Dynamic systems such as robots, autonomous vehicles, and process plants require careful design and control to achieve optimal performance. This paper presents an integrated framework for the simultaneous optimization of system design parameters and control policies. The underlying mathematical formulation utilizes optimization techniques to find the best system configuration and control strategy according to specified objectives. These objectives may include metrics such as tracking error, energy consumption, safety margins, and cost. Both model-based and data-driven techniques are explored for learning the system dynamics and synthesizing optimal controllers. The optimization algorithms leveraged include gradient-based methods, evolutionary algorithms, and reinforcement learning. The benefits of the joint optimization approach are demonstrated through case studies on representative dynamic systems. Results show that the integrated design and control framework outperforms sequential optimization, leading to improved efficiency, responsiveness, and robustness. This underscores the importance of co-optimizing design and control parameters, especially for complex, uncertain systems. The proposed methods provide an effective tool for next-generation automated design of smart, adaptable systems.

The Marangoni convective phenomena have a unique impact on industries and medical tools. These phenomena are more prominent in the presence of dual nanoparticles (NPs) over base fluids such as blood that are surrounded by a thin interfacial nanolayer, an important feature to control the physical and thermal properties of the NP. In this problem, we have analysed the thermo-solutal Marangoni convective Darcy-Forchheimer flow of nanomaterials with the impact of the interfacial nanolayer. The results of the system of an exponential heat source, non-linear radiation, joule heating, and activation energy are discussed. An appropriate transition is applied to rationalise the substantially paired and nonlinear governing equations and then processed by the Galerkin finite element method (G-FEM). The impression of different governing parameters on the governing systems in conjunction with entropy and Bejan number is demonstrated through graphical and tabular form. Graphs are drawn with an evaluation of general and hybrid nanofluids (HNFs) and different nanolayer thicknesses of NPs. Activation energy and chemical reaction parameters restrict the Sherwood number, and the same is observed for the Nusselt number with an increase in the Brinkman and Eckert numbers. The thickness of the interfacial nanolayer of the NPs restricts the entropy generation of the system, while the entropy is higher for the HNF than the nanofluid. An opposite feature was observed for the Bejan number.

On stretched magnetic surfaces, we present a numerical study of Casson nanofluids moving through porous materials. The Casson liquid model explains how non-Newtonian liquids behave. Numerical techniques are utilized to solve the nonlinear partial differential equations produced by similarity transformations. Results are gathered for the Nusselt number, skin friction coefficient, temperature and velocity. The impacts of physical variables on the flow and heat transfer characteristics of nanofluids are depicted in graphs. They include the Prandtl number, magnetic parameter, radiation parameter, porosity parameter and Casson parameter. Findings indicate that as the Casson nanofluid parameters are increased, the temperature profile rises but the velocity field decreases. With increasing magnetic parameters alone, it is possible to see a decrease in the thickness of the pulse boundary layer and an increase in the thickness of the thermal boundary layer. All the results are depicted in graphical representations.

In this paper, we study the Ulam-Hyers-Mittag-Leffler stability for a linear fractional order differential equation with a fractional Caputo-type derivative using the fractional Fourier transform. Finally, we provide an enumeration of the chemical reactions of the differential equation.

A simplified mathematical model has been developed for understanding combined effects of surface roughness, viscosity variation and couple stresses on the squeeze film behaviour of a flat and a curved circular plate in the presence of transverse magnetic field. The Stokes (1966) couple stress fluid model is included to account for the couple stresses arising due to the presence of microstructure additives in the lubricant. In the context of Christensen’s (1969) stochastic theory for the lubrication of rough surfaces, two types of one-dimensional roughness patterns (radial and azimuthal) are considered. The governing modified stochastic Reynolds type equations are derived for these roughness patterns. Expressions for the mean squeeze film characteristics are obtained. Numerical computations of the results show that the azimuthal roughness pattern on the curved circular and flat plate results in more pressure buildup whereas performance of the squeeze film suffers due to the radial roughness pattern. Further the Lorentz force characterized by the Hartmann number, couple stress parameter and viscosity variation parameter improve the performance of the squeeze film lubrication as compared to the classical case (Non-magnetic, Newtonian case and non-viscous case).