A modified double inverted pendulum – modified by connecting the mass carrying the pendulum with another mass through a spring makes the general inverted pendulum become a more interesting problem. The system is defined as a linear spring connected double inverted pendulum as proposed by Hou et al. [1],[2]. The system is highly nonlinear and unstable. However, the system can be simplified to a ...

In this paper we compare the behaviour of the LQR solution for a finite platoon model with its infinite version. We give examples where these are similar and some where they are quite different. For the scalar case we obtain sufficient conditions for the LQR solutions to be similar by relating the Toeplitz approximations to circulant approximating systems.

The design of MIMO PI controller is formulated as an LQR problem. The weighting matrices of the quadratic performance index are chosen so that tuning can be done for each inputoutput channel and for tradeoff between transient response and robustness with respect to modeling error. The number of tuning parameters is the same as that of a decentralized PI controller. A d&ign example is given to d...

In this paper we present stability and convergence results for Dynamic Programming-based reinforcement learning applied to Linear Quadratic Regulation (LQR). The specific algorithm we analyze is based on Q-learning and it is proven to converge to the optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. This is the first c...

gantry crane system becomes an interesting issue in the field of control technology development. In this paper, dynamic model of gantry crane is extracted using Lagrange method. This model has been linearized and weaknesses of state feedback control of this model is reviewed. To solve these problems, state feedback gain matrix is calculated using LQR method and results are fully investigated. F...

Designing the optimal linear quadratic regulator (LQR) for a large-scale multiagent system is time consuming since it involves solving large-size matrix Riccati equation. The situation further exasperated when design needs to be done in model-free way using schemes such as reinforcement learning (RL). To reduce this computational complexity, we decompose LQR problem into multiple small-size pro...

In this work, we propose a framework to address the autonomous impedance regulation problem of robots in class constrained manipulation tasks. framework, human arm endpoint stiffness model is used extract task geometry along trajectory, which then encoded offline and reproduced online by Gaussian Mixture Model (GMM) Regression (GMR), respectively. Furthermore, full Cartesian robot formulated th...

A two-wheeled self-balancing robot system bases on the physical problem of an inverted pendulum. Stabilization this type mobile requires applying active control approach. This paper proposes efficient Linear Quadratic Gaussian (LQG) optimal for system. The LQG (a combination a Kalman Filter (KF) and Regulator (LQR)) controller is designed to stabilize while reducing effect process measurement n...

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has delay. underlying problem actually falls into field asymmetric information control because nonidentical measurability induced by In contrast single-channel single-delay problems, challenge under study lies in interaction between are measurable ...

It is studied how system structure can be utilized to derive reduced dimension multi-parametric quadratic programs that lead to sub-optimal explicit piecewise linear feedback solutions to the state and input constrained LQR problem. This results in a controller of lower complexity and associated computational advantages in the online implementation. At heart of the methods are state space proje...