Related papers: The averaged control system of fast oscillating co…
The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these…
This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
We show that the averaged equation for a one-frequency fast-oscillating Hamiltonian system is the result of symplectic reduction of a certain natural system on the corresponding $S^1$-bundle with respect to the circle action. Furthermore,…
The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such as system without invoking the standard rotating…
This work studies optimal control problems of systems with uncertain, probabilistically distributed parameters to optimize average performance. Known as Riemann-Stieltjes, average, or ensemble optimal control, this kind of problem is…
We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of…
We investigate cellular automata where some global quantity varies periodically or quasiperiodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We…
We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…
In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency $1/\delta$ ($0 < \delta \ll 1$), together with small white noise…
We consider a vibrational system control problem over a finite time horizon. The performance measure of the system is taken to be $p$-mixed $H_2$ norm which generalizes the standard $H_2$ norm. We present an algorithm for efficient…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
This paper studies optimal control under the average-reward/cost criterion for deterministic linear systems. We derive the value function and optimal policy, and propose an approximate solution using Model Predictive Control to enable…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
We present a novel extremum seeking method for affine connection mechanical control systems. The proposed control law involves periodic perturbation signals with sufficiently large amplitudes and frequencies. A suitable averaging analysis…
Two different controlling methods are proposed to stabilize unstable continuous-sliding states of a dry-friction oscillator. Both methods are based on a delayed-feedback mechanism well-known for stabilizing periodic orbits in deterministic…