One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below.

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 …

[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 …

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 …

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.

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 …

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 …

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 …

Sep 16, 2019 · Since the plant is linear and the PI is quadratic, the problem of determining the SVFB K to minimize J is called the Linear Quadratic Regulator (LQR). The word 'regulator' …