Model reduction methods for bilinear controlsystems are compared by means of practical examples of Liouville-von Neumann and Fokker-Planck type. Methods based on balancing generalized system Gramians and on minimizin...
详细信息
In this paper, we propose a stabilization scheme for nonlinear controlsystems whose vector fields satisfy Hormander's condition with the second-order Lie brackets. This scheme is based on the use of trigonometric...
详细信息
In this paper, we propose a stabilization scheme for nonlinear controlsystems whose vector fields satisfy Hormander's condition with the second-order Lie brackets. This scheme is based on the use of trigonometric controls with bounded frequencies. By using the Volterra series and a modification of Lyapunov's direct method, we reduce the stabilization problem to a system of cubic equations and prove its local solvability. Our approach ensures exponential stability of the equilibrium and gives explicit formulas for the coefficients of the control functions. The proposed methodology is illustrated by a rolling disc example.
On the basis of geometric invariants of the space of moduli of manifold for linear dynamical systems of minimum differential realization there are determined, to a certain extent studied and constructed the estimates ...
详细信息
Large sparse second order index-1 descriptor systems arise in various disciplines of science and engineering, such as constraint mechanics or multibody dynamics, mechatronics (where mechanical and electrical elements ...
详细信息
ISBN:
(纸本)9781509040919
Large sparse second order index-1 descriptor systems arise in various disciplines of science and engineering, such as constraint mechanics or multibody dynamics, mechatronics (where mechanical and electrical elements are coupled), but also RLC circuit design. Simulation, controller design and design optimization are only some applications of such models. Either of these tasks, just like any other many-query situation becomes unfeasible when the system is high dimensional. This paper discusses an algorithm to obtain a reduced state space model of a large sparse second order index-1 system using an interpolatory projection method based on the iterative rational Krylov algorithm (IRKA). In each iteration of this algorithm, we need to solve a number of linear systems. The main contribution of this paper is to solve these linear systems by exploiting the sparsity of the original model, which reduces the computational cost drastically. The algorithm is applied to a micro-mechanical piezo-actuated structural FEM model of a certain building block of a machine tool. Numerical experiments with a complex 3d model of an adaptive spindle support (a piezo-mechanical multiphysics system) show the effectivity and efficiency of the techniques.
Nonlinear Model Predictive control (NMPC) employs a plant model to compute a sequence of optimal control inputs for a finite horizon. As, in reality, there always exists a plant-model mismatch and not all states of th...
详细信息
We consider (max, +)-linear systems (i.e., discrete event systems ruled by conditions of the form: 'for all k ≥l, occurrence k of event β2 is at least τ units of time after occurrence k-l of event e1' with ...
详细信息
Free boundary and moving boundary problems, that can be used to model crystal growth or the solidification and melting of pure materials, receive growing attention in science and technology. The optimal control of the...
We investigate the numerical solution to a low rank perturbed Lyapunov equation A T X + XA = W via the sign function method (SFM). The sign function method has been proposed to solve Lyapunov equations, see e.g. [1], ...
Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will f...
We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. control constraint...
详细信息
暂无评论