Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems
102
0
0.0
(
0
)
Added by
Sahin Lale
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or convex quadratic regulating costs. Under strongly convex cost functions, we design an adaptive control algorithm based on online gradient descent to design and update the controllers that are constructed via a convex controller reparametrization. We show that our algorithm has $tilde{mathcal{O}}(sqrt{T})$ regret via explore and commit approach and if the model estimates are updated in epochs using closed-loop data collection, it attains the optimal regret of $text{polylog}(T)$ after $T$ time-steps of interaction. For the case of convex quadratic cost functions, we propose an adaptive control algorithm that deploys the optimism in the face of uncertainty principle to design the controller. In this setting, we show that the explore and commit approach has a regret upper bound of $tilde{mathcal{O}}(T^{2/3})$, and the adaptive control with continuous model estimate updates attains $tilde{mathcal{O}}(sqrt{T})$ regret after $T$ time-steps.
rate research
Read More
The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which systems outputs are contaminated by possibly large values of noise for the both case of measurement noise in switched autoregressive models and process noise in switched autoregressive exogenous models. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise, which are compatible with the collected data. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.
We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has been studied from different perspectives by different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, recent results in interval prediction, and tree-based planning. Combining and adapting the theoretical guarantees at each layer is non trivial, and we provide the first end-to-end suboptimality analysis for this setting. Interestingly, our analysis naturally adapts to handle many models and combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions. Last, we strive to preserve tractability at any stage of the method, that we illustrate on two challenging simulated environments.
We introduce reachability analysis for the formal examination of robots. We propose a novel identification method, which preserves reachset conformance of linear systems. We additionally propose a simultaneous identification and control synthesis scheme to obtain optimal controllers with formal guarantees. In a case study, we examine the effectiveness of using reachability analysis to synthesize a state-feedback controller, a velocity observer, and an output feedback controller.
In this paper, we develop a system identification algorithm to identify a model for unknown linear quantum systems driven by time-varying coherent states, based on empirical single-shot continuous homodyne measurement data of the systems output. The proposed algorithm identifies a model that satisfies the physical realizability conditions for linear quantum systems, challenging constraints not encountered in classical (non-quantum) linear system identification. Numerical examples on a multiple-input multiple-output optical cavity model are presented to illustrate an application of the identification algorithm.
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and optimal control. By viewing deep neural networks as discrete-time nonlinear dynamical systems, we can analyze how information propagates through layers using mean field theory. When optimization algorithms are further recast as controllers, the ultimate goal of training processes can be formulated as an optimal control problem. In addition, we can reveal convergence and generalization properties by studying the stochastic dynamics of optimization algorithms. This viewpoint features a wide range of theoretical study from information bottleneck to statistical physics. It also provides a principled way for hyper-parameter tuning when optimal control theory is introduced. Our framework fits nicely with supervised learning and can be extended to other learning problems, such as Bayesian learning, adversarial training, and specific forms of meta learning, without efforts. The review aims to shed lights on the importance of dynamics and optimal control when developing deep learning theory.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
