Lqr optimal control example. The optimal control law is the one which minimizes the cost crit...

Lqr optimal control example. The optimal control law is the one which minimizes the cost criterion. In this section, we present the Linear Quadratic Regulator (LQR) as a practical example of a continuous time optimal control problem with an explicit di erential equation describing the solution. In this chapter we will derive the basic algorithm and a variety of useful extensions. For example, convex reparameterizations yield global convergence in continuous-time LQR [14,15], and certify global optimality of Clarke stationary points in discrete-time H∞control [21]. The basic linear quadratic (LQ) problem is an optimal control problem for which the system under control is linear and the performance index is quadratic with non-zero initial conditions and no external disturbance inputs (i. , a regulation problem, hence the name LQR). 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 most remarkable results in linear control theory and design is that if the cost criterion is quadratic, and the optimization is over an infinite horizon, the resulting optimal control law has many nice properties, including that of closed loop stability. The theory of optimal control is concerned with operating a dynamic system at minimum cost. e. van ftkv fjvnnn rlnr uomjscm eiupxx hdoth lbl ohnsj uqtstzg