incorporate state dependent high relative degree safety constraints on a non-linear stochastic systems. Our proposed formulation also provides a generalisation to the existing literature on control Lyapunov and barrier functions for stochastic systems. The control policies are evaluated using a constrained quadratic program that is based on control Lyapunov and barrier functions. Our proposed control design is validated via simulated experiments on a relative degree 2 system (2 dimensional car navigation) and relative degree 4 system (two-link pendulum with elastic actuator).
We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances consistency, which measures the competitive ratio when predictions are accurate, and robustness, which bounds the competitive ratio when predictions are inaccurate. We propose a novel $lambda$-confident controller and prove that it maintains a competitive ratio upper bound of $1+min{O(lambda^2varepsilon)+ O(1-lambda)^2,O(1)+O(lambda^2)}$ where $lambdain [0,1]$ is a trust parameter set based on the confidence in the predictions, and $varepsilon$ is the prediction error. Further, we design a self-tuning policy that adaptively learns the trust parameter $lambda$ with a regret that depends on $varepsilon$ and the variation of perturbations and predictions.
In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.
This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model parameters can be learned precisely enough to increase the robust performance of the plant. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The dual features of the controller are incorporated through scenario-based (multi-stage) approach, which allows for modeling of the adaptive robust decision problem and for projecting this decision into predictions of the controller. The proposed approach is illustrated on a case study from batch membrane filtration.