arXiv subjects

Joseph Moyalan

Publications and source records attributed to Joseph Moyalan.

10 recordsLinked to original sources

arXiv2026

Model-Free Based Computations of Recursive Control Barrier Function: Ultra-Local Model Approach

Control barrier functions (CBFs) provide a systematic framework for enforcing safety constraints in nonlinear control systems. However, their implementation typically relies on accurate system models, which can limit their applicability in the presence of significant modeling uncertainties or unknown dynamics. This paper proposes a model-free framework for the computation of recursive control barrier functions based on the ultra-local model approach that leverages online estimation of the unknown system dynamics to construct CBF constraints. This approach does not require an explicit model of the system dynamics and enhances robustness with respect to disturbances and model mismatch. The resulting control architecture enables the enforcement as well as the anticipation of safety constraints for systems with higher relative degree. The effectiveness of the proposed approach is illustrated on the adaptive cruise control benchmark.

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arXiv2026

Equivalent Circuit Model based Electric Vehicle Evacuation with Mobile Charging Stations

The increasing penetration of electric vehicles (EVs) introduces new challenges for emergency evacuation planning due to limited driving range, long charging times, and constrained charging infrastructure, particularly under disaster induced disruptions. This paper proposes a novel optimization based evacuation framework for EVs using Equivalent Circuit Models (ECMs) to jointly address routing, charging, and congestion management. By leveraging electrical analogies, traffic flow is modeled as electrical current, travel time as resistance, and driving range as voltage, enabling the use of Kirchhoff laws to enforce flow balance and energy feasibility constraints. The proposed controllable ECM incorporates binary switches to regulate route selection and explicitly models charging delays and range replenishment at both Fixed Charging Stations (FCSs) and Mobile Charging Stations (MCSs). The resulting formulation leads to an integer programming problem that determines optimal evacuation routes, charging durations, and the placement and number of MCSs to minimize evacuation time. The framework is extended to multiple origin destination pairs using the principle of superposition and supports fairness aware performance metrics, including worst case, average, and variance based evacuation times. Simulation studies on large scale transportation networks in California demonstrate that the proposed approach significantly improves evacuation efficiency and robustness, particularly in scenarios with limited charging access, highlighting the critical role of MCSs in EV based emergency evacuations.

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arXiv2024

Safe Navigation in Dynamic Environments using Density Functions

This work presents a density-based framework for safe navigation in dynamic environments characterized by time-varying obstacle sets and time-varying target regions. We propose an analytical construction of time-varying density functions that enables the synthesis of a feedback controller defined as the positive gradient of the resulting density field. The primary contribution of this paper is a rigorous convergence proof demonstrating almost-everywhere safe navigation under the proposed framework, specifically for systems governed by single-integrator dynamics. To the best of our knowledge, these are the first analytical guarantees of their kind for navigation in dynamic environments using density functions. We illustrate the applicability of the framework to systems with more complex dynamics, including multi-agent systems and robotic manipulators, using standard control design techniques such as backstepping and inverse dynamics. These results provide a foundation for extending density-based navigation methods to a broad class of robotic systems operating in time-varying environments.

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arXiv2024

Control Density Function for Robust Safety and Convergence

We introduce a novel approach for safe control design based on the density function. A control density function (CDF) is introduced to synthesize a safe controller for a nonlinear dynamic system. The CDF can be viewed as a dual to the control barrier function (CBF), a popular approach used for safe control design. While the safety certificate using the barrier function is based on the notion of invariance, the dual certificate involving the density function has a physical interpretation of occupancy. This occupancy-based physical interpretation is instrumental in providing an analytical construction of density function used for safe control synthesis. The safe control design problem is formulated using the density function as a quadratic programming (QP) problem. In contrast to the QP proposed for control synthesis using CBF, the proposed CDF-based QP can combine both the safety and convergence conditions to target state into single constraints. Further, we consider robustness against uncertainty in system dynamics and the initial condition and provide theoretical results for robust navigation using the CDF. Finally, we present simulation results for safe navigation with single integrator and double-gyre fluid flow-field examples, followed by robust navigation using the bicycle model and autonomous lane-keeping examples.

