The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is …

Most of these involve variants on the case of linear dynamics and convex (e.g. positive quadratic) cost. The simplest case, called the linear quadratic regulator (LQR), is formulated as stabilizing a time …

[K,S,P] = lqr(A,B,Q,R,N) calculates the optimal gain matrix K, the solution S of the associated algebraic Riccati equation and the closed-loop poles P using the continuous-time state-space matrices A and …

One of these [Kalman and Bertram 1960], presented the vital work of Lyapunov in the time-domain control of nonlinear systems. The next [Kalman 1960a] discussed the optimal control of systems, …

Linear Quadratic Regulator (LQR) While LQ assumptions might (at first) seem very restrictive, we will see the method can be made applicable for non-linear systems, e.g., helicopter.

LQR finds applications in aerospace, robotics, and process control. It determines the best control inputs to minimize a quadratic cost function, balancing system state regulation and control effort. LQR …

Jun 10, 2025 · The LQR problem is a fundamental concept in optimal control theory. It involves finding a control law that minimizes a quadratic cost function subject to a linear dynamic system.

Jul 2, 2025 · In robotics, LQR enables precise manipulation and path tracking for robotic arms and mobile robots. Industrial automation systems utilize LQR for process control, enhancing efficiency …

The Linear Quadratic Regulator (LQR) is an optimal control strategy used in control theory and engineering. It aims to operate a dynamic system in an optimal manner by minimizing a cost function …

Mar 1, 2024 · Despite Linear Quadratic Regulator’s (LQR) strong performance and solid resilience, developing these controllers have been challenging, largely because there is no reliable way to …