arXiv subjects

Rushikesh Kamalapurkar

Publications and source records attributed to Rushikesh Kamalapurkar.

At least 55 records · Page 3Linked to original sources

arXiv2023

Output Feedback Adaptive Optimal Control of Affine Nonlinear systems with a Linear Measurement Model

Real-world control applications in complex and uncertain environments require adaptability to handle model uncertainties and robustness against disturbances. This paper presents an online, output-feedback, critic-only, model-based reinforcement learning architecture that simultaneously learns and implements an optimal controller while maintaining stability during the learning phase. Using multiplier matrices, a convenient way to search for observer gains is designed along with a controller that learns from simulated experience to ensure stability and convergence of trajectories of the closed-loop system to a neighborhood of the origin. Local uniform ultimate boundedness of the trajectories is established using a Lyapunov-based analysis and demonstrated through simulation results, under mild excitation conditions.

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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

Safe Model-Based Reinforcement Learning for Systems with Parametric Uncertainties

Reinforcement learning has been established over the past decade as an effective tool to find optimal control policies for dynamical systems, with recent focus on approaches that guarantee safety during the learning and/or execution phases. In general, safety guarantees are critical in reinforcement learning when the system is safety-critical and/or task restarts are not practically feasible. In optimal control theory, safety requirements are often expressed in terms of state and/or control constraints. In recent years, reinforcement learning approaches that rely on persistent excitation have been combined with a barrier transformation to learn the optimal control policies under state constraints. To soften the excitation requirements, model-based reinforcement learning methods that rely on exact model knowledge have also been integrated with the barrier transformation framework. The objective of this paper is to develop safe reinforcement learning method for deterministic nonlinear systems, with parametric uncertainties in the model, to learn approximate constrained optimal policies without relying on stringent excitation conditions. To that end, a model-based reinforcement learning technique that utilizes a novel filtered concurrent learning method, along with a barrier transformation, is developed in this paper to realize simultaneous learning of unknown model parameters and approximate optimal state-constrained control policies for safety-critical systems.

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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

The Occupation Kernel Method for Nonlinear System Identification

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS) dubbed an occupation kernel. The manuscript thoroughly explores the concept of occupation kernels in the contexts of RKHSs of continuous functions, and establishes Liouville operators over RKHS where several dense domains are found for specific examples of this unbounded operator. The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. This framework allows for trajectories of a nonlinear dynamical system to be treated as a fundamental unit of data for nonlinear system identification routine. The approach to nonlinear system identification is demonstrated to identify parameters of a dynamical system accurately, while also exhibiting a certain robustness to noise.

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arXiv2021

Singular Dynamic Mode Decompositions

This manuscript is aimed at addressing several long standing limitations of dynamic mode decompositions in the application of Koopman analysis. Principle among these limitations are the convergence of associated Dynamic Mode Decomposition algorithms and the existence of Koopman modes. To address these limitations, two major modifications are made, where Koopman operators are removed from the analysis in light of Liouville operators (known as Koopman generators in special cases), and these operators are shown to be compact for certain pairs of Hilbert spaces selected separately as the domain and range of the operator. While eigenfunctions are discarded in the general analysis, a viable reconstruction algorithm is still demonstrated, and the sacrifice of eigenfunctions realizes the theoretical goals of DMD analysis that have yet to be achieved in other contexts. However, in the case where the domain is embedded in the range, an eigenfunction approach is still achievable, where a more typical DMD routine is established, but that leverages a finite rank representation that converges in norm. The manuscript concludes with the description of two Dynamic Mode Decomposition algorithms that converges when a dense collection of occupation kernels, arising from the data, are leveraged in the analysis.

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arXiv2021

An occupation kernel approach to optimal control

In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of optimal control problems in dynamical systems. Trajectory information in the dynamical systems is embedded in a reproducing kernel Hilbert space (RKHS) through what are called occupation kernels. The occupation kernels are tied to the dynamics of the system through the densely defined Liouville operator. The pairing of Liouville operators and occupation kernels allows for lifting of nonlinear finite-dimensional optimal control problems into the space of infinite-dimensional linear programs over RKHSs.

