Estimation of the Region of Attraction of Underactuated Systems and Its Enlargement Using Impulsive Inputs

Kant, Nilay; Mukherjee, Ranjan; Chowdhury, Dhrubajit; Khalil, Hassan K.

doi:10.1109/tro.2019.2893599

Cited by 30 publications

(10 citation statements)

References 43 publications

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“…whereĖ = u Tq 1 follows from the passivity property of underactuated Euler-Lagrange systems -see [32] 4 and proposition 2.5 of [35]. By substitutingq 1 from (9a) in (24) and using the symmetry of B(q), we geṫ…”

Section: Resultsmentioning

confidence: 99%

“…Prior works on impulsive control [15][16][17][18][19][20][21] have been theoretical in nature but in recent works [6,[22][23][24][25][26][27][28][29], impulsive inputs have been utilized for control of underactuated systems in both simulations and experiments. In experiments, impulsive inputs have been implemented in standard hardware using high-gain feedback [23,24], dispelling the notion that impulsive inputs require large actuators and are impractical. A combination of continuous and impulsive inputs was used recently for stabilization of homoclinic orbits of two-DOF underactuated systems [27].…”

Section: Introductionmentioning

confidence: 99%

“…Finally, using a state-dependent impulsive dynamical system model [16], we present sufficient conditions for stabilization. To demonstrate the generality of our approach, we demonstrate stabilization of energy level sets for the three-DOF Tiptoebot [24] through simulations. Experimental validation is carried out on a rotary pendulum to show the applicability of our approach in real hardware.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

2021

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Recent investigations of underactuated systems have demonstrated the benefits of control inputs that are impulsive in nature. Here we consider the problem of stabilization of energy level sets of underactuated systems exploiting impulsive braking. We consider systems with one passive degree-of-freedom (DOF) and the energy level set is a manifold where the active coordinates are fixed and the mechanical energy equals some desired value. A control strategy comprised of continuous inputs and intermittent impulsive braking inputs is presented. The generality of the approach is shown through simulation of a three-DOF Tiptoebot; the feasibility of implementation of impulsive control using standard hardware is demonstrated using a rotary pendulum.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

2021

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“…where q− and q+ are the velocities immediately before and after application of u I . Since the system is underactuated, the jump in the passive velocity q2 is dependent on the jumps in the active velocity q1 ; this relationship is described by the (n−1) dimensional impulse manifold [8,10], which can be obtained from (23):…”

Section: Impulse Controlled Poincaré Map (Icpm)mentioning

confidence: 99%

“…The control design is comprised of continuous inputs that enforce the VHC and impulsive inputs that exponentially stabilize the orbit. Impulsive inputs have been used for control of underactuated systems [1,[8][9][10][11]15] and it has been established that such inputs can be implemented in standard hardware using high-gain feedback. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincare Maps

Kant,

Mukherjee

2020

Preprint

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The problem of orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom (DOF) is revisited. Virtual holonomic constraints are enforced using a continuous controller; this results in a dense set of closed orbits on a constraint manifold. A desired orbit is selected on the manifold and a Poincaré section is constructed at a fixed point on the orbit. The corresponding Poincaré map is linearized about the fixed point; this results in a discrete linear time-invariant system. To stabilize the desired orbit, impulsive inputs are applied when the system trajectory crosses the Poincaré section; these inputs can be designed using standard techniques such as LQR. The Impulse Controlled Poincaré Map (ICPM) based control design has lower complexity and computational cost than control designs proposed earlier. The generality of the ICPM approach is demonstrated using the 2-DOF cart-pendulum and the 3-DOF tiptoebot.

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Successive estimations of bilateral bounds and trapping/stability regions of solution to some nonlinear nonautonomous systems

Pinsky

2021

Nonlinear Dyn

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Estimation of the degree of stability and the bounds of solutions to nonautonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are unable to effectively gage these characteristics in time-varying nonlinear systems. This paper develops a novel methodology providing successive approximations to solutions that are stemmed from the trapping/stability regions of these systems and estimate the errors of such approximations. In turn, this leads to successive approximations of both the bilateral bounds of solutions and the boundaries of trapping/stability regions of the underlying systems. Along these lines we formulate enhanced stability/boundedness criteria and contrast our inferences with inclusive simulations which reveal dependence of the trapping/stability regions upon the structure of timedependent components and initial time-moment.

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Estimation of the Region of Attraction of Underactuated Systems and Its Enlargement Using Impulsive Inputs

Cited by 30 publications

References 43 publications

Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

Stabilization of energy level sets of underactuated mechanical systems exploiting impulsive braking

Orbital Stabilization of Underactuated Systems using Virtual Holonomic Constraints and Impulse Controlled Poincare Maps

Successive estimations of bilateral bounds and trapping/stability regions of solution to some nonlinear nonautonomous systems

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