arXiv subjects

Mayuresh V. Kothare

Publications and source records attributed to Mayuresh V. Kothare.

3 recordsLinked to original sources

arXiv2026

Optimal Control and Closed-Loop Stability of Droplet Transport in a Microchannel

Understanding the efficient transport of fluid droplets in confined geometries has been a domain of interest for industrial applications in recent times. In the present work, we focus on designing control strategies that optimally steer droplet motion. Here, we apply optimal control framework to the droplet transport problem in a microchannel based on lubrication theory that minimizes viscous dissipation. Two complementary modeling routes are adopted: a reduced-order ordinary differential equation (ODE) model optimized via Pontryagin's Maximum Principle, and a full nonlinear partial differential equation (PDE) model optimized using a Covariance Matrix Adaptation-Evolutionary Strategy. By parameterizing target displacement, droplet size, and capillary number, we uncover two distinct optimal transport regimes: a "translate-relax" strategy for short distances and a "compact-translate-relax" strategy for longer targets. In continuum mechanics, the competition between surface forces and cumulative viscous dissipation decides the optimal transport strategies. We further show that the displacement range over which the reduced-order controller transfers to the continuum model is governed by capillary stiffness. We finally address closed-loop stability by adapting a control Lyapunov function (CLF) framework to the reduced-order dynamics. We demonstrate that the terminal cost which penalizes deviation from the target, serves as a cost-compatible CLF on the physical domain, and prove that the CLF-compatible feedback exponentially stabilizes the target state.

eess.SY↗

arXiv2026

Autonomous Droplet Navigation via Model-Based Reinforcement Learning

Precise manipulation of liquid droplets underpins lab-on-a-chip platforms for diagnostics, chemical synthesis, and biological assays. Yet autonomous droplet transport through confined geometries of varying complexity remains an open challenge. Droplets exhibit contact-angle hysteresis, deformability, and capillary pinning, which make their response to actuation nonlinear and history dependent, that classical controllers and pre-programmed trajectories cannot cope in multi-turn environments. Here we demonstrate autonomous navigation of a liquid droplet through geometries of increasing complexity on a gravity driven (Labyrinth) platform using model-based reinforcement learning. A thin silicone oil film reduces contact-line pinning while two-axis tilt supplies the gravitational driving force, and an overhead camera tracks the droplet in real time. An offline-trained policy discovers effective tilt strategies from limited physical interaction data, without simulation or analytical droplet models. The system operates under partial observability, as oil-film thickness, instantaneous contact angle, and droplet deformation state remain hidden from the controller. Despite these challenges, the learned policy achieves reliable navigation across straight, right-angle, and curved-arc paths, including outside-corner geometries. We further demonstrate that a policy trained on a simpler geometry transfers to complex ones, succeeding zero-shot on right-angle and staircase paths and reaching full success on a curved arc with a fifth of the training data. The findings suggest promising avenues for enabling droplet based microfluidic systems to serve as intelligent chemical laboratories.

cs.LG↗

arXiv2015

Optimal Sparse Output Feedback Control Design: a Rank Constrained Optimization Approach

We consider the problem of optimal sparse output feedback controller synthesis for continuous linear time invariant systems when the feedback gain is static and subject to specified structural constraints. Introducing an additional term penalizing the number of non-zero entries of the feedback gain into the optimization cost function, we show that this inherently non-convex problem can be equivalently cast as a rank constrained optimization, hence, it is an NP-hard problem. We further exploit our rank constrained approach to define a structured output feedback control feasibility test with global convergence property, then, obtain upper/lower bounds for the optimal cost of the sparse output feedback control problem. Moreover, we show that our problem reformulation allows us to incorporate additional implementation constraints, such as norm bounds on the control inputs or system output, by assimilating them into the rank constraint. We propose to utilize a version of the Alternating Direction Method of Multipliers (ADMM) as an efficient method to sub-optimally solve the equivalent rank constrained problem. As a special case, we study the problem of designing the sparsest stabilizing output feedback controller, and show that it is, in fact, a structured matrix recovery problem where the matrix of interest is simultaneously sparse and low rank. Furthermore, we show that this matrix recovery problem can be equivalently cast in the form of a canonical and well-studied rank minimization problem. We finally illustrate performance of our proposed methodology using numerical examples.

math.OC↗