Poulomee Ghosh
Research Work
My research focuses on the development of adaptive control strategies for uncertain dynamical systems, to ensure satisfaction of user-defined constraints on states, control inputs, and input rates. The overall goal is to provide safe, robust, and feasible controllers that are practically implementable and do not rely on computationally intensive real-time optimization.
Modern engineering systems, from autonomous vehicles to industrial robots, must operate within stringent physical and safety constraints. While classical Model Reference Adaptive Control (MRAC) guarantees asymptotic tracking, it does not account for user-defined bounds on states or inputs. This becomes a critical limitation in real-world applications, where constraint violations can lead to instability, saturation, or system failure.Although various methods in the literature handle either state or input constraints independently, very few offer a unified solution that addresses both simultaneously. Existing solutions such as Model Predictive Control (MPC) or Control Barrier Functions (CBFs) typically rely on real-time optimization and full model knowledge, making them computationally intensive and less adaptive in the presence of uncertainties or disturbances. My research aims to fill this gap by developing adaptive, optimization-free control strategies that can enforce state, input, and even input-rate constraints, while still ensuring robust tracking under bounded disturbances and model uncertainty.
State and Input Constrained MRAC for Uncertain LTI Systems
We developed a model reference adaptive control (MRAC) strategy for uncertain linear time-invariant (LTI) systems that must operate within strict safety limits. The goal was to ensure that both the plant states and the magnitude of the control inputs remain within user-defined boundaries, even in the presence of external disturbances and parametric uncertainties.
Unlike traditional methods like MPC or CBFs that rely on online optimization, this approach is entirely optimization-free. Instead, it integrates a saturated adaptive controller with a Barrier Lyapunov Function (BLF) to enforce constraints throughout the system's evolution.
A major achievement of this work is the formulation of verifiable feasibility condition, a practical tests that determine whether a safe and feasible control policy exists for the given system. This makes the approach not only theoretically rigorous but also practically applicable.
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Fig.1. (a) Classical MRAC ; (b) Barrier Lyapunov Function (BLF)
Related Research:
P. Ghosh and S. Bhasin, 'State and Input Constrained Model Reference Adaptive Control', in IEEE Conference on Decision and Control (CDC), Mexico, 2022.
P. Ghosh and S. Bhasin, 'State and Input Constrained Model Reference Adaptive Control with Robustness and Feasibility Analysis', in IEEE Transactions on Automatic Control (TAC), 2026.
Extension to Uncertain Euler-Lagrange Systems
Building on the controller designed for LTI systems, the approach was extended to a broader class of systems described by Euler-Lagrange (E-L) dynamics, commonly encountered in robotic arms, mechanical systems and many other practical systems. These systems add complexity due to their nonlinear behavior, inertia-coupling, and dependence on both position and velocity states.
To address these challenges, we developed a constraint-compliant robust adaptive tracking controller that handles state and input bounds while maintaining tracking performance under external disturbances. The design avoids any real-time optimization routine by combining a Barrier Lyapunov Function (BLF) for managing state constraints with a saturated control law that keeps the control input within bounds.
A key contribution of this work is the incorporation of verifiable feasibility conditions which ensures the existence of a feasible control policy that will guarantee tracking to a desired reference trajectory while keeping the states and input within the pre-defined safe limits.
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Fig.2. (a) 2-link robot manipulator ; (b) Feasibility set; (c),(d) Simulation result of tracking performance and control input of (a).
Related Research:
P. Ghosh and S. Bhasin, 'Adaptive Tracking Control of Uncertain Euler-Lagrange Systems with State and Input Constraints', in American Control Conference (ACC) , San Diego, USA, 2023.
P. Ghosh and S. Bhasin, 'State and Input Constrained Adaptive Tracking Control of Uncertain Euler-Lagrange Systems with Robustness and Feasibility Analysis', arXiv:2505.22352.
Inclusion of Input Rate Constraints
In real-world applications, actuators not only have limits on their magnitude but also on the rate at which they can change. Very high rates of change in control input can lead to actuator fatigue, chattering, and excitation of unmodeled high-frequency dynamics, ultimately degrading the performance and safety of the closed-loop system. Imposing constraints on the input rate is therefore essential for practical feasibility.
To address this, we propose an adaptive control law that guarantees satisfaction of state, input magnitude, and input rate constraints for both LTI and E-L systems. These constraints are modeled as an augmented state, and a unified BLF framework is employed to enforce all three bounds systematically. The resulting controller remains optimization-free and ensures satisfactory tracking performance despite disturbances and parametric model uncertainties.
This final contribution establishes a unified framework that ensures all safety-critical constraints are systematically enforced in uncertain, nonlinear systems, paving the way for practical implementation of adaptive controllers in safety-critical environments.
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Fig. 3. (a) Combined BLF; (b) Control Input with very high magnitude and rate; (c) Desired input magnitude and rate.
Related Research:
P. Ghosh and S. Bhasin, 'State Constrained Model Reference Adaptive Control with Input Amplitude and Rate Limits', in International Journal of Systems Science (IJSS), 2025.
What if the consraints are time-varying?
In practice, the admissible bounds on system states and control inputs are rarely fixed. Actuator limitations, safety margins, and environmental factors may evolve over time, leading to time-varying constraint sets. For example, the maximum allowable torque in a robotic manipulator may decrease as the system heats up, or the permissible deviation of a vehicle from its lane center may shrink when approaching a curve. From a control design perspective, static constraints can be overly conservative, since they enforce the most restrictive condition at all times. In contrast, time-varying constraints provide a dynamic envelope, which can adapt according to the user's requirement. To this end, we employ time-varying BLF with saturated feedback controller to impose time-varying constraints to both state and input. A special case of this general framework can be compared to existing constrained control strategies – prescribed performance control (PPC) and funnel control (FC) that are known to ensure both transient and steady-state performance.
Related Research:
P. Ghosh and S. Bhasin, 'Model Reference Adaptive Control with Time-Varying State and Input Constraints', arXiv:2508.21586.