We focus on the development of a Lyapunov-based economic model predictive control (LEMPC) method for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule. In contrast to steady-state operation of conventional model predictive control (MPC) methods which use a quadratic objective function in their formulations, LEMPC utilize...

Quadratic elements place stringent requirements on a surface mesh smoother. One of the biggest challenges is that a good linear element may become invalid when mid-side nodes are introduced. To help alleviate this problem, a new objective function for optimization-based smoothing is proposed for triangular and quadrilateral elements, linear or quadratic. Unlike the current popular approaches, t...

The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[(xt − x)] ≥ O(t) on the rate of convergence of a sequence (x0, x1, . . .) generated by an unbiased feedback process observing noisy evaluations of an unknown quadratic functio...

Two new Bayesian approaches to Robust Parameter Design (RPD) are presented that recompute the optimal control factor settings based on on-line measurements of the noise factors. A dual response model approach to RPD is taken. The first method uses the posterior predictive density of the responses to determine the optimal control factor settings. A second method uses in addition the predictive d...

The results from classical asymptotic theory typically require assumptions of pointwise differentiability of a criterion function with respect an unknown parameter. Taylor expansion about some " true " value in the parameter space then gives a quadratic approximation to the criterion function, within error terms that can be bounded using the remainder from the Taylor expansion. With appropriate...

Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity i...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...

We propose a class of quadratic optimization problems whose exact optimal objective values can be computed by their completely positive cone programming relaxations. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities, except one inhomogeneous equality whe...