An adaptive algorithm based on wavelets is proposed for the efficient numerical solution of a control problem governed by a linear parabolic evolution equation. First, the constraints are represented by means of a full weak space-time formulation as a linear system in `2 in wavelet coordinates, following a recent approach by Schwab and Stevenson. Second, a quadratic cost functional involving a ...

We develop a new approach towards error control and adaptivity for nite element discretizations in optimization problems governed by partial diierential equations. Using the Lagrangian formalism the goal is to compute stationary points of the rst-order necessary opti-mality conditions. The mesh adaptation is driven by residual-based a posteriori error estimates derived by duality arguments. Thi...

Optimal feedback control has been proposed as an attractive movement generation strategy in goal reaching tasks for anthropomorphic manipulator systems. The optimal feedback control law for systems with non-linear dynamics and non-quadratic costs can be found by iterative methods, such as the iterative Linear Quadratic Gaussian (iLQG) algorithm. So far this framework relied on an analytic form ...

The article is concerned with the derivation of a posteriori error estimates for optimization problems subject to an obstacle problem. To circumvent the nondifferentiability inherent to this type of problem, we introduce a sequence of penalized but differentiable problem. We show differentiability of the central path and derive separate a posteriori dual weighted residual estimates for the erro...

An optimal indirect stochastic adaptive control is obtained explicitly for linear time-varying discrete-time systems with general delay and white noise perturbation, while minimizing the variance of the output around a desired value one step ahead. The resulting controller incorporates parameter uncertainties. The solution unifies and generalizes previously known results, which become special c...

In this paper two different control methods are combined for controlling a typical nonholonomic device (a bicycle) the dynamic model and parameters of which are only approximately known. Most of such devices suffer from the problem that the time-derivatives of the coordinates of their location and orientation cannot independently be set so an arbitrarily prescribed trajectory cannot precisely b...

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adapt...

In the presence of large uncertainty, a controller needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. As the adaptive g...

friction is a nonlinear phenomenon which has destructive effects on performance of control systems. to obviate these effects, friction compensation is an effectual solution. in this paper, an adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. the proposed approach works for n...