Related papers: PID Optimization Using Lagrangian Mechanics
The paper explains iterative and non-iterative approaches to control optimization with use of the Fourier series-based method. Both variants of the presented algorithm are used to numerically approximate optimal control of a discontinuous…
Linear quadratic Gaussian (LQG) control is a well-established method for optimal control through state estimation, particularly in stabilizing an inverted pendulum on a cart. In standard laboratory setups, sensor redundancy enables direct…
This paper analyzes the motion of solutions to non-homogeneous linear differential equations. It further clarifies that a proportional-integral-derivative (PID) controller essentially comprises two parts: a homogeneous controller and a…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
A Proportional- Integral- Derivative (PID) controller is required to bring a system back to the stable operating region as soon as possible following a disturbance or discrepancy. For successful operation of the PID controller, it is…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…
We consider linear time-invariant dynamic systems in the single-input, single-output (SISO) framework. In particular, we consider stabilization of an inverted pendulum on a cart using a force on the cart. This system is easy to stabilize…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase…
Mobile robotic manipulators (MRMs), which integrate mobility and manipulation capabilities, present significant control challenges due to their nonlinear dynamics, underactuation, and coupling between the base and manipulator subsystems.…
In this paper, we propose to use a nonlinear adaptive PID controller to regulate the joint variables of a mobile manipulator. The motion of the mobile base forces undue disturbances on the joint controllers of the manipulator. In designing…
In this paper, we will consider a class of continuous-time stochastic control systems with both unknown nonlinear structure and unknown disturbances, and investigate the capability of the classical proportional-integral-derivative(PID)…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the…
Proportional-integral-derivative (PID) control is the most widely used in industrial control, robot control and other fields. However, traditional PID control is not competent when the system cannot be accurately modeled and the operating…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…