What do you mean by optimal control theory?

Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. Optimal control can be seen as a control strategy in control theory.

What is optimal control theory in economics?

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This book is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigor.

What is LQ controller?

Introduction. The Linear Quadratic Regulator (LQR) is a well-known method that provides optimally controlled feedback gains to enable the closed-loop stable and high performance design of systems.

What is linear quadratic regulation in machine learning?

Linear Quadratic Regulator LQR and iLQR calculate an optimal trajectory from the initial to the target state by optimizing a cost function. LQR assumes the model is locally linear. iLQR uses an iterative version of LQR to find the optimal trajectory for non-linear systems.

How to calculate a linear quadratic optimal control?

LINEAR QUADRATIC OPTIMAL CONTROL We assume that the state x is available. We define the class of admissible control laws Φ to be of the form u = φ(x) (6.2) such that the following conditions are satisfied: (i) φ is a continuous function (ii) The closed loop system has a unique solution (iii) The closed loop system results in limt→∞x(t) = 0.

What is the theory of optimal control concerned with?

The theory of optimal controlis concerned with operating a dynamic systemat minimum cost. The case where the system dynamics are described by a set of linear differential equationsand the cost is described by a quadraticfunctionis called the LQ problem.

Which is a case of a linear quadratic regulator?

Linear–quadratic regulator. The theory of optimal control is concerned with operating a dynamic system at minimum cost. 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.

Is the LQ problem a quadratic or linear problem?

The case where the system dynamics are described by a set of linear differential equationsand the cost is described by a quadraticfunctionis called the LQ problem. 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.