Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems--the bouncing pendulum and the simplest walker--with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control.

Y ou can use this material personally. The DOI will be supplied as soon as it becomes available. Abstract --6G networks aim to achieve global coverage, massive connectivity, and ultra-stringent requirements. Space-Air-Ground Integrated Networks (SAGINs) and Semantic Communication (SemCom) are essential for realizing these goals, yet they introduce considerable complexity in resource orchestration. Drawing inspiration from research in robotics, a viable solution to manage this complexity is the application of Large Language Models (LLMs). Although the use of LLMs in network orchestration has recently gained attention, existing solutions have not sufficiently addressed LLM hallucinations or their adaptation to network dynamics. T o address this gap, this paper proposes a framework called Autonomous Reinforcement Coordination (ARC) for a SemCom-enabled SAGIN. This framework employs an LLM-based Retrieval-Augmented Generator (RAG) monitors services, users, and resources and processes the collected data, while a Hierarchical Action Planner (HAP) orchestrates resources. The LLMs utilize Chain-of-Thought (CoT) reasoning for few-shot learning, empowered by contrastive learning, while the RL agents employ replay buffer management for continual learning, thereby achieving efficiency, accuracy, and adaptability. Simulations are provided to demonstrate the effectiveness of ARC, along with a comprehensive discussion on potential future research directions to enhance and upgrade ARC.

Codes and demo are available. This article explores what are states, actions and rewards in reinforcement learning, and how agent can learn through simulation to determine the best actions to take in any given state. After a long day at work, you are deciding between 2 choices: to head home and write an article or hang out with friends at a bar. If you choose to hang out with friends, your friends will make you feel happy; whereas heading home to write an article, you'll end up feeling tired after a long day at work. In this example, enjoying yourself is a reward and feeling tired is viewed as a negative reward, so why write articles?

Chance Constrained Markov Decision Processes maximize reward subject to a bounded probability of failure, and have been frequently applied for planning with potentially dangerous outcomes or unknown environments. Solution algorithms have required strong heuristics or have been limited to relatively small problems with up to millions of states, because the optimal action to take from a given state depends on the probability of failure in the rest of the policy, leading to a coupled problem that is difficult to solve. In this paper we examine a generalization of a CCMDP that trades off probability of failure against reward through a functional relationship. We derive a constraint that can be applied to each state history in a policy individually, and which guarantees that the chance constraint will be satisfied. The approach decouples states in the CCMDP, so that large problems can be solved efficiently. We then introduce Vulcan, which uses our constraint in order to apply Monte Carlo Tree Search to CCMDPs. Vulcan can be applied to problems where it is unfeasible to generate the entire state space, and policies must be returned in an anytime manner. We show that Vulcan and its variants run tens to hundreds of times faster than linear programming methods, and over ten times faster than heuristic based methods, all without the need for a heuristic, and returning solutions with a mean suboptimality on the order of a few percent. Finally, we use Vulcan to solve for a chance constrained policy in a CCMDP with over $10^{13}$ states in 3 minutes.