Direct method to solve linear-quadratic optimal control problems

Bézier control points method to solve constrained quadratic optimal control of time varying linear systems

A computational method based on Bézier control points is presented to solve optimal control problems governed by time varying linear dynamical systems subject to terminal state equality constraints and state inequality constraints. The method approximates each of the system state variables and each of the control variables by a Bézier curve of unknown control points. The new approximated proble...

Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

Optimal Linear Quadratic Control

Linear Quadratic Optimal Control

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...

Domain Decomposition Preconditioners for Linear–quadratic Elliptic Optimal Control Problems

We develop and analyze a class of overlapping domain decomposition (DD) preconditioners for linear-quadratic elliptic optimal control problems. Our preconditioners utilize the structure of the optimal control problems. Their execution requires the parallel solution of subdomain linear-quadratic elliptic optimal control problems, which are essentially smaller subdomain copies of the original pro...