arXiv subjects

Shima Nazari

Publications and source records attributed to Shima Nazari.

17 recordsLinked to original sources

arXiv2026

Koopman Lifted Finite Memory Identification via Truncated Grunwald Letnikov Kernels

We propose a data-driven linear modeling framework for controlled nonlinear hereditary systems that combines Koopman lifting with a truncated Grunwald-Letnikov memory term. The key idea is to model nonlinear state dependence through a lifted observable representation while imposing history dependence directly in the lifted coordinates through fixed fractional-difference weights. This preserves linearity in the lifted state-transition and input matrices, yielding a memory-compensated regression that can be identified from input-state data by least squares and extending standard Koopman-based identification beyond the Markovian setting. We further derive an equivalent augmented Markovian realization by stacking a finite window of lifted states, thereby rewriting the finite-memory recursion as a standard discrete-time linear state-space model. Numerical experiments on a nonlinear hereditary benchmark with a non-Grunwald-Letnikov Prony-series ground-truth kernel demonstrate improved multi-step open-loop prediction accuracy relative to memoryless Koopman and non-lifted state-space baselines.

eess.SY↗

arXiv2026

Asymmetric Nash Seeking via Best Response Maps: Global Linear Convergence and Robustness to Inexact Reaction Models

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and constraints, an assumption that is often unrealistic in practice. This letter studies a class of asymmetric-information two-player constrained games with decoupled feasible sets, in which Player 1 knows its own objective and constraints while Player 2 is available only through a best-response map. For this class of games, we propose an asymmetric projected gradient descent-best response iteration that does not require full mutual knowledge of both players' optimization problems. Under suitable regularity conditions, we establish the existence and uniqueness of the Nash equilibrium and prove global linear convergence of the proposed iteration when the best-response map is exact. Recognizing that best-response maps are often learned or estimated, we further analyze the inexact case and show that, when the approximation error is uniformly bounded by $\varepsilon$, the iterates enter an explicit $O(\varepsilon)$ neighborhood of the true Nash equilibrium. Numerical results on a benchmark game corroborate the predicted convergence behavior and error scaling.

cs.GT↗

arXiv2026

A Data Driven Structural Decomposition of Dynamic Games via Best Response Maps

Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested optimization structures, and poor numerical conditioning. Existing game-theoretic solvers address these challenges by directly solving the joint game, typically requiring explicit modeling of all agents' objective functions and constraints, while learning-based approaches often decouple interaction through prediction or policy approximation, sacrificing equilibrium consistency. This paper introduces a conceptually novel formulation for dynamic games by restructuring the equilibrium computation. Rather than solving a fully coupled game or decoupling agents through prediction or policy approximation, a data-driven structural reduction of the game is proposed that removes nested optimization layers and derivative coupling by embedding an offline-compiled best-response map as a feasibility constraint. Under standard regularity conditions, when the best-response operator is exact, any converged solution of the reduced problem corresponds to a local open-loop Nash (GNE) equilibrium of the original game; with a learned surrogate, the solution is approximately equilibrium-consistent up to the best-response approximation error. The proposed formulation is supported by mathematical proofs, accompanying a large-scale Monte Carlo study in a two-player open-loop dynamic game motivated by the autonomous racing problem. Comparisons are made against state-of-the-art joint game solvers, and results are reported on solution quality, computational cost, and constraint satisfaction.

cs.GT↗

arXiv2025

Fractional Calculus in Optimal Control and Game Theory: Theory, Numerics, and Applications -- A Survey

Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and controller/game design for systems with memory. We unify notation for Caputo, Riemann-Liouville, and Grunwald-Letnikov derivatives and relate them to practical approximations, including diffusive (sum-of-exponentials) state augmentation and frequency-domain realizations (e.g., Oustaloup). We review fractional extensions of the calculus of variations and the Pontryagin maximum principle, and dynamic-programming formulations with memory, including path-dependent HJB for optimal control and HJI for zero-sum games. We cover design tools such as LQR, MPC, and fractional-order PID, as well as fractional differential games with Nash, Stackelberg, and minimax equilibria. Computational approaches are compared across time-domain schemes, frequency-domain approximations, and diffusive augmentations, highlighting accuracy-complexity trade-offs and remedies for the curse of history (windowing and sum-of-exponentials). We conclude with applications and open problems on equilibria with memory, Isaacs-type conditions, constraint handling, and scalable solvers.

