Related papers: Approximation Methods for Geometric Regulation
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
The controller design of the so-called "difference algebraic equation" (DAE) systems that are frequently shown in industrial processes, tend to be challenging because of the combination of algebraic equations and high state dimensions. In…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…
This paper presents a novel methodology to develop scheduling algorithms. The scheduling problem is phrased as a control problem, and control-theoretical techniques are used to design a scheduling algorithm that meets specific requirements.…
The article outlines the methodology of structural and parametric synthesis of neural network controllers for controlling objects with limiters under incomplete information about the controlled object. Artificial neural networks are used to…
The search of controlled approximations to study strongly coupled systems remains a very general open problem. Wilson's renormalization group has shown to be an ideal framework to implement approximations going beyond perturbation theory.…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
Existing methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities…
Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Regularization plays a crucial role in supervised learning. Most existing methods enforce a global regularization in a structure agnostic manner. In this paper, we initiate a new direction and propose to enforce the structural simplicity of…
Since gene regulatory systems contain sometimes only a small number of molecules, these systems are not described well by macroscopic rate equations; a master equation approach is needed for such cases. We develop an approximation scheme…
We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…
The ability to achieve precise and smooth trajectory tracking is crucial for ensuring the successful execution of various tasks involving robotic manipulators. State-of-the-art techniques require accurate mathematical models of the robot…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…