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Register a new userOrbital stabilization of underactuated mechanical systems without Euler-Lagrange structure after of a collocated pre-feedback
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Added by
Bowen Yi
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model losses Euler-Lagrange structures after the collocated pre-feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and the model class identified in the paper is characterized via some easily apriori verifiable assumptions on the inertia matrix and potential energy.
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At the quantum level, feedback-loops have to take into account measurement back-action. We present here the structure of the Markovian models including such back-action and sketch two stabilization methods: measurement-based feedback where an open quantum system is stabilized by a classical controller; coherent or autonomous feedback where a quantum system is stabilized by a quantum controller with decoherence (reservoir engineering). We begin to explain these models and methods for the photon box experiments realized in the group of Serge Haroche (Nobel Prize 2012). We present then these models and methods for general open quantum systems.
We consider optimization problems for (networked) systems, where we minimize a cost that includes a known time-varying function associated with the systems outputs and an unknown function of the inputs. We focus on a data-based online projected gradient algorithm where: i) the input-output map of the system is replaced by measurements of the output whenever available (thus leading to a closed-loop setup); and ii) the unknown function is learned based on functional evaluations that may occur infrequently. Accordingly, the feedback-based online algorithm operates in a regime with inexact gradient knowledge and with random updates. We show that the online algorithm generates points that are within a bounded error from the optimal solution of the problem; in particular, we provide error bounds in expectation and in high-probability, where the latter is given when the gradient error follows a sub-Weibull distribution and when missing measurements are modeled as Bernoulli random variables. We also provide results in terms of input-to-state stability in expectation and in probability. Numerical results are presented in the context of a demand response task in power systems.
In this paper, we study the boundary feedback stabilization of a quasilinear hyperbolic system with partially dissipative structure. Thanks to this structure, we construct a suitable Lyapunov function which leads to the exponential stability to the equilibrium of the $H^2$ solution. As an application, we also obtain the feedback stabilization for the Saint-Venant-Exner model under physical boundary conditions.
Systems whose movement is highly dissipative provide an opportunity to both identify models easily and quickly optimize motions. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the dissipative nature minimizes the role of second order (inertial) features in the dynamics. Here we extend the tools of geometric system identification to ``Shape-Underactuated Dissipative Systems (SUDS) -- systems whose motions are more dissipative than inertial, but whose actuation is restricted to a subset of the body shape coordinates. Many animal motions are SUDS, including micro-swimmers such as nematodes and flagellated bacteria, and granular locomotors such as snakes and lizards. Many soft robots are also SUDS, particularly those robots using highly damped series elastic actuators. Whether involved in locomotion or manipulation, these robots are often used to interface less rigidly with the environment. We motivate the use of SUDS models, and validate their ability to predict motion of a variety of simulated viscous swimming platforms. For a large class of SUDS, we show how the shape velocity actuation inputs can be directly converted into torque inputs suggesting that systems with soft pneumatic actuators or dielectric elastomers can be modeled with the tools presented. Based on fundamental assumptions in the physics, we show how our model complexity scales linearly with the number of passive shape coordinates. This offers a large reduction on the number of trials needed to identify the system model from experimental data, and may reduce overfitting. The sample efficiency of our method suggests its use in modeling, control, and optimization in robotics, and as a tool for the study of organismal motion in friction dominated regimes.
In this paper, we present an impedance control design for multi-variable linear and nonlinear robotic systems. The control design considers force and state feedback to improve the performance of the closed loop. Simultaneous feedback of forces and states allows the controller for an extra degree of freedom to approximate the desired impedance port behaviour. A numerical analysis is used to demonstrate the desired impedance closed-loop behaviour.
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