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Results for “Lyapunov function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

Bayard, D. S.↗
NASA NTRS1988

Globally stable control laws for the attitude maneuver problem - Tracking control and adaptive control

An approach using a globally nonsingular representation is proposed for the attitude control problem of a rigid body. The attitude dynamics are described by the nonlinear Euler equation together with the nonlinear kinematic equations which relate a representation of attitude to the angular velocity of the body. When this approach is combined with an energy-motivated Lyapunov function, a large class of globally stable attitude control laws can be derived. This class includes model-independent tracking control, model-dependent tracking control, and adaptive control, allowing tradeoffs between controller complexity, attainable performance, and available model information.

Wen, John T.↗
NASA NTRS1988

Stability analysis of multiple rigid robot manipulators holding a common rigid object

The authors consider several possible control structures for multiple-arm systems by regarding either joint torques, tip force, or a generalized acceleration of the control input. They emphasize the first case, since a class of relatively model-independent control laws can be generated for both motion and internal force control. The recently developed move/squeeze orthogonal subspace decomposition coupled with the energy Lyapunov function formulation provides a basic analytical framework within which motion and force control are considered as independent problems. Simulation results of two three-link planar arms are included to demonstrate good transient performance for both motion and force that can be attained with the full dynamics control paradigm.

Wen, John T.↗
NASA NTRS1989

Bandwidth-limited robust nonlinear sliding control of pointing and tracking maneuvers

It is shown how multiaxial spacecraft tracking and pointing maneuvers with known control bandwidth and given tracking error bounds can be implemented by variable-structure control in the presence of uncertain vehicle and target dynamics. It is shown how to select a nonlinear sliding surface relating attitude and rate variables, as well as a Lyapunov function in the surface variables that absorbs multiplicative model undertainties, thereby simplifying the computation of control corrections. It is then shown how a boundary layer envelope can be designed, within which the components of the surface error dynamics can be modeled as the outputs of designer-selected decoupled low-pass filters. Closed-loop stability conditions accounting for the coupling between the attitude error dynamics and the surface error dynamics are then obtained.

Dwyer, Thomas A. W., III↗
NASA NTRS1990

Laws For Stable Control Of Orientation

Class of globally stable laws for control of orientation of rigid body established. Tradeoffs made among complexity, performance, and information available for mathematical models. New approach involves use of globally nonsingular four-parameter unit-quaternion (Euler-parameter) representation. Attitude dynamics described by nonlinear Euler equation together with nonlinear kinematic equations, which relate representation of attitude to angular velocity of body. Suitable energy-motivated Lyapunov function to analyze stability.

Kreutz, Kenneth K.↗
NASA NTRS1989

Redundancy of space manipulator on free-flying vehicle and its nonholonomic path planning

The nonholonomic mechanical structure of space robots and path planning is discussed. The angular momentum conservation works as a nonholonomic constraint while the linear momentum conservation is a holonomic one. Thus, a vehicle with a 6 d.o.f. manipulator is described as a 9 variable system with 6 inputs. This implies the possibility of controlling the vehicle orientation and the joint variables of the manipulator by actuating the joint variables, but only if the trajectory is carefully planned; however, both of them cannot be controlled independently. It means that by assuming feasible-path planning, a system that consists of a vehicle and a 6 d.o.f. manipulator can be utilized as 9 d.o.f. system. Initially, the nonholonomic mechanical structure of space vehicle/manipulator system is shown. Then a path planning scheme for nonholonomic systems is proposed using Lyapunov functions.

Nakamura, Yoshihiko↗
NASA NTRS1989

Stability analysis of multiple-robot control systems

In a space telerobotic service scenario, cooperative motion and force control of multiple robot arms are of fundamental importance. Three paradigms to study this problem are proposed. They are distinguished by the set of variables used for control design. They are joint torques, arm tip force vectors, and an accelerated generalized coordinate set. Control issues related to each case are discussed. The latter two choices require complete model information, which presents practical modeling, computational, and robustness problems. Therefore, focus is on the joint torque control case to develop relatively model independent motion and internal force control laws. The rigid body assumption allows the motion and force control problems to be independently addressed. By using an energy motivated Lyapunov function, a simple proportional derivative plus gravity compensation type of motion control law is always shown to be stabilizing. The asymptotic convergence of the tracing error to zero requires the use of a generalized coordinate with the contact constraints taken into account. If a non-generalized coordinate is used, only convergence to a steady state manifold can be concluded. For the force control, both feedforward and feedback schemes are analyzed. The feedback control, if proper care has been taken, exhibits better robustness and transient performance.

Wen, John T.↗
NASA NTRS1991

Square patterns and secondary instabilities in driven capillary waves

Amplitude equations (including nonlinear damping terms) are derived which describe the evolution of patterns in large-aspect-ratio driven capillary wave experiments. For drive strength just above threshold, a reduction of the number of marginal modes (from traveling capillary waves to standing waves) leads to simpler amplitude equations, which have a Lyapunov functional. This functional determines the wavenumber and symmetry (square) of the most stable uniform state. The original amplitude equations, however, have a secondary instability to transverse amplitude modulation (TAM), which is not present in the standing-wave equations. The TAM instability announces the restoration of the full set of marginal modes.

Milner, S. T.↗
NASA NTRS1991

The attitude control problem

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body. The controllers share the common structure of a proportional-derivative feedback plus some feedforward which can be zero (the model-independent case), the Coriolis torque compensation, or an adaptive compensation. These controller structures are compared in terms of the requirement on the a priori model information, guaranteed transient performance, and robustness. The global stability of the Luh-Walker-Paul robot end-effector controller is also analyzed in this framework.

Wen, John Ting-Yung↗
NASA NTRS1994

Neural networks applications to control and computations

Several interrelated problems in the area of neural network computations are described. First an interpolation problem is considered, then a control problem is reduced to a problem of interpolation by a neural network via Lyapunov function approach, and finally a new, faster method of learning as compared with the gradient descent method, was introduced.

Luxemburg, Leon A.↗
NASA NTRS1994

Some Properties and Stability Results for Sector-Bounded LTI Systems

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Gupta, Sandeep↗
NASA NTRS2004

Switching LPV Control for High Performance Tactical Aircraft

This paper examines a switching Linear Parameter-Varying (LPV) control approach to determine if it is practical to use for flight control designs within a wide angle of attack region. The approach is based on multiple parameter-dependent Lyapunov functions. The full parameter space is partitioned into overlapping subspaces and a family of LPV controllers are designed, each suitable for a specific parameter subspace. The hysteresis switching logic is used to accomplish the transition among different parameter subspaces. The proposed switching LPV control scheme is applied to an F-16 aircraft model with different actuator dynamics in low and high angle of attack regions. The nonlinear simulation results show that the aircraft performs well when switching among different angle of attack regions.

Lu, Bei↗
NASA NTRS2017

Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.

Switching LPV control↗
DOE OSTI2021

A Neural Lyapunov Approach to Transient Stability Assessment in Interconnected Microgrids

We propose a neural Lyapunov approach to assessing transient stability in power electronic-interfaced microgrid interconnections. The problem of transient stability assessment is cast as one of learning a neural network-structured Lyapunov function in the state space. Based on the function learned, a security region is estimated for monitoring the security of interconnected microgrids in real-time operation. The efficacy of the approach is tested and validated in a grid-connected microgrid and a three-microgrid interconnection. A comparison study suggests that the proposed method can achieve a less conservative characterization of the security region, as compared with a conventional approach.

Huang, Tong↗
DOE OSTI2023

Circulating Current Reduction of Back-to-Back MMC with Advanced Grid-Support Functionalities for Medium-Voltage Applications

A Lyapunov energy function based circulating current reduction scheme for a back to back modular multilevel converter based system for a microgrid application has been proposed in this digest. In order to ensure no circulating or zero sequence currents within the modules, the dynamics from one leg of the converter to the other are evaluated. A Lyapunov energy function is then developed and utilizing the circulating current dynamics of the converter the overall control law is implemented. In this digest a decentralized hierarchical control architecture has been implemented for the main current control; where the outer loop or the central controller implements the higher level grid interconnection functions as per IEEE 1547-2018 standards and the inner loop based on synchronous reference frame implements the current control architecture. The inner loops' outputs are the commanded converter voltages either on either side which are augmented by the Lyapunov energy function based circulating current suppression architecture. To evaluate the efficacy of the overall system, the overall system is modeled around a 300kVA back to back SiC multilevel modular converter used as a direct-connected medium voltage (MV) grid intertie based on MATLAB/Simulink domain. Several important case studies are presented in this paper to prove the effectiveness of the proposed architecture. case study results are presented.

circulating current↗
DOE OSTI2014

A model with competition between the cell lines in leukemia under treatment

The evolution of leukemia is modeled with a delay differential equation model of four cell populations: two populations (healthy and leukemic) ) of stem-like cells involving a larger category consisting of proliferating stem and progenitor cells with self-renew capacity and two populations (healthy and leukemic) of mature cells, considering the competition of healthy vs. leukemic cell populations and three types of division that a stem-like cell can exhibit: self-renew, asymmetric division and differentiation. In the model it is assumed that the treatment acts on the proliferation rate of the leukemic stem cells and on the apoptosis of stem and mature cells. The emphasis in this model is on establishing relevant parameters for chronic and acute manifestations of leukemia. Stability of equilibria is investigated and sufficient conditions for local asymptotic stability will be given using a Lyapunov-Krasovskii functional.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