Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMulti-layered simulation relations for linear stochastic systems
191
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The design of provably correct controllers for continuous-state stochastic systems crucially depends on approximate finite-state abstractions and their accuracy quantification. For this quantification, one generally uses approximate stochastic simulation relations, whose constant precision limits the achievable guarantees on the control design. This limitation especially affects higher dimensional stochastic systems and complex formal specifications. This work allows for variable precision by defining a simulation relation that contains multiple precision layers. For bi-layered simulation relations, we develop a robust dynamic programming approach yielding a lower bound on the satisfaction probability of temporal logic specifications. We illustrate the benefit of bi-layered simulation relations for linear stochastic systems in an example.
rate research
Read More
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local linear-quadratic approximations of system dynamics and reward, such methods can find both a target-optimal trajectory and time-variant optimal feedback controllers. However, the local linear-quadratic assumptions are a major source of optimization bias that leads to catastrophic greedy updates, raising the issue of proper regularization. Moreover, the approximate models disregard for any physical state-action limits of the system causes further aggravation of the problem, as the optimization moves towards unreachable areas of the state-action space. In this paper, we address the issue of constrained systems in the scenario of online-fitted stochastic linear dynamics. We propose modeling state and action physical limits as probabilistic chance constraints linear in both state and action and introduce a new trajectory optimization technique that integrates these probabilistic constraints by optimizing a relaxed quadratic program. Our empirical evaluations show a significant improvement in learning robustness, which enables our approach to perform more effective updates and avoid premature convergence observed in state-of-the-art algorithms.
This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the leader. Meanwhile, the PET mechanism is considered not only in the communication between various agents, but also in the sensor-to-controller and controller-to-actuator transmission channels for each agent. The above problem set-up will bring some challenges to the controller design and stability analysis. Based on a novel PET distributed observer, a PET dynamic output feedback control method is developed for each follower. Compared with the existing works, our method can naturally exclude the Zeno behavior, and the inter-event time becomes multiples of the sampling period. Furthermore, for every follower, the minimum inter-event time can be determined textit{a prior}, and computed directly without the knowledge of the leader information. An example is given to verify and illustrate the effectiveness of the new design scheme.
Consensusability is an important property for many multi-agent systems (MASs) as it implies the existence of networked controllers driving the states of MAS subsystems to the same value. Consensusability is of interest even when the MAS subsystems are physically coupled, which is the case for real-world systems such as power networks. In this paper, we study necessary and sufficient conditions for the consensusability of linear interconnected MASs. These conditions are given in terms of the parameters of the subsystem matrices, as well as the eigenvalues of the physical and communication graph Laplacians. Our results show that weak coupling between subsystems and fast information diffusion rates in the physical and communication graphs favor consensusability. Technical results are verified through computer simulations.
In this paper, we propose a distributed output-feedback controller design for a linear time-invariant plant interacting with networked agents, where interaction and communication of each agent are limited to its associated input-output channel and its neighboring agents, respectively. The design scheme has a decentralized structure so that each agent can self-organize its own controller using the locally accessible information only. Furthermore, under mild conditions, the proposed controller is capable of maintaining stability even when agents join/leave the network during the operation without requiring any manipulation on other agents. This plug-and-play feature leads to efficiency for controller maintenance as well as resilience against changes in interconnections. The key idea enabling these features is the use of Bass algorithm, which allows the distributed computation of stabilizing gains by solving a Lyapunov equation in a distributed manner.
Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns. Finite-state abstractions, capturing the sampling behaviour of ETC systems, have proven promising in this respect. So far, such abstractions have been constructed for non-stochastic systems. Here, inspired by this framework, we abstract the sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC) systems via Interval Markov Chains (IMCs). Particularly, we define functions over sequences of state-measurements and interevent times that can be expressed as discounted cumulative sums of rewards, and compute bounds on their expected values by constructing appropriate IMCs and equipping them with suitable rewards. Finally, we argue that our results are extendable to more general forms of functions, thus providing a generic framework to define and study various ETC sampling indicators.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
