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Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
In this paper we consider the minimum time population transfer problem for a two level quantum system driven by {\em two} external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave…
In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's…
A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is…
A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. Optimal control path minimizing the energy cost of the reversal is identified and used to derive time-dependent direction and…
We present the results of linear stability of a damped coplanar double pendulum and its non-linear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude $a$ and frequency $\omega $. A double…
In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
We consider the energy-optimal control problem for double-integrator systems subject to state and control constraints, with fixed terminal time and free terminal speed. When the constraints become active, the optimal trajectory consists of…
We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving…
We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic…
This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…
Both the shortest and the longest blowup time for a controlled system are considered. Existence result and maximum principle for optimal triple are established. Thanks to some monotonicity of the controlled system, some kinds of "the front…
We investigate the long-term dynamics of a five-dimensional nonlinear system describing the non-ideal excitation of a spherical pendulum coupled to a limited-power electric motor. By analyzing the phase trajectories y(t) = (y1, y2, y3, y4,…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of…
We revisit the inverted pendulum problem with the goal of understanding and computing the true optimal value function. We start with an observation that the true optimal value function must be nonsmooth ($i.e.$, not globally $C^1$) due to…
In this paper, a novel recurrent adaptive backstepping optimal control strategy for a single inverted pendulum system is studied. By this method, an inverted pendulum is stabilized using projection recurrent neural network-based adaptive…