In this paper an algorithm to optimize switching sequences for a class of switched linear problems is presented. The algorithm searches for solutions which are arbitrarily close to optimal – finding the optimal solution does often require a much larger search. Both deterministic and stochastic problems are considered.

In practice, all physical processes exhibit some non-linear behaviour. Furthermore, when a process shows strong non-linear behaviour, a linear model may be inadequate; a non-linear model will be more realistic. Unfortunately, this improved closeness to reality is attained at a cost: the convenience and simplicity offered by the linear model is sacrificed. Since many processes exhibit only mildl...

In this course, we will be dealing primarily with linear systems, a special class of systems for which a great deal is known. During the first half of the twentieth century, linear systems were analyzed using frequency domain (e.g., Laplace and z-transform) based approaches in an effort to deal with issues such as noise and bandwidth issues in communication systems. While they provided a great ...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...