An overview of recent results concerning the non-standard, finite horizon Linear Quadratic Regulator problem for a class of boundary control systems is provided.

Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the simulation, parameter estimation, and control of mechanical sys...

In this paper we consider a discrete linear-quadratic regulator problem in the setting of discrete symplectic systems (S). We derive minimal conditions which guarantee the solvability of this problem. The matrices appearing in these conditions have close connection to the focal point definition of conjoined bases of (S). We show that the optimal solution of this problem has a feedback form and ...

In this paper we consider a class of matrix Riccati equations arising from stochastic LQR problems. We prove a monotonicity of solutions to the differential Riccati equations, which leads to a necessary and sufficient condition for the existence of solutions to the algebraic Riccati equations. In addition, we obtain results on comparison, uniqueness, stabilizability and approximation for soluti...

This paper presents the modelling and simulation for optimal control design of nonlinear inverted pendulum-cart dynamic system using Proportional-Integral-Derivative (PID) controller and Linear Quadratic Regulator (LQR). LQR, an optimal control technique, and PID control method, both of which are generally used for control of the linear dynamical systems have been used in this paper to control ...

This paper studies the lateral control problem for intelligent vehicles based on concept of shared control. Considering participation drivers in loop, a control-based controller is designed, which consists two differed controllers: one an LQR-based autonomous driving and other driver’s intention-based fuzzy controller. For vehicle dynamic model with two-degrees freedom, LQR are designed. Then, ...

This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant me...