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Adaptive Systems


Technical Report: Adaptive Control for Linearizable Systems Using On-Policy Reinforcement Learning

arXiv.org Machine Learning

This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over standard model-reference adaptive control techniques is that it does not require the learned inverse model to be invertible at all instances of time. This enables the use of general function approximators to approximate the linearizing controller for the system without having to worry about singularities. However, the discrete-time and stochastic nature of these algorithms precludes the direct application of standard machinery from the adaptive control literature to provide deterministic stability proofs for the system. Nevertheless, we leverage these techniques alongside tools from the stochastic approximation literature to demonstrate that with high probability the tracking and parameter errors concentrate near zero when a certain persistence of excitation condition is satisfied. A simulated example of a double pendulum demonstrates the utility of the proposed theory. 1 I. INTRODUCTION Many real-world control systems display nonlinear behaviors which are difficult to model, necessitating the use of control architectures which can adapt to the unknown dynamics online while maintaining certificates of stability. There are many successful model-based strategies for adaptively constructing controllers for uncertain systems [1], [2], [3], but these methods often require the presence of a simple, reasonably accurate parametric model of the system dynamics. Recently, however, there has been a resurgence of interest in the use of model-free reinforcement learning techniques to construct feedback controllers without the need for a reliable dynamics model [4], [5], [6]. As these methods begin to be deployed in real world settings, a new theory is needed to understand the behavior of these algorithms as they are integrated into safety-critical control loops.


Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG) Systems

arXiv.org Machine Learning

One of the core challenges in the field of control theory and reinforcement learning is adaptive control. It is the problem of controlling dynamical systems when the dynamics of the systems are unknown to the decision-making agents. In adaptive control, agents interact with given systems in order to explore and control them while the long-term objective is to minimize the overall average associated costs. The agent has to balance between exploration and exploitation, learn the dynamics, strategize for further exploration, and exploit the estimation to minimize the overall costs. The sequential nature of agent-system interaction results in challenges in the system identifying, estimation, and control under uncertainty, and these challenges are magnified when the systems are partially observable, i.e. contain hidden underlying dynamics. In the linear systems, when the underlying dynamics are fully observable, the asymptotic optimality of estimation methods has been the topic of study in the last decades [Lai et al., 1982, Lai and Wei, 1987]. Recently, novel techniques and learning algorithms have been developed to study the finite-time behavior of adaptive control algorithms and shed light on the design of optimal methods [Peña et al., 2009, Fiechter, 1997, Abbasi-Yadkori and Szepesvári, 2011]. In particular, Abbasi-Yadkori and Szepesvári [2011] proposes to use the principle of optimism in the face of uncertainty (OFU) to balance exploration and exploitation in LQR, where the state of the system is observable.


Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

Neural Information Processing Systems

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that achieves sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints. Papers published at the Neural Information Processing Systems Conference.


Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

Neural Information Processing Systems

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.


Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

Neural Information Processing Systems

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.


Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator

arXiv.org Machine Learning

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs. Leveraging recent developments in the estimation of linear systems and in robust controller synthesis, we present the first provably polynomial time algorithm that provides high probability guarantees of sub-linear regret on this problem. We further study the interplay between regret minimization and parameter estimation by proving a lower bound on the expected regret in terms of the exploration schedule used by any algorithm. Finally, we conduct a numerical study comparing our robust adaptive algorithm to other methods from the adaptive LQR literature, and demonstrate the flexibility of our proposed method by extending it to a demand forecasting problem subject to state constraints.


Multifunction Cognitive Radar Task Scheduling Using Monte Carlo Tree Search and Policy Networks

arXiv.org Artificial Intelligence

A modern radar may be designed to perform multiple functions, such as surveillance, tracking, and fire control. Each function requires the radar to execute a number of transmit-receive tasks. A radar resource management (RRM) module makes decisions on parameter selection, prioritization, and scheduling of such tasks. RRM becomes especially challenging in overload situations, where some tasks may need to be delayed or even dropped. In general, task scheduling is an NP-hard problem. In this work, we develop the branch-and-bound (B&B) method which obtains the optimal solution but at exponential computational complexity. On the other hand, heuristic methods have low complexity but provide relatively poor performance. We resort to machine learning-based techniques to address this issue; specifically we propose an approximate algorithm based on the Monte Carlo tree search method. Along with using bound and dominance rules to eliminate nodes from the search tree, we use a policy network to help to reduce the width of the search. Such a network can be trained using solutions obtained by running the B&B method offline on problems with feasible complexity. We show that the proposed method provides near-optimal performance, but with computational complexity orders of magnitude smaller than the B&B algorithm.


When Edge Meets Learning: Adaptive Control for Resource-Constrained Distributed Machine Learning

arXiv.org Machine Learning

Emerging technologies and applications including Internet of Things (IoT), social networking, and crowd-sourcing generate large amounts of data at the network edge. Machine learning models are often built from the collected data, to enable the detection, classification, and prediction of future events. Due to bandwidth, storage, and privacy concerns, it is often impractical to send all the data to a centralized location. In this paper, we consider the problem of learning model parameters from data distributed across multiple edge nodes, without sending raw data to a centralized place. Our focus is on a generic class of machine learning models that are trained using gradient-descent based approaches. We analyze the convergence rate of distributed gradient descent from a theoretical point of view, based on which we propose a control algorithm that determines the best trade-off between local update and global parameter aggregation to minimize the loss function under a given resource budget. The performance of the proposed algorithm is evaluated via extensive experiments with real datasets, both on a networked prototype system and in a larger-scale simulated environment. The experimentation results show that our proposed approach performs near to the optimum with various machine learning models and different data distributions.


Stability Analysis of Optimal Adaptive Control using Value Iteration with Approximation Errors

arXiv.org Machine Learning

Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This analysis includes the system operated using any single/constant resulting control policy and also using an evolving/time-varying control policy. A feature of the presented results is providing estimations of the \textit{region of attraction} so that if the initial condition is within the region, the whole trajectory will remain inside it and hence, the function approximation results remain valid.


Lazily Adapted Constant Kinky Inference for Nonparametric Regression and Model-Reference Adaptive Control

arXiv.org Machine Learning

Techniques known as Nonlinear Set Membership prediction, Lipschitz Interpolation or Kinky Inference are approaches to machine learning that utilise presupposed Lipschitz properties to compute inferences over unobserved function values. Provided a bound on the true best Lipschitz constant of the target function is known a priori they offer convergence guarantees as well as bounds around the predictions. Considering a more general setting that builds on Hoelder continuity relative to pseudo-metrics, we propose an online method for estimating the Hoelder constant online from function value observations that possibly are corrupted by bounded observational errors. Utilising this to compute adaptive parameters within a kinky inference rule gives rise to a nonparametric machine learning method, for which we establish strong universal approximation guarantees. That is, we show that our prediction rule can learn any continuous function in the limit of increasingly dense data to within a worst-case error bound that depends on the level of observational uncertainty. We apply our method in the context of nonparametric model-reference adaptive control (MRAC). Across a range of simulated aircraft roll-dynamics and performance metrics our approach outperforms recently proposed alternatives that were based on Gaussian processes and RBF-neural networks. For discrete-time systems, we provide stability guarantees for our learning-based controllers both for the batch and the online learning setting.