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arXiv2021

Theoretical Foundations for the Dynamic Mode Decomposition of High Order Dynamical Systems

Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to formulate first order dynamical systems in higher dimensions. However, solution of the augmented problem typically requires knowledge of the full augmented state, which requires numerical differentiation of the original output, frequently resulting in noisy signals. This manuscript develops the theory necessary for a direct analysis of higher order dynamical systems using higher order Liouville operators. Fundamental to this theoretical development is the introduction of signal valued RKHSs and new operators posed over these spaces. Ultimately, it is observed that despite the added abstractions, the necessary computations are remarkably similar to that of first order DMD methods using occupation kernels.

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arXiv2021

Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator

Dynamic Mode Decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are examined through a discrete time proxy determined by a fixed timestep using Koopman (i.e. composition) operators. Using the newly introduced "occupation kernels," the present manuscript develops an approach to DMD that treats continuous time dynamics directly through the Liouville operator, which can include Koopman generators. This manuscript outlines the technical and theoretical differences between Koopman based DMD for discrete time systems and Liouville based DMD for continuous time systems, which includes an examination of these operators over several reproducing kernel Hilbert spaces (RKHSs). While Liouville operators are modally unbounded, this manuscript introduces the concept of a scaled Liouville operator, which for many dynamical systems yields a compact operator over the exponential dot product kernel's native space. Hence, norm convergence of the DMD procedure is established when using scaled Liouville operators, which is a decided advantage over Koopman based DMD methods.

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arXiv2021

Motion Tomography via Occupation Kernels

The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from trajectory data with the use of occupation kernels developed by Rosenfeld et al.. Specifically, we use the occupation kernels as an adaptive basis; that is, the trajectories defining our occupation kernels are iteratively updated to improve the estimation on the next stage. Initial estimates are established, then under mild assumptions, such as relatively straight trajectories, convergence is proven using the Contraction Mapping Theorem. We then compare to the established method by Chang et al. by defining a set of error metrics. We found that for simulated data, which provides a ground truth, our method offers a marked improvement and that for a real-world example we have similar results to the established method.

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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 limited data

This paper addresses the problem of online inverse reinforcement learning for systems with limited data and uncertain dynamics. In the developed approach, the state and control trajectories are recorded online by observing an agent perform a task, and reward function estimation is performed in real-time using a novel inverse reinforcement learning approach. Parameter estimation is performed concurrently to help compensate for uncertainties in the agent's dynamics. Data insufficiency is resolved by developing a data-driven update law to estimate the optimal feedback controller. The estimated controller can then be queried to artificially create additional data to drive reward function estimation.

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arXiv2020

Extension of Full and Reduced Order Observers for Image-based Depth Estimation using Concurrent Learning

In this paper concurrent learning (CL)-based full and reduced order observers for a perspective dynamical system (PDS) are developed. The PDS is a widely used model for estimating the depth of a feature point from a sequence of camera images. Building on the current progress of CL for parameter estimation in adaptive control, a state observer is developed for the PDS model where the inverse depth appears as a time-varying parameter in the dynamics. The data recorded over a sliding time window in the near past is used in the CL term to design the full and the reduced order state observers. A Lyapunov-based stability analysis is carried out to prove the uniformly ultimately bounded (UUB) stability of the developed observers. Simulation results are presented to validate the accuracy and convergence of the developed observers in terms of convergence time, root mean square error (RMSE) and mean absolute percentage error (MAPE) metrics. Real world depth estimation experiments are performed to demonstrate the performance of the observers using aforementioned metrics on a 7-DoF manipulator with an eye-in-hand configuration.

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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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arXiv2019

On reduction of differential inclusions and Lyapunov stability

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory.

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arXiv2019

Output-feedback online optimal control for a class of nonlinear systems

In this paper an output-feedback model-based reinforcement learning (MBRL) method for a class of second-order nonlinear systems is developed. The control technique uses exact model knowledge and integrates a dynamic state estimator within the model-based reinforcement learning framework to achieve output-feedback MBRL. Simulation results demonstrate the efficacy of the developed method.

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arXiv2018

Online inverse reinforcement learning for nonlinear systems

This paper focuses on the development of an online inverse reinforcement learning (IRL) technique for a class of nonlinear systems. The developed approach utilizes observed state and input trajectories, and determines the unknown cost function and the unknown value function online. A parameter estimation technique is utilized to allow the developed IRL technique to determine the cost function weights in the presence of unknown dynamics. Simulation results are presented for a nonlinear system showing convergence of both unknown reward function weights and unknown dynamics.

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