Bounded Time Derivatives Research Articles

Robust Interaction using Generalized Super-Twisting Impedance Control

With the goal of performing robotic intervention tasks reliably with high accuracy under uncertainty and unknown disturbances, robust control methods such as sliding mode are appealing. However, contact forces cannot be considered as disturbances in this setting and compliance to the unknown contact geometry and forces is crucial. Impedance control and passivity-based techniques can guarantee closed-loop stability when interacting with passive environments, but at the loss of precision. In this paper, we use the generalized super-twisting algorithm to obtain a controller which achieves the desired impedance even with disturbances like ocean currents and model errors. Global asymptotic stability is proved under perturbations with a bounded time derivative. The performance of the proposed super-twisting impedance control law is demonstrated in simulations of an underwater vehicle. It is compared with pure impedance control and first-order sliding mode and achieves the desired impedance with respect to the contact force despite model errors and ocean currents, with a continuous control input.

Rigid-Body Noncertainty Equivalence Adaptive Control on the Tangent Bundle of SE(3)

This paper addresses an adaptive rigid-body pose-tracking control problem with unknown system parameters. The proposed control is based on a noncertainty equivalence (NCE) adaptive principle applied to the configuration manifold of rigid-body motion, i.e., special Euclidean group SE(3), and its tangent bundle TSE(3). The controller drives the system to follow an arbitrary reference trajectory with bounded time derivatives. The system states are composed of the elements of SE(3), consisting of rotations and translations, and the six-dimensional vector of angular and translational velocities in Euclidean space. Almost-global-asymptotic stability of the system is demonstrated using a Morse–Lyapunov stability analysis. Then, the performance of the proposed controller is verified and is compared to the results obtained by a certainty-equivalence (CE) adaptive control applied to exponential coordinates associated with the linear space of the Lie algebra . It is shown that the TSE(3)-based NCE adaptive control design can eliminate the performance degradation due to the cancellation of uncertain parameter effects that would otherwise appear when the CE adaptive controller is used. As a result, the proposed NCE-based adaptive pose-tracking controller recovers the closed-loop pose-tracking controller performance with the system parameters fully known to the controller.

Error assessment of biogeochemical models by lower bound methods (NOMMA-1.0)

Abstract. Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.

Functional observer based controller for stabilizing Takagi–Sugeno fuzzy systems with time-delays

This paper investigates the construction of a fuzzy functional observer for nonlinear systems with time-delays, and the application of the observer to estimate the state functions of the parallel distributed compensation controller for stabilizing the system. Two types of time-delays are considered: constant and time-varying delays with bounded time derivative. Stability conditions are obtained using Lyapunov–Krasovskii functional approach; and the conditions are transformed into linear matrix inequalities with equality constraints so that observer parameters can be calculated using the solution of these inequalities. Functional observer construction procedures are presented considering both constant and time-varying time-delays. Two examples, including one for obtaining a power system stabilizer for a single machine infinite bus system, are presented to illustrate effectiveness of the proposed design procedures.

Formation control of multiple elliptical agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov’s method, and smooth or p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings under the agents’ limited sensing ranges.

Formation control of multiple elliptic agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptic shape and limited sensing ranges to perform a desired formation and that guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on explicit algebraic separation conditions between ellipses, root conditions of cubic polynomials, the Lyapunov direct method, and smooth or p-times differentiable step functions. These functions are incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings despite the agents' limited sensing ranges. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Formation control of multiple elliptical agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptical shape and with limited sensing ranges to perform a desired formation. The controllers guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on an algebraic separation condition between ellipses, Lyapunov’s method, and smooth or p -times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings under the agents’ limited sensing ranges.

Practical Formation Control of Multiple Unicycle-Type Mobile Robots with Limited Sensing Ranges

This paper presents a design of cooperative controllers that force a group of N unicycle-type mobile robots with limited sensing ranges to perform a desired tight formation and that guarantee no collisions between any robots in the group. The desired formation can be stabilized at any reference trajectories with bounded time derivatives. The formation control design is based on several nonlinear coordinate changes, the transverse function approach, the backstepping technique, the Lyapunov direct method, and smooth or p??times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need of switchings despite of the robots' limited sensing ranges. The proposed formation control system is applied to solve a gradient climbing problem.

On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays

This paper investigates the asymptotic stability of switched linear time-varying systems with constant point delays under not very stringent conditions on the matrix functions of parameters. Such conditions are their boundedness, the existence of bounded time derivatives almost everywhere, and small amplitudes of the appearing Dirac impulses where such derivatives do not exist. It is also assumed that the system matrix for zero delay is stable with some prescribed stability abscissa for all time in order to obtain sufficiency-type conditions of asymptotic stability dependent on the delay sizes. Alternatively, it is assumed that the auxiliary system matrix defined for all the delayed system matrices being zero is stable with prescribed stability abscissa for all time to obtain results for global asymptotic stability independent of the delays. A particular subset of the switching instants is the so-called set of reset instants where switching leads to the parameterization to reset to a value within a prescribed set.

Robust Adaptive Asymptotic Tracking of Nonlinear Systems With Additive Disturbance

This note deals with the tracking control of multiple-input-multiple-output (MIMO) nonlinear parametric strict-feedback systems in the presence of additive disturbances and parametric uncertainties. For such systems, C/sup 0/ robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation. In this work, under the assumption the disturbances are C/sup 2/ with bounded time derivatives, we present a C/sup 0/ robust adaptive control construction that guarantees the tracking error is asymptotically driven to zero.

Nonlinear output feedback tracking with almost disturbance decoupling

Addresses the design of global output feedback controls for a class of uncertain nonlinear single-input/single-output systems which are globally transformable into an observable minimum phase system whose nonlinearities depend on the output only. They may be affected by unknown time-varying disturbances or parameter variations entering linearly in the state equations. The proposed dynamic controller is of order /spl rho/-1 (/spl rho/ is the relative degree of the given system) and ensures that the closed-loop system enjoys for any initial condition and for any smooth bounded output reference signal (with bounded time derivatives up to order /spl rho/) the following properties: input-to-state stability with respect to disturbance inputs and almost disturbance decoupling, i.e., the influence of disturbances both on the L/sub 2/ and on the L/sub /spl infin// norm of the output tracking error is arbitrarily attenuated by increasing a positive scalar control parameter. When disturbances are zero the reference signal is exponentially tracked by the output and the equilibrium point corresponding to the reference signal is globally asymptotically stable.

A proof of the non-existence of a bounded-derivative continuous model for a discrete chaotic system

Takens' theorem states that for any dynamical system there exists a dimension in which the system can be embedded as a sampling of a continuous function. This paper presents a result which shows that a non-constant continuous model with a bounded time derivative does not exist when the system to be embedded is a discrete chaotic process. The result presented here does not contradict Takens' theorem which has no requirement of a bounded time derivative. The assumption of a bounded derivative is an important one since recurrent neural network learning rules usually implicitly assume that a bounded time derivative exists for the network dynamics equations which define the system model.

Exponential Stability of Large-Scale Nonlinear Systems with Multiple Time Delays

The exponential stability of large-scale nonlinear parabolic systems with time-varying delays is studied in this paper using a new generalization of Gronwalrs inequality and Lyapunov theory. The systems are interconnected by bounded operators, although this can be generalized. All the time-delays will be assumed to have bounded time derivatives for simplicity here.