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. It has numerous applications in science, engineering and operations research.
What is optimal control method?
Optimal control is the process of determining control and state trajectories for a dynamic system over a period of time to minimise a performance index.
How do you solve optimal control problems?
There are two straightforward ways to solve the optimal control problem: (1) the method of Lagrange multipliers and (2) dynamic programming. We have already outlined the idea behind the Lagrange multipliers approach. The second way, dynamic programming, solves the constrained problem directly.
How do you find optimal control?
To find the optimal control, we form the Hamiltonian H =1+ λT (Ax + Bu)=1+(λT A)x + (λT B)u. Now apply the conditions in the maximum principle: ˙x = ∂H ∂λ = Ax + Bu −˙λ = ∂H ∂x = AT λ u = arg min H = −sgn(λT B)
What is optimal control 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 are the benefits of optimal control?
Optimal control focuses on a subset of problems, but solves these problems very well, and has a rich history. RL can be thought of as a way of generalizing or extending ideas from optimal control to non-traditional control problems. For example, optimal control assumes a well understood or modeled transition dynamics.
What is optimal control in robotics?
So what Pontryagin proved is that for a time-optimal control problem, the optimal controls are the set of controls that at every time t is at the extreme limits of their admissible boundaries.
Why optimal control is needed?
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. … An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost function.
