arXiv subjects

Saber Omidi

Publications and source records attributed to Saber Omidi.

4 recordsLinked to original sources

arXiv2026

Optimal Derivative Feedback Control for an Active Magnetic Levitation System: An Experimental Study on Data-Driven Approaches

This paper presents the design and implementation of data-driven optimal derivative feedback controllers for an active magnetic levitation system. A direct, model-free control design method based on the reinforcement learning framework is compared with an indirect optimal control design derived from a numerically identified mathematical model of the system. For the direct model-free approach, a policy iteration procedure is proposed, which adds an iteration layer called the epoch loop to gather multiple sets of process data, providing a more diverse dataset and helping reduce learning biases. This direct control design method is evaluated against a comparable optimal control solution designed from a plant model obtained through the combined Dynamic Mode Decomposition with Control (DMDc) and Prediction Error Minimization (PEM) system identification. Results show that while both controllers can stabilize and improve the performance of the magnetic levitation system when compared to controllers designed from a nominal model, the direct model-free approach consistently outperforms the indirect solution when multiple epochs are allowed. The iterative refinement of the optimal control law over the epoch loop provides the direct approach a clear advantage over the indirect method, which relies on a single set of system data to determine the identified model and control.

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arXiv2025

Probabilistic Safety Guarantee for Stochastic Control Systems Using Average Reward MDPs

Safety in stochastic control systems, which are subject to random noise with a known probability distribution, aims to compute policies that satisfy predefined operational constraints with high confidence throughout the uncertain evolution of the state variables. The unpredictable evolution of state variables poses a significant challenge for meeting predefined constraints using various control methods. To address this, we present a new algorithm that computes safe policies to determine the safety level across a finite state set. This algorithm reduces the safety objective to the standard average reward Markov Decision Process (MDP) objective. This reduction enables us to use standard techniques, such as linear programs, to compute and analyze safe policies. We validate the proposed method numerically on the Double Integrator and the Inverted Pendulum systems. Results indicate that the average-reward MDPs solution is more comprehensive, converges faster, and offers higher quality compared to the minimum discounted-reward solution.

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arXiv2025

SDC-Based Model Predictive Control: Enhancing Computational Feasibility for Safety-Critical Quadrotor Control

Nonlinear Model Predictive Control (NMPC) is widely used for controlling high-speed robotic systems such as quadrotors. However, its significant computational demands often hinder real-time feasibility and reliability, particularly in environments requiring robust obstacle avoidance. This paper proposes a novel SDC-Based Model Predictive Control (MPC) framework, which preserves the high-precision performance of NMPC while substantially reducing computational complexity by over 30%. By reformulating the nonlinear quadrotor dynamics through the State-Dependent Coefficient (SDC) method, the original nonlinear program problem is transformed into a sequential quadratic optimization problem. The controller integrates an integral action to eliminate steady-state tracking errors and imposes constraints for safety-critical obstacle avoidance. Additionally, a disturbance estimator is incorporated to enhance robustness against external perturbations. Simulation results demonstrate that the SDC-Based MPC achieves comparable tracking accuracy to NMPC, with greater efficiency in terms of computation times, thereby improving its suitability for real-time applications. Theoretical analysis further establishes the stability and recursive feasibility of the proposed approach.

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arXiv2025

On Suboptimal Safety-Critical Tracking Controller Design

This paper proposes a novel framework for safety-critical optimal trajectory tracking in nonlinear systems based on the state-dependent Riccati equation (SDRE) methodology. By embedding barrier states into the system dynamics, the proposed strategy simultaneously ensures safety and tracking requirements, even in scenarios where these objectives may be inherently conflicting. A discounted pseudo-quadratic cost function is formulated to achieve a suboptimal trade-off between tracking accuracy, control effort, and safety objective. We present two distinct controller designs: one utilizing a single barrier state to enforce overall safety constraints, and another employing multiple barrier states to individually tuning the system's conservatism with respect to each safety constraint, providing enhanced flexibility in tuning the system's conservatism toward individual constraints. We establish sufficient conditions to ensure the solvability of the associated Riccati equations. The proposed safe controller is well-suited for real-time implementation in practical systems, given its reasonable computational requirements and compatibility with widely available embedded microprocessors. This is supported by simulation studies involving a mechanical system and a mobile robot collision avoidance scenario, where the safe SDRE controller consistently maintained safety while achieving trajectory tracking objectives in challenging conditions. Additionally, experimental results on a cable-driven parallel robot further demonstrate the practical applicability and effectiveness of the proposed method in real-world control tasks.

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