arXiv subjects

Moad Abudia

Publications and source records attributed to Moad Abudia.

11 recordsLinked to original sources

arXiv2026

A Dynamic Mode Decomposition Approach to Parameter Identification

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action measurements and various known values at the parameters of interest. The predictive model is then used in conjunction with state-action data corresponding to unknown values of the parameters to estimate the said unknown value. Numerical experiments on the controlled Duffing oscillator with unknown damping, stiffness, and nonlinearity coefficients demonstrate accurate recovery of both the system trajectories and the unknown parameter values from data collected under open-loop excitation.

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arXiv2025

On Dynamic Mode Decomposition of Control-affine Systems

This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville operators and control occupation kernels are used to separate the drift dynamics from the input dynamics. A provably convergent finite-rank estimation of a compact control Liouville operator is obtained, provided sufficiently rich data are available. A matrix representation of the finite-rank operator is used to construct a data-driven representation of its singular values, left singular functions, and right singular functions. The singular value decomposition is used to generate a data-driven model of the control-affine nonlinear system. The developed method generates a model that can be used to predict the trajectories of the system in response to any admissible control input. Numerical experiments are included to demonstrate the efficacy of the developed technique.

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arXiv2024

On Convergent Dynamic Mode Decomposition and its Equivalence with Occupation Kernel Regression

This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator (also known as the Koopman generator) can be made to be compact. In this paper, it is shown that by selecting appropriate collections of finite basis functions in the domain and the range, a novel finite-rank representation of the Liouville operator may be obtained. It is also shown that the model resulting from dynamic mode decomposition of the finite-rank representation is closely related to regularized regression using the so-called occupation kernels as basis functions.

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arXiv2023

Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators

Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature.

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arXiv2023

The kernel perspective on dynamic mode decomposition

This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and compactness of Koopman operators. Counterexamples that illustrate restrictiveness of the assumptions are provided for each of the assumptions. In particular, this manuscript proves that the native reproducing kernel Hilbert space (RKHS) of the Gaussian RBF kernel function only supports bounded Koopman operators if the dynamics are affine. In addition, a new framework for DMD, that requires only densely defined Koopman operators over RKHSs is introduced, and its effectiveness is demonstrated through numerical examples.

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arXiv2022

Carleman Lifting for Nonlinear System Identification with Guaranteed Error Bounds

This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The objective is to ensure that the trajectories of the identified systems are close to the trajectories of the real system, as quantified by an error bound that is prescribed a priori. A majority of existing methods for nonlinear system identification rely on techniques such as neural networks, autoregressive moving averages, and spectral decomposition that do not provide systematic approaches to meet pre-defined error bounds. The developed method is based on Carleman linearization-based lifting of the nonlinear system to an infinite dimensional linear system. The linear system is then truncated to a suitable order, computed based on the prescribed error bound, and parameters of the truncated linear system are estimated from data. The effectiveness of the technique is demonstrated by identifying an approximation of the Van der Pol oscillator from data within a prescribed error bound.

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arXiv2022

Safe Controller for Output Feedback Linear Systems using Model-Based Reinforcement Learning

The objective of this research is to enable safety-critical systems to simultaneously learn and execute optimal control policies in a safe manner to achieve complex autonomy. Learning optimal policies via trial and error, i.e., traditional reinforcement learning, is difficult to implement in safety-critical systems, particularly when task restarts are unavailable. Safe model-based reinforcement learning techniques based on a barrier transformation have recently been developed to address this problem. However, these methods rely on full state feedback, limiting their usability in a real-world environment. In this work, an output-feedback safe model-based reinforcement learning technique based on a novel barrier-aware dynamic state estimator has been designed to address this issue. The developed approach facilitates simultaneous learning and execution of safe control policies for safety-critical linear systems. Simulation results indicate that barrier transformation is an effective approach to achieve online reinforcement learning in safety-critical systems using output feedback.

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arXiv2021

Safety aware model-based reinforcement learning for optimal control of a class of output-feedback nonlinear systems

The ability to learn and execute optimal control policies safely is critical to realization of complex autonomy, especially where task restarts are not available and/or the systems are safety-critical. Safety requirements are often expressed in terms of state and/or control constraints. Methods such as barrier transformation and control barrier functions have been successfully used, in conjunction with model-based reinforcement learning, for safe learning in systems under state constraints, to learn the optimal control policy. However, existing barrier-based safe learning methods rely on full state feedback. In this paper, an output-feedback safe model-based reinforcement learning technique is developed that utilizes a novel dynamic state estimator to implement simultaneous learning and control for a class of safety-critical systems with partially observable state.

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arXiv2021

Control Occupation Kernel Regression for Nonlinear Control-Affine Systems

This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in vector-valued reproducing kernel Hilbert space (vvRKHS). The trajectories are embedded as the so-called higher order control occupation kernels which represent an operator on the vvRKHS corresponding to iterated integration after multiplication by a given controller. The solution to the system identification problem is then the unique solution of an infinite dimensional regularized regression problem. The representer theorem is then used to express the solution as finite linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem. The vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the developed approach.

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arXiv2020

Switched Optimal Control and Dwell Time Constraints: A Preliminary Study

Most modern control systems are switched, meaning they have continuous as well as discrete decision variables. Switched systems often have constraints called dwell-time constraints (e.g., cycling constraints in a heat pump) on the switching rate. This paper introduces an embedding-based-method to solve optimal control problems that have both discrete and continuous decision variables. Unlike existing methods, the developed technique can heuristically incorporate dwell-time constraints via an auxiliary cost, while also preserving other state and control constrains of the problem. Simulations results for a switched optimal control problem with and without the auxiliary cost showcase the utility of the developed method.

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arXiv2020

Online inverse reinforcement learning with unknown disturbances

This paper addresses the problem of online inverse reinforcement learning for nonlinear systems with modeling uncertainties while in the presence of unknown disturbances. The developed approach observes state and input trajectories for an agent and identifies the unknown reward function online. Sub-optimality introduced in the observed trajectories by the unknown external disturbance is compensated for using a novel model-based inverse reinforcement learning approach. The observer estimates the external disturbances and uses the resulting estimates to learn the dynamic model of the demonstrator. The learned demonstrator model along with the observed suboptimal trajectories are used to implement inverse reinforcement learning. Theoretical guarantees are provided using Lyapunov theory and a simulation example is shown to demonstrate the effectiveness of the proposed technique.

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