Suboptimal Safety-Critical Control for Continuous Systems Using Prediction-Correction Online Optimization

This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using more efficient online algorithms by the time-varying optimization method. The idea of the algorithms is that when quadratic programming (QP) or other convex optimization algorithms needed in the CBF-based method is not computation affordable, the alternative suboptimal feasible solutions can be obtained more economically. By using the barrier-based interior point method, the constrained CBF-QP problems are transformed into unconstrained ones with suboptimal solutions tracked by two continuous descent-based algorithms. Considering the lag effect of tracking and exploiting the system information, the prediction method is added to the algorithms, which achieves exponential convergence to the time-varying suboptimal solutions. The convergence and robustness of the designed methods as well as the safety criteria of the algorithms are studied theoretically. The effectiveness is illustrated by simulations on the anti-swing and obstacle avoidance tasks

Distributed Online Optimization via Gradient Tracking with Adaptive Momentum

This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient tracking with adaptive momentum estimation (GTAdam) distributed algorithm, which combines a gradient tracking mechanism with first and second order momentum estimates of the gradient. The algorithm is analyzed in the online setting for strongly convex and smooth cost functions. We prove that the average dynamic regret is bounded and that the convergence rate is linear. The algorithm is tested on a time-varying classification problem, on a (moving) target localization problem and in a stochastic optimization setup from image classification. In these numerical experiments from multi-agent learning, GTAdam outperforms state-of-the-art distributed optimization methods

Approximate Sensitivity Conditioning and Singular Perturbation Analysis for Power Converters

A feed-forward sensitivity conditioning control strategy is analyzed in this paper and it is applied to power electronic converters. The feed-forward term is used to improve closed loop systems, such as power converters with cascaded inner and outer loop controllers. The impact of the feed-forward sensitivity term is analyzed using singular perturbation theory. In addition, the implementation of the feed-forward control term is addressed for practical systems, where the number of inputs is generally not sufficient for exact sensitivity conditioning. Simulation results are presented for a buck converter with output capacitor voltage regulation and a Permanent Magnet Synchronous Machine (PMSM), used as a generator with an active rectifier. Finally, experimental results are presented for the buck converter, demonstrating the advantages and feasibility in implementing the approximate sensitivity conditioning term for closed loop power converters

Distributed Asynchronous Discrete-Time Feedback Optimization

In this article, we present an algorithm that drives the outputs of a network of agents to jointly track the solutions of time-varying optimization problems in a way that is robust to asynchrony in the agents' operations. We consider three operations that can be asynchronous: (1) computations of control inputs, (2) measurements of network outputs, and (3) communications of agents' inputs and outputs. We first show that our algorithm converges to the solution of a time-invariant feedback optimization problem in linear time. Next, we show that our algorithm drives outputs to track the solution of time-varying feedback optimization problems within a bounded error dependent upon the movement of the minimizers and degree of asynchrony in a way that we make precise. These convergence results are extended to quantify agents' asymptotic behavior as the length of their time horizon approaches infinity. Then, to ensure satisfactory network performance, we specify the timing of agents' operations relative to changes in the objective function that ensure a desired error bound. Numerical experiments confirm these developments and show the success of our distributed feedback optimization algorithm under asynchrony