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We study the safety verification problem for discrete-time stochastic systems. We propose an approach for safety verification termed set-erosion strategy that verifies the safety of a stochastic system on a safe set through the safety of its associated deterministic system on an eroded subset. The amount of erosion is captured by the probabilistic bound on the distance between stochastic trajectories and their associated deterministic counterpart. Building on our recent work [1], we establish a sharp probabilistic bound on this distance. Combining this bound with the set-erosion strategy, we establish a general framework for the safety verification of stochastic systems. Our method is flexible and can work effectively with any deterministic safety verification techniques. We exemplify our method by incorporating barrier functions designed for deterministic safety verification, obtaining barrier certificates much tighter than existing results. Numerical experiments are conducted to demonstrate the efficacy and superiority of our method.

In this paper we study the reachability problem for discrete-time nonlinear stochastic systems. Our goal is to present a unified framework for calculating the probabilistic reachable set of discrete-time systems in the presence of both deterministic input and stochastic noise. By adopting a suitable separation strategy, the probabilistic reachable set is decoupled into a deterministic reachable set and the effect of the stochastic noise. To capture the effect of the stochastic noise, in particular sub-Gaussian noise, we provide a probabilistic bound on the distance between a stochastic trajectory and its deterministic counterpart. The key to our approach is a novel energy function called the Averaged Moment Generating Function, which we leverage to provide a high probability bound on this distance. We show that this probabilistic bound is tight for a large class of discrete-time nonlinear stochastic systems and is exact for linear stochastic dynamics. By combining this tight probabilistic bound with the existing methods for deterministic reachability analysis, we propose a flexible framework that can efficiently compute probabilistic reachable sets of stochastic systems. We also provide two case studies for applying our framework to Lipschitz bound reachability and interval-based reachability. Three numerical experiments are conducted to validate the theoretical results., Comment: arXiv admin note: text overlap with arXiv:2407.12225

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and deterministic inputs. To achieve this, we devise a strategy that effectively decouples the effects of deterministic inputs and stochastic disturbances on the reachable sets of the system. For the deterministic part, many existing methods can capture the deterministic reachability. As for the stochastic disturbances, we introduce a novel technique that probabilistically bounds the difference between a stochastic trajectory and its deterministic counterpart. The key to our approach is introducing a novel energy function termed the Averaged Moment Generating Function that yields a high probability bound for this difference. This bound is tight and exact for linear stochastic dynamics and applicable to a large class of nonlinear stochastic dynamics. By combining our innovative technique with existing methods for deterministic reachability analysis, we can compute estimations of reachable sets that surpass those obtained with current approaches for stochastic reachability analysis. We validate the effectiveness of our framework through various numerical experiments. Beyond its immediate applications in reachability analysis, our methodology is poised to have profound implications in the broader analysis and control of stochastic systems. It opens avenues for enhanced understanding and manipulation of complex stochastic dynamics, presenting opportunities for advancements in related fields.

In this paper, we present a new computer-controlled weaving technology that enables the fabrication of woven structures in the shape of given 3D surfaces by using threads in non-traditional materials with high bending-stiffness, allowing for multiple applications with the resultant woven fabrics. A new weaving machine and a new manufacturing process are developed to realize the function of 3D surface weaving by the principle of short-row shaping. A computational solution is investigated to convert input 3D freeform surfaces into the corresponding weaving operations (indicated as W-code) to guide the operation of this system. A variety of examples using cotton threads, conductive threads and optical fibres are fabricated by our prototype system to demonstrate its functionality.

We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains unclear whether data-driven approaches, which bypass the system identification step, can solve the problem. In this work, we present a novel data-driven online adaptive control algorithm to address this online control problem. Our algorithm leverages the behavioral systems theory to learn a non-parametric system representation and then adopts a perturbation-based controller updated by online gradient descent. We prove that our algorithm guarantees an $\tmO(T^{2/3})$ regret bound with high probability, which matches the best-known regret bound for this problem. Furthermore, we extend our algorithm and performance guarantee to the cases with output feedback.

In this paper, we investigate the problem of coordination between economic dispatch (ED) and demand response (DR) in multi-energy systems (MESs), aiming to improve the economic utility and reduce the waste of energy in MESs. Since multiple energy sources are coupled through energy hubs (EHs), the supply-demand constraints are nonconvex. To deal with this issue, we propose a linearization method to transform the coordination problem to a convex social welfare optimization one. Then a decentralized algorithm based on parallel Alternating Direction Method of Multipliers (ADMM) and dynamic average tracking protocol is developed, where each agent could only make decisions based on information from their neighbors. Moreover, by using variational inequality and Lyapunov-based techniques, we show that our algorithm could always converge to the global optimal solution. Finally, a case study on the modified IEEE 14-bus network verifies the feasibility and effectiveness of our algorithm., Comment: The paper has been submitted to 2021 60th IEEE Conference on Decision and Control (CDC)