Modern data-driven techniques have rapidly progressed beyond modelling and systems identification, with a growing interest in learning high-level dynamical properties of system, such as safe-set invariance, reachability, input-to-state stability etc. In this paper, we propose novel supervised Deep Learning technique for constructing Lyapunov certificates, by leveraging Koopman Operator theory-b...

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...

In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

It is shown that any convex function can be approximated by a family of differentiable with Lipschitz continuous gradient and strongly convex approximates in a “self-dual” way: the conjugate of each approximate is the approximate of the conjugate of the original function. The approximation technique extends to saddle functions, and is self-dual with respect to saddle function conjugacy and also...