Keywords: Optimal Control, Optimization Methods, Model-based Predictive Control
Abstract: Ensuring both safety and performance in autonomous driving remains a major challenge. Model Predictive Path Integral (MPPI) control is a sampling-based stochastic optimal control method well-suited for nonlinear vehicle dynamics, but it does not inherently guarantee safety. Control Barrier Functions (CBFs) provide formal safety guarantees by defining forward-invariant safe sets. In this paper, we propose a framework for lane keeping that integrates MPPI with CBF constraints applied to polynomial representations of lane boundaries. We derive higher-order barrier formulations suitable for the bicycle model and demonstrate, through simulations, that the proposed method improves safety while maintaining competitive performance compared to baseline Model Predictive Control (MPC) and unconstrained MPPI approaches.

Keywords: Robust Control and Stabilization, Optimal Control, Numerical Methods for Optimization
Abstract: This paper presents a robust H_{infty} control framework for nonlinear robotic systems using Takagi-Sugeno modeling with PCA-based model reduction. The approach transforms second-order matrix dynamics into polytopic Linear Parameter Varying representations, reducing computational complexity from exponential vertex growth through principal component analysis while preserving a prescribed percentage of system energy. Sufficient LMI conditions guarantee closed-loop stability and prescribed disturbance attenuation with explicit stability region characterization. The methodology is validated on an omnidirectional mobile platform supporting an inverted pendulum cane for elderly assistance, demonstrating superior disturbance rejection and smooth control transitions. Simulation results confirm theoretical guarantees with exponential convergence and constraint satisfaction.

Keywords: Optimal Control, Multi-Objective Control and Optimization
Abstract: This paper deals with the state feedback control of positive systems based on coupled differential-difference equations with bounded delays. The design conditions are defined using linear matrix inequalities with diagonal positive definite matrix variables to satisfy the diagonal stabilization rule and parametric system constraints. Finally, a numerical example is given to confirm the validity of the synthesis result.

Keywords: Optimization for Learning and Control, Real-Time Control Problems, Optimization under Uncertainties Including the Theory of Noise Measurements
Abstract: Humanoid-robots are increasingly relevant to industrial production, yet deployment is limited by the sim-to-real gap - the difficulty of transferring control and perception policies trained in simulation to real factories. We propose a Formal Conceptual Framework (FCF) to reduce this gap and accelerate technology transfer to aerospace manufacturing. The FCF integrates three pillars: domain randomization (DR) to build robustness, whole-body control (WBC) to ensure dynamic feasibility and balance, and hybrid reinforcement/imitation learning (RL/IL) to leverage demonstrations while optimizing performance. As a case study, we consider assembly and inspection of aircraft fuselage components, a task demanding precision, stability, and safe human robot collaboration. Our contribution is a unified sim-to-real validation loop that couples DR-trained policies with optimization-based WBC under privileged learning, together with a reproducible, laboratory-backed workflow for iterative data collection, system identification, and simulator updating. The AI and Humanoid-Robots Laboratory at Rzeszow University of Technology provides the testbed for this loop, enabling quantitative evaluation of robustness, success rate, and safety across repeated sim ↔ real cycles.

Keywords: Optimal Control, Robust Control and Stabilization, Optimization for Learning and Control
Abstract: This paper presents a distributed observer design incorporating sparse optimal control. A distributed observer is a networked estimation system in which an observer is assigned to each sensor node, and accurate state estimation can be achieved when all observers synchronize. However, when the network topology becomes disconnected, synchronization among observers fails, resulting in incorrect state estimation. To resolve this issue, we propose a distributed observer that retains accurate state estimation even when the communication topology becomes disconnected by employing pinning synchronization combined with sparse optimal control. The effectiveness of the proposed method is demonstrated through numerical simulations.

Keywords: Stochastic Optimization, Robust Control and Stabilization, Optimal Control
Abstract: We consider linear input-delayed stochastic uncertain state-multiplicative systems in the discrete-time setting. The system uncertainties include both norm-bounded and polytopic type ones. An H_infty single predictor control is applied to the norm-bounded uncertain system assuming the system states are accessible, thus rendering the system to a state delayed one and resulting in a single LMI condition. The latter application is extended to the case where an assembly of two sub-predictors are applied, resulting in an improved performance of the closed-loop control system. The solution obtained for the norm-bounded uncertain case is extended to the case where the system matrices reside in given polytope. An example is given that demonstrates the applicability of the theory.