Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach

This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential equations that are discretized using the forward difference method. The main advantages of using the discrete-inverse optimal control to regulate state variables in dynamic systems are (i) the control input is an optimal signal as it guarantees the minimum of the Hamiltonian function, (ii) the control signal makes the dynamical system passive, and (iii) the control input ensures asymptotic stability in the sense of Lyapunov. Numerical simulations in the MATLAB environment allow demonstrating the effectiveness and robustness of the studied control design for state variables regulation with a wide gamma of dynamic behaviors as a function of the assigned control gains

Finite-time thermodynamics of port-Hamiltonian systems

In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell's demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.Comment: To appear in Physica D (accepted July 2013

Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation

In this paper, two methods for approximating the stabilizing solution of the Hamilton–Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable system is also integrable and regards the corresponding Hamiltonian system of the Hamilton–Jacobi equation as an integrable Hamiltonian system with a perturbation caused by control. The second method directly approximates the stable flow of the Hamiltonian systems using a modification of stable manifold theory. Both methods provide analytical approximations of the stable Lagrangian submanifold from which the stabilizing solution is derived. Two examples illustrate the effectiveness of the methods.

Port-based modeling and optimal control for a new very versatile energy efficient actuator

In this paper, we analyze in depth the innovative very versatile and energy efficient (V2E2) actuator proposed in Stramigioli et al. (2008). The V2E2 actuator is intended to be used in all kind of robotics and powered prosthetic applications in which energy consumption is a critical issue. In particular, this work focuses on the development of a port-based Hamiltonian model of the V2E2 and presents an optimal control architecture which exploits the intrinsic hybrid characteristics of the actuator design. The optimal control guarantees the minimization of dissipative power losses during torque tracking transients

Control and Synchronization of Neuron Ensembles

Synchronization of oscillations is a phenomenon prevalent in natural, social, and engineering systems. Controlling synchronization of oscillating systems is motivated by a wide range of applications from neurological treatment of Parkinson's disease to the design of neurocomputers. In this article, we study the control of an ensemble of uncoupled neuron oscillators described by phase models. We examine controllability of such a neuron ensemble for various phase models and, furthermore, study the related optimal control problems. In particular, by employing Pontryagin's maximum principle, we analytically derive optimal controls for spiking single- and two-neuron systems, and analyze the applicability of the latter to an ensemble system. Finally, we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations. The methodology developed here is universal to the control of general nonlinear phase oscillators.Comment: 29 pages, 6 figure

An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory

In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique. Using the fact that the Hamiltonian lifted system of an integrable system is also integrable, the Hamiltonian system (canonical equation) that is derived from the theory of 1-st order partial differential equations is considered as an integrable Hamiltonian system with a perturbation caused by control. Assuming that the approximating Riccati equation from the Hamilton-Jacobi equation at the origin has a stabilizing solution, we construct approximating behaviors of the Hamiltonian flows on a stable Lagrangian submanifold, from which an approximation to the stabilizing solution is obtained

Secure Trajectory Planning Against Undetectable Spoofing Attacks

This paper studies, for the first time, the trajectory planning problem in adversarial environments, where the objective is to design the trajectory of a robot to reach a desired final state despite the unknown and arbitrary action of an attacker. In particular, we consider a robot moving in a two-dimensional space and equipped with two sensors, namely, a Global Navigation Satellite System (GNSS) sensor and a Radio Signal Strength Indicator (RSSI) sensor. The attacker can arbitrarily spoof the readings of the GNSS sensor and the robot control input so as to maximally deviate his trajectory from the nominal precomputed path. We derive explicit and constructive conditions for the existence of undetectable attacks, through which the attacker deviates the robot trajectory in a stealthy way. Conversely, we characterize the existence of secure trajectories, which guarantee that the robot either moves along the nominal trajectory or that the attack remains detectable. We show that secure trajectories can only exist between a subset of states, and provide a numerical mechanism to compute them. We illustrate our findings through several numerical studies, and discuss that our methods are applicable to different models of robot dynamics, including unicycles. More generally, our results show how control design affects security in systems with nonlinear dynamics.Comment: Accepted for publication in Automatic