Linear-quadratic optimal control of descriptor systems

Linear-Quadratic Optimal Controller 10.3 Optimal Linear Control Systems

In Chapters 8 and 9 of this book we have designed dynamic controllers such that the closed-loop systems display the desired transient response and steady state characteristics. The design techniques presented in those chapters have sometimes been limited to trial and error methods while searching for controllers that meet the best given specifications. Furthermore, we have seen that in some cas...

Optimal Control for Descriptor Systems: Tracking Problem (RESEARCH NOTE)

Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...

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...

Infinite horizon optimal control and stabilizability for linear descriptor systems

In this paper we construct an infinite horizon LQ optimal controller for a linear stationary differential-algebraic equation (DAE) and prove that stabilizability from the given initial state is necessary and sufficient for the controller existence. We also solve the problem of finite horizon LQ optimal control. Our approach is based on ideas from linear geometric control theory that allows one ...