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arXiv2024

Synthesizing Controller for Safe Navigation using Control Density Function

We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving navigation problems with safety constraints. The occupancy-based interpretation of the measure associated with the density function is instrumental in imposing the safety constraints. The navigation problem with safety constraints is formulated as a quadratic program (QP) using CDF. The existing approach using the control barrier function (CBF) also formulates the navigation problem with safety constraints as QP. One of the main advantages of the proposed QP using CDF compared to QP formulated using CBF is that both the convergence/stability and safety can be combined and imposed using the CDF. Simulation results involving the Duffing oscillator and safe navigation of Dubin car models are provided to verify the main findings of the paper.

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arXiv2023

Data-driven optimal control under safety constraints using sparse Koopman approximation

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which is computationally intractable for fine discretizations and high dimensions. The state transitional physical meaning of the Koopman operator leads to a sparse LS problem in this space. Leveraging this sparsity, we propose an efficient method to solve the sparse LS problem where we reduce the problem dimension dramatically by formulating the problem using only the non-zero elements in the approximation matrix with known sparsity pattern. The obtained matrix approximation of the operators is then used in a dual optimal reach-safe problem formulation where a linear program with sparse linear constraints naturally appears. We validate our proposed method on various dynamical systems and show that the computation time for operator approximation is greatly reduced with high precision in the solutions.

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arXiv2023

Off-Road Navigation of Legged Robots Using Linear Transfer Operators

This paper presents the implementation of off-road navigation on legged robots using convex optimization through linear transfer operators. Given a traversability measure that captures the off-road environment, we lift the navigation problem into the density space using the Perron-Frobenius (P-F) operator. This allows the problem formulation to be represented as a convex optimization. Due to the operator acting on an infinite-dimensional density space, we use data collected from the terrain to get a finite-dimension approximation of the convex optimization. Results of the optimal trajectory for off-road navigation are compared with a standard iterative planner, where we show how our convex optimization generates a more traversable path for the legged robot compared to the suboptimal iterative planner.

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arXiv2023

Data-Driven Convex Approach to Off-road Navigation via Linear Transfer Operators

We consider the problem of optimal navigation control design for navigation on off-road terrain. We use traversability measure to characterize the degree of difficulty of navigation on the off-road terrain. The traversability measure captures the property of terrain essential for navigation, such as elevation map, terrain roughness, slope, and terrain texture. The terrain with the presence or absence of obstacles becomes a particular case of the proposed traversability measure. We provide a convex formulation to the off-road navigation problem by lifting the problem to the density space using the linear Perron-Frobenius (P-F) operator. The convex formulation leads to an infinite-dimensional optimal navigation problem for control synthesis. The finite-dimensional approximation of the infinite-dimensional convex problem is constructed using data. We use a computational framework involving the Koopman operator and the duality between the Koopman and P-F operator for the data-driven approximation. This makes our proposed approach data-driven and can be applied in cases where an explicit system model is unavailable. Finally, we demonstrate the application of the developed framework for the navigation of vehicle dynamics with Dubin's car model.

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arXiv2022

Navigation with Probabilistic Safety Constraints: Convex Formulation

We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The deterministic unsafe set will arise as a particular case of the proposed probabilistic description of safety. We provide a convex formulation to the navigation problem with probabilistic safety constraints. The convex formulation is made possible by lifting the navigation problem in the dual space of density using linear transfer operator theory methods involving Perron-Frobenius and Koopman operators. The convex formulation leads to an infinite-dimensional feasibility problem for probabilistic safety verification and control design. The finite-dimensional approximation of the optimization problem relies on the data-driven approximation of the linear transfer operator.

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arXiv2022

Data-Driven Optimal Control via Linear Transfer Operators: A Convex Approach

This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount factor. The convex approach relies on lifting nonlinear system dynamics in the space of densities using the linear Perron-Frobenius (P-F) operator. This lifting leads to an infinite-dimensional convex optimization formulation of the optimal control problem. The data-driven approximation of the optimization problem relies on the approximation of the Koopman operator using the polynomial basis function. We write the approximate finite-dimensional optimization problem as a polynomial optimization which is then solved efficiently using a sum-of-squares-based optimization framework. Simulation results are presented to demonstrate the efficacy of the developed data-driven optimal control framework.

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