A stochastic variational inequality is proposed to model a white noise excited elasto-plastic osc... more A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii's method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions.
We consider control problems for the variational inequality describing a single degree of freedom... more We consider control problems for the variational inequality describing a single degree of freedom elasto-plastic oscillator. We are particularly interested in finding the "critical excitation", i.e., the lowest energy input excitation that drives the system between the prescribed initial and final states within a given time span. This is a control problem for a state evolution described by a variational inequality. We obtain Pontryagin's necessary condition of optimality. An essential difficulty lies with the non continuity of adjoint variables. * Dedicated to John Baillieul on the Occasion of His 65th Birthday.
AIAA Guidance, Navigation and Control Conference and Exhibit, 2007
Assistant Professor, College Station, TX, 77843, U.S.A János Turi ‡ Professor, Dallas, Texas, 750... more Assistant Professor, College Station, TX, 77843, U.S.A János Turi ‡ Professor, Dallas, Texas, 75083, U.S.A
In this paper we deal with a class of parabolic partial differential equations containing a conti... more In this paper we deal with a class of parabolic partial differential equations containing a continuous hysteresis operator. We get an existence result by means of a technique based on an implicit time discretization scheme and we also analyse the dependence of the solution on the data. This model equation appears in the context of magnetohydrodynamics.
In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time ... more In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic) introduces a nonlinearity known as "backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results. * Mathematics Subject Classifications: 34K35, 37C75.
... To evaluate the last integral on the right hand side of (20) we substitute (16) for -y4(t,s) ... more ... To evaluate the last integral on the right hand side of (20) we substitute (16) for -y4(t,s) to get (see [l] for details) and (28) + j1 -1 xF~l l+z -1 plo 1-y -ry-l+UT r;(t + drdydx) cI(T)rb(t + r)dr, (21) where c1 and cz are constant vectors and c ~ ( T ) = $&TZ - 2Ur. ...
Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002
In the paper the dynamics of an inverted pendulum on a cart is investigated assuming backlash and... more In the paper the dynamics of an inverted pendulum on a cart is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by control force which is provided by a motor driving the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic)
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991
... Mf(t) + Bi(t) + Kt(t) = iF(t) + Gu(t) 'The work of this author wan supported in part by ... more ... Mf(t) + Bi(t) + Kt(t) = iF(t) + Gu(t) 'The work of this author wan supported in part by the National Science Foundation under grant DMS-6907019. ... 0 Procedure for computing C,: Given data A, b, &, &, c, IEz(s) = NkZ(s), (sIE~(s))-l = Nkl(s), follow the steps below. ...
... If p> l/(la), then Abel's equation has a unique solution for each (n,<)>( in a ... more ... If p> l/(la), then Abel's equation has a unique solution for each (n,<)>( in a dense subset of lR* t» p. However, A does not generate a CQ-semigroup on IRxLp. Theorem 1 above lead Kappel and Zhang [12, 17] to consider more general necessary conditions for well-posedness ...
ABSTRACT We have extended earlier results concerning the well-posedness of FDEs on product spaces... more ABSTRACT We have extended earlier results concerning the well-posedness of FDEs on product spaces. In particular, we have