We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi(2)) nonlinear interfaces embedded in a linear layered structure--a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second...

We present a method of solving an linear quadratic regulator problem approximately in the case of discrete-time systems. This method leaves parameters as symbols in the evaluation function. We introduce the concept of the approximate linear quadratic regulator problem. We also propose a computation method to solve the problem. A numerical example of the approximate linear quadratic regulator pr...

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to nd the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a...

In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extende...

For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the "nite horizon problem (model predictive control) and the usual in"nite time measure (constrained line...

We present a quadratic Discrete-time Optimal Control problem generator, written in C, with options for Degeneracy, Activity and Conditioning (DOCDAC). We use the generator to investigate badly conditioned and degenerate extended linear-quadratic problems (ELQPs) by solving such problems with primal-dual projected gradient and interior-point methods. The benefit of using second-order information...

This paper studies the quadratic optimal control problem for the discrete-time switched linear stochastic system with nonautonomous subsystems perturbed by Gaussian random noises. The goal is to jointly design a deterministic switching sequence and a continuous feedback law to minimize the expectation of a finite-horizon quadratic cost function. Both the value function and the optimal control s...