|This project studies the discrete-time switched LQR problem based on a dynamic programming approach.
We provide an analytical characterization of both the value function and the optimal hybrid control strategy of the DSLQR problem. Their connections to the Riccati equation and the Kalman gain of the classical LQR problem are also investigated.
The study connects with the problem of stabilizability of switched linear systems, which is achieved by a stationary hybrid-control law that consists of a homogeneous switching-control law and a piecewise-linear continuous-control law under which the closed-loop system has a piecewise quadratic Lyapunov function.
Efficient algorithms are proposed to solve the finite-horizon and infinite-horizon DSLQR problems, or to provide sub-optimal solutions with proven error bounds.
We are currently looking at theoretical extensions of the project, as well as into practical applications (e.g., optimal sensor scheduling).
In collaboration with Dr. W. Zhang (UC Berkeley), Prof. J. Hu (Purdue), and Prof. C. Tomlin (UC Berkeley).