The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based on the extended Kalman lter.

In this study, a convex proximal point algorithm (CPPA) is considered for solving constrained non-convex problems, and new theoretical results are proposed. It proved that every cluster of CPPA stationary point, the initial key to global optimization. Several sufficient conditions selection provided find minimum. Motivated by these results, numerical experiments were conducted on quadratic prog...

This paper proposes the design of a robust fault estimator for a class of nonlinear uncertain NCSs that ensures the fault estimation error is less than prescribed H performance level, irrespective of the uncertainties and networkinduced effects. T-S fuzzy models are firstly employed to describe the nonlinear plant. Markov processes are used to model these random network-induced effects. Suffici...

In this paper we present a framework to generate tight convex relaxations for nonconvex generalized disjunctive programs. The proposed methodology builds on our recent work on bilinear and concave generalized disjunctive programs for which tight linear relaxations can be generated, and extends its application to nonlinear relaxations. This is particularly important for those cases in which the ...

A class of trust region based algorithms is presented for the solution of nonlinear optimization problems with a convex feasible set. At variance with previously published analysis of this type, the theory presented allows for the use of general norms. Furthermore, the proposed algorithms do not require the explicit computation of the projected gradient, and can therefore be adapted to cases wh...

Motivated by recent increased interest in optimization algorithms for non-convex application to training deep neural networks and other problems data analysis, we give an overview of theoretical results on global performance guarantees optimization. We start with classical arguments showing that general could not be solved efficiently a reasonable time. Then list can find the minimizer exploiti...

We lower bound the complexity of finding $$\epsilon $$ -stationary points (with gradient norm at most ) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased oracle with bounded variance, we prove that (in worst case) any algorithm requires least ^{-4}$$ find point. The is tight, and establis...

This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-...