Shubhendu Bhasin

Rushikesh Kamalapurkar, Huyen Dinh, Shubhendu Bhasin et al.

Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has remained a non-trivial open problem. The control development in this paper guarantees ultimately bounded tracking of a desired trajectory, while also ensuring that the controller converges to an approximate optimal policy.

Sayan Basu Roy, Shubhendu Bhasin, Indra Narayan Kar

Convergence of controller parameters in standard model reference adaptive control (MRAC) requires the system states to be persistently exciting (PE), a restrictive condition to be verified online. A recent data-driven approach, concurrent learning, uses information-rich past data concurrently with the standard parameter update laws to guarantee parameter convergence without the need of the PE condition. This method guarantees exponential convergence of both the tracking and the controller parameter estimation errors to zero, whereas, the classical MRAC merely ensures asymptotic convergence of tracking error to zero. However, the method requires knowledge of the state derivative, at least at the time instances when the state values are stored in memory. The method further assumes knowledge of the control allocation matrix. This paper addresses these limitations by using a memory-based finite-time system identifier in conjunction with a data-driven approach, leading to convergence of both the tracking and the controller parameter estimation errors without the PE condition and knowledge of the system matrices and the state derivative. A Lyapunov based stability proof is included to justify the validity of the proposed data-driven approach. Simulation results demonstrate the efficacy of the suggested method.

Anchita Dey, Shubhendu Bhasin

This paper proposes an adaptive tube framework for model predictive control (MPC) of discrete-time linear time-invariant systems subject to parametric uncertainty and additive disturbances. In contrast to conventional tube-based MPC schemes that employ fixed tube geometry and constraint tightening designed for worst-case uncertainty, the proposed approach incorporates online parameter learning to progressively refine the parametric uncertainty set and update the parameter estimates. These updates are used to adapt the components of the MPC optimization problem, including the prediction model, feedback gain, terminal set, and tube cross-sections. As the uncertainty set contracts, the required amount of constraint tightening reduces and the tube shrinks accordingly, yielding less conservative control actions. Recursive feasibility, robust constraint satisfaction, and closed-loop stability are formally established. Furthermore, the framework does not require the existence of a common quadratically stabilizing linear feedback gain for the entire parametric uncertainty set, thereby relaxing a standard assumption in existing tube-based MPC formulations. Numerical examples illustrate the effectiveness of the proposed approach.

Anchita Dey, Shubhendu Bhasin

An output feedback model predictive control (MPC) framework with adaptive tubes is proposed for linear time-invariant systems subject to parametric and additive uncertainties. An adaptive observer provides point estimates of the system state, model parameters, and initial condition, while jointly updating the corresponding sets containing the true parameters and initial state. These estimates parameterize the constrained optimal control problem, enabling constraint tightening, terminal ingredients, and tube geometry to be updated as the estimates evolve. In contrast to standard robust tube-based MPC formulations, the proposed approach does not require a common quadratically stabilizing linear feedback gain across the parametric uncertainty set. As the available uncertainty information improves, the tube geometry evolves accordingly, resulting in an adaptive tube MPC framework with improved performance over time. Recursive feasibility and robust exponential stability are established, and a numerical example is presented.

Jatin Kumar Arora, Soutrik Bandyopadhyay, Shubhendu Bhasin

Path planning for autonomous robots presents a fundamental trade-off between optimality and safety. While conventional algorithms typically prioritize one of these objectives, we introduce the Unified Path Planner (UPP), a unified framework that simultaneously addresses both. UPP is a graph-search-based algorithm that employs a modified heuristic function incorporating a dynamic safety cost, enabling an adaptive balance between path length and obstacle clearance. We establish theoretical sub-optimality bounds for the planner and demonstrate that its safety-to-optimality ratio can be tuned via adjustable parameters, with a trade-off in computational complexity. Extensive simulations show that UPP achieves a high success rate, generating near-optimal paths with only a negligible increase in cost over traditional A*, while ensuring safety margins that closely approach those of the classical Voronoi planner. Finally, the practical efficacy of UPP is validated through a hardware implementation on a TurtleBot, confirming its ability to navigate cluttered environments by generating safe, sub-optimal paths.