Mahdis Rabbani

Mohammad Abtahi, Mahdis Rabbani, Shima Nazari

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.

Mahdis Rabbani, Navid Mojahed, Shima Nazari

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.

Navid Mojahed, Mahdis Rabbani, Shima Nazari

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.

Mahdis Rabbani, Navid Mojahed, Shima Nazari

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.

Mohammad Abtahi, Mahdis Rabbani, Armin Abdolmohammadi et al.

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.