arXiv subjects

Siddhartha Ganguly

Publications and source records attributed to Siddhartha Ganguly.

22 records · Page 2Linked to original sources

arXiv2024

A novel trajectory optimization algorithm for continuous-time model predictive control

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying optimal control problem (OCP) are a linear time-invariant system, quadratic instantaneous and terminal cost functions, and convex path constraints. The thrust of the method involves finitely parameterizing the admissible space of control trajectories and solving the OCP satisfying the given constraints at every time instant in a tractable manner without explicit time-discretization. The ensuing OCP turns out to be a convex semi-infinite program (SIP), and some recently developed results are employed to obtain an optimal solution to this convex SIP. Numerical illustrations on some benchmark models are included to show the efficacy of the algorithm.

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arXiv2023

QuITO: Numerical software for constrained nonlinear optimal control problems -- extended version

We introduce the MATLAB-based software QuITO (Quasi-Interpolation based Trajectory Optimization) to numerically solve a wide class of constrained nonlinear optimal control problems (OCP). The solver is based on the QuITO (the same abbreviation) algorithm, which is a direct multiple shooting (DMS) technique that leverages a particular type of quasi-interpolation scheme for control trajectory parameterization. The software is equipped with several options for numerical integration, and optimization solvers along with a Graphical User Interface (GUI) to make the process of designing and solving the OCPs smooth and seamless for users with minimum coding experience. We demonstrate with two benchmark numerical examples the procedure to generate constrained state and control trajectories using QuITO.

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arXiv2023

A discrete-time Pontryagin maximum principle under rate constraints

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the global behavior of their paths. While the problem of actuator saturation has been studied extensively, little attention has been devoted to the problem of actuators having limited bandwidth. While attempts have been made in the direction of incorporating frequency constraints on state-action trajectories before, rate constraints on the control at the design stage have not been studied extensively in the discrete-time regime. This article contributes toward filling this lacuna. In particular, we establish a new discrete-time Pontryagin maximum principle with rate constraints being imposed on the control trajectories, and derive first-order necessary conditions for optimality. A brief discussion on the existence of optimal control is included, and numerical examples are provided to illustrate the results.

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arXiv2020

Robust Tracking and Model Following Controller Based on Higher Order Sliding Mode Control and Observation: With an Application to MagLev System

This paper deals with the design of robust tracking and model following (RTMF) controller for linear time-invariant (LTI) systems with uncertainties. The controller is based on the second order sliding mode (SOSM) algorithm (super twisting) which is the most effective and popular in the family of higher order sliding modes (HOSM). The use of super twisting algorithm (STA) eliminates the chattering problem encountered in traditional sliding mode control while retaining its robustness properties. The proposed robust tracking controller can guarantee the asymptotic stability of tracking error in the presence of time varying uncertain parameter and exogenous disturbances. Finally, this strategy is implemented on a magnetic levitation system (MagLev) which is inherently unstable and nonlinear. While implementing this proposed RTMF controller for MagLev system, a super twisting observer (STO) is used to estimate the unknown state i.e the velocity of the ball which is not directly available for measurement. It has been observed that the RTMF controller based on STA-STO pair, is not good enough to achieve SOSM for a chosen sliding surface using continuous control. As a remedy, continuous RTMF controller based on STA is implemented with a higher order sliding mode observer (HOSMO). The simulated as well as the experimental results are provided to illustrate the effectiveness of the proposed controller-observers pair.

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