Sequence Of Ellipsoids Research Articles

An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes

In this paper, a novel off-line model predictive control strategy for linear parameter varying systems is presented. The on-line computational burdens are reduced by pre-computing off-line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured. The real-time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two examples of continuous stirred tank reactors.

An ellipsoidal off-line robust model predictive control strategy for uncertain polytopic discrete-time systems

In this paper, an off-line robust model predictive control strategy for uncertain polytopic discrete-time systems is presented. The on-line computational burdens are reduced by precomputing off-line the sequence of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids. The real-time state feedback gain is then calculated by solving a numerically low-demanding optimization problem. The nominal model of the plant is included in the controller design in order to improve control performance. An overall algorithm is proved to guarantee robust stability.

Containing and shrinking ellipsoids in the path-following algorithm

We describe a new potential function and a sequence of ellipsoids in the path-following algorithm for convex quadratic programming. Each ellipsoid in the sequence contains all of the optimal primal and dual slack vectors. Furthermore, the volumes of the ellipsoids shrink at the ratio $$2^{ - \Omega (\sqrt n )} $$ , in comparison to 2−Ω(1) in Karmarkar's algorithm and 2−Ω(1/n) in the ellipsoid method. We also show how to use these ellipsoids to identify the optimal basis in the course of the algorithm for linear programming.

A SIMPLER PROOF OF C 1 CLOSING LEMMA

The infinite sequence of n-dimensional ellipsoids corresponding to invertible linear transformations is considered. Using this sequence of ellipsoids, we can realize the N-fold-nondisturbing movement of one point onto another. Thus we obtain a simpler and more geometrically visual proof of C 1 Closing Lemma.