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Control science is a core representative of the third industrial revolution and is so important to modern civilization. Control systems are the main subject of control science and may involve many aspects of consideration, such as hardware…
The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…
We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua's circuit.
In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the…
Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic…
We prove a squeezing/stability theorem for delta-epsilon controlled L-groups when the control map is a fibration on a finite polyhedron. A relation with boundedly-controlled L-groups is also discussed.
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
In this paper, we study a class of stochastic time-inconsistent linear-quadratic (LQ) control problems with control input constraints. These problems are investigated within the more general framework associated with random coefficients.…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…
Doctoral Thesis, year 2002, about Lie systems and applications in Physics and Control Theory. The text is in English. Advisor: Jos\'e F. Cari\~nena
Recent progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time. The advent of such new technical capabilities provides strong motivation for the…
We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…
Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…