math.OC↗

arXiv2025

Fleet Size and Mix Capacitated Vehicle Routing Problem with Time Windows for Mobile Fast Chargers

The electrification of off-road heavy equipment presents operational challenges for agencies serving remote sites with limited fixed charging infrastructure. Existing mobile fast charging vehicle (MFCV) planning approaches typically treat fleet design and routing as separate problems, fixing vehicle characteristics before dispatch. This paper formulates a fleet size and mix capacitated vehicle routing problem with time windows (FSMCVRPTW) for MFCV deployment, jointly optimizing fleet composition, charger specifications, routing, and scheduling within a unified mixed-integer linear program. The model incorporates heterogeneous MFCV types with varying power ratings, battery capacities, fuel range, and cost structures, minimizing total daily cost from labor, fuel, amortized capital expenditure, and energy purchase under temporal service windows, resource budgets, and energy-delivery constraints. The formulation is implemented in Python/Gurobi and applied to two case studies using California Department of Transportation wheel-loader data in Los Angeles (dense urban) and Truckee (sparse mountainous). Results show that simultaneous optimization yields compact, well-utilized fleets that meet all service windows while revealing strong sensitivity of unit cost to demand density and geography. The proposed FSMCVRPTW framework provides a generalizable decision-support methodology that co-designs fleet size, charger power, routing, and service schedules in a single optimization layer for context-aware, cost-efficient mobile fast charging.

eess.SY↗

arXiv2025

Predictive Compensation in Finite-Horizon LQ Games under Gauss-Markov Deviations

This paper develops a predictive compensation framework for finite-horizon, discrete-time linear quadratic dynamic games subject to Gauss-Markov execution deviations from feedback Nash strategies. One player's control is corrupted by temporally correlated stochastic perturbations modeled as a first-order autoregressive (AR(1)) process, while the opposing player has causal access to past deviations and employs a predictive feedforward strategy that anticipates their future effect. We derive closed-form recursions for mean and covariance propagation under the resulting perturbed closed loop, establish boundedness and sensitivity properties of the equilibrium trajectory, and characterize the reduction in expected cost achieved by optimal predictive compensation. Numerical experiments corroborate the theoretical results and demonstrate performance gains relative to nominal Nash feedback across a range of disturbance persistence levels.

eess.SY↗

arXiv2025

Efficient Optimal Path Planning in Dynamic Environments Using Koopman MPC

This paper presents a data-driven model predictive control framework for mobile robots navigating in dynamic environments, leveraging Koopman operator theory. Unlike the conventional Koopman-based approaches that focus on the linearization of system dynamics only, our work focuses on finding a global linear representation for the optimal path planning problem that includes both the nonlinear robot dynamics and collision-avoidance constraints. We deploy extended dynamic mode decomposition to identify linear and bilinear Koopman realizations from input-state data. Our open-loop analysis demonstrates that only the bilinear Koopman model can accurately capture nonlinear state-input couplings and quadratic terms essential for collision avoidance, whereas linear realizations fail to do so. We formulate a quadratic program for the robot path planning in the presence of moving obstacles in the lifted space and determine the optimal robot action in an MPC framework. Our approach is capable of finding the safe optimal action 320 times faster than a nonlinear MPC counterpart that solves the path planning problem in the original state space. Our work highlights the potential of bilinear Koopman realizations for linearization of highly nonlinear optimal control problems subject to nonlinear state and input constraints to achieve computational efficiency similar to linear problems.

cs.RO↗

arXiv2025

RSV-SLAM: Toward Real-Time Semantic Visual SLAM in Indoor Dynamic Environments

Simultaneous Localization and Mapping (SLAM) plays an important role in many robotics fields, including social robots. Many of the available visual SLAM methods are based on the assumption of a static world and struggle in dynamic environments. In the current study, we introduce a real-time semantic RGBD SLAM approach designed specifically for dynamic environments. Our proposed system can effectively detect moving objects and maintain a static map to ensure robust camera tracking. The key innovation of our approach is the incorporation of deep learning-based semantic information into SLAM systems to mitigate the impact of dynamic objects. Additionally, we enhance the semantic segmentation process by integrating an Extended Kalman filter to identify dynamic objects that may be temporarily idle. We have also implemented a generative network to fill in the missing regions of input images belonging to dynamic objects. This highly modular framework has been implemented on the ROS platform and can achieve around 22 fps on a GTX1080. Benchmarking the developed pipeline on dynamic sequences from the TUM dataset suggests that the proposed approach delivers competitive localization error in comparison with the state-of-the-art methods, all while operating in near real-time. The source code is publicly available.

cs.RO↗

arXiv2025

Optimal Path Planning for Wheel Loader Automation Enabled by Efficient Soil-Tool Interaction Modeling

Earthmoving operations with wheel loaders require substantial power and incur high operational costs. This work presents an efficient automation framework based on the Fundamental Earthmoving Equation (FEE) for soil-tool interaction modeling. A reduced-order multi-step parameter estimation method guided by Sobol's global sensitivity analysis is deployed for accurate, online excavation force prediction. An optimal control problem is then formulated to compute energy-efficient bucket trajectories using soil parameters identified in the previous digging cycle. High-fidelity simulations in Algoryx Dynamics confirm accurate force prediction and demonstrate 15-40% energy savings compared to standard paths. The total computation time is comparable to a single digging cycle, highlighting the framework's potential for real-time, energy-optimized wheel loader automation.

eess.SY↗

arXiv2025

Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame

Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control techniques, learning a finite-dimensional invariant subspace for high-fidelity modeling continues to be an open problem. This paper presents a deep Koopman approach for modeling and control of vehicle dynamics within the curvilinear Frenet frame. The proposed framework uses a deep neural network architecture to simultaneously learn the Koopman operator and its associated invariant subspace from the data. Input-state bilinear interactions are captured by the algorithm while preserving convexity, which makes it suitable for real-time model predictive control (MPC) application. A multi-step prediction loss is utilized during training to ensure long-horizon prediction capability. To further enhance real-time trajectory tracking performance, the model is integrated with a cumulative error regulator (CER) module, which compensates for model mismatch by mitigating accumulated prediction errors. Closed-loop performance is evaluated through hardware-in-the-loop (HIL) experiments using a CarSim RT model as the target plant, with real-time validation conducted on a dSPACE SCALEXIO system. The proposed controller achieved significant reductions in tracking error relative to baseline controllers, confirming its suitability for real-time implementation in embedded autonomous vehicle systems.

eess.SY↗

arXiv2025

Data-Efficient Excavation Force Estimation for Wheel Loaders

Accurate prediction of excavation forces is critical for enabling autonomous operation and optimizing control strategies in earthmoving machinery. Conventional approaches often depend on extensive data collection or computationally expensive simulations across multiple soil types, which limits their scalability and adaptability. This study presents a data-efficient framework that calibrates soil parameters using force measurements from the preceding bucket-loading cycle. The proposed method is based on an analytical soil-tool interaction model formulated through the fundamental earthmoving equation, and employs a multi-stage optimization procedure during the loading phase to identify relevant soil parameters. These estimated parameters are then used to predict excavation forces in the subsequent cycle, allowing the system to adapt its control inputs without relying on large-scale datasets or machine learning model training. The framework is validated through high-fidelity simulations in the Algoryx Dynamics engine under different soil types and excavation trajectories, achieving root-mean-square prediction errors between 10% and 15%. This cycle-to-cycle adaptation demonstrates strong potential for scalable, online force estimation and efficient path planning in wheel loader operations.

eess.SY↗

arXiv2025

Inverted Gaussian Process Optimization for Probabilistic Koopman Operator Discovery

Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and the dependency on a finite dictionary of heuristically chosen observable functions. We leverage Gaussian Process Regression (GPR) to learn a probabilistic Koopman linear model from data, while removing the need for heuristic observable specification. We present inverted Gaussian Process optimization based Koopman operator learning (iGPK), an automatic differentiation-based approach to simultaneously learn the observable-operator combination. Our numerical results show that the iGPK method is able to learn complex nonlinearities from simulation data while being resilient to measurement noise in the training data and consistently encapsulating the ground truth in the predictive distribution.

eess.SY↗

arXiv2025

Optimal Modified Feedback Strategies in LQ Games under Control Imperfections

Game-theoretic approaches and Nash equilibrium have been widely applied across various engineering domains. However, practical challenges such as disturbances, delays, and actuator limitations can hinder the precise execution of Nash equilibrium strategies. This work investigates the impact of such implementation imperfections on game trajectories and players' costs in the context of a two-player finite-horizon linear quadratic (LQ) nonzero-sum game. Specifically, we analyze how small deviations by one player, measured or estimated at each stage affect the state trajectory and the other player's cost. To mitigate these effects, we construct a compensation law for the influenced player by augmenting the nominal game with the measurable deviation dynamics. The resulting policy is shown to be optimal within a causal affine policy class, and, for sufficiently small deviations, it locally outperforms the uncompensated equilibrium-derived feedback. Rigorous analysis and proofs are provided, and the effectiveness of the proposed approach is demonstrated through a representative numerical example.

cs.GT↗

arXiv2025

Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame

The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.

eess.SY↗

arXiv2023

Powertrain Hybridization for Autonomous Vehicles

The powertrains of today's hybrid electric vehicles (HEVs) are developed for human drivers and, therefore, may not be the optimum choice for future Autonomous vehicles (AVs), given that AVs can accurately manipulate their velocity profile to avoid unnecessary energy loss. In this work, we closely examine the necessary degree of hybridization for AVs compared to human drivers by deploying real-world urban driving profiles and generating equivalent AV drive cycles in a mixed autonomy scenario. We solve the optimal energy management problem for HEVs with various motor sizes from the automotive market, and demonstrate that while human drivers typically require a motor size of around 30 kW to fully benefit from hybridization, AVs can achieve similar gains with only a 12 kW motor. This greater benefit from a smaller motor size can be attributed to a more optimal torque request, allowing for higher gains from regenerative braking and a more efficient engine operation. Furthermore, We investigate the benefits of velocity smoothing for both traditional cars and HEVs and explore the role of different mechanisms contributing to fuel consumption reduction. Our analysis reveals that velocity smoothing provides greater benefits to HEVs equipped with small motors compared to non-hybrid vehicles and HEVs with larger motors.

eess.SY↗

arXiv2023

An Automatic Tuning MPC with Application to Ecological Cruise Control

Model predictive control (MPC) is a powerful tool for planning and controlling dynamical systems due to its capacity for handling constraints and taking advantage of preview information. Nevertheless, MPC performance is highly dependent on the choice of cost function tuning parameters. In this work, we demonstrate an approach for online automatic tuning of an MPC controller with an example application to an ecological cruise control system that saves fuel by using a preview of road grade. We solve the global fuel consumption minimization problem offline using dynamic programming and find the corresponding MPC cost function by solving the inverse optimization problem. A neural network fitted to these offline results is used to generate the desired MPC cost function weight during online operation. The effectiveness of the proposed approach is verified in simulation for different road geometries.

math.OC↗

arXiv2018

Safe Adaptive Cruise Control with Road Grade Preview and V2V Communication

We present the design of a safe Adaptive Cruise Control (ACC) which uses road grade and lead vehicle motion preview. The ACC controller is designed by using a Model Predictive Control (MPC) framework to optimize comfort, safety, energy-efficiency and speed tracking accuracy. Safety is achieved by computing a robust invariant terminal set. The paper presents a novel approach to compute such set which is less conservative than existing methods. The proposed controller ensures safe inter-vehicle spacing at all times despite changes in the road grade and uncertainty in the predicted motion of the lead vehicle. Simulation results compare the proposed controller with a controller that does not incorporate prior grade knowledge on two scenarios including car-following and autonomous intersection crossing. The results demonstrate the effectiveness of the proposed control algorithm.

eess.SY↗