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An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
To achieve efficient and reliable control of microscopic systems one should look for driving protocols that mitigate both the average dissipation and stochastic fluctuations in work. This is especially important in fast driving regimes in…
We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…
Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use…
Autonomous systems are composed of several subsystems such as mechanical, propulsion, perception, planning and control. These are traditionally designed separately which makes performance optimization of the integrated system a significant…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
Sampling-based motion planning algorithms have been continuously developed for more than two decades. Apart from mobile robots, they are also widely used in manipulator motion planning. Hence, these methods play a key role in collaborative…
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…
Biological molecular machines convert free energy between different forms in cells, often at high efficiency. Optimal control theory provides a framework to elucidate design principles governing energetically efficient driving. Here, we use…
Using classical description of spin degrees of freedom, we extend recent formulation of the perfect-fluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic…
It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary.…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
Actuator location and design are important choices in controller design for distributed parameter systems. Semi-linear partial differential equations model a wide spectrum of physical systems with distributed parameters. It is shown that…
We present parametric trajectory optimization, a method for simultaneously computing physical parameters, actuation requirements, and robot motions for more efficient robot designs. In this scheme, robot dimensions, masses, and other…
This work presents a control-oriented structural design approach for a 2-DOF underactuated mechanical system, with the purpose of generating an optimal oscillatory behavior of the end-effector. To achieve the desired periodic motion, we…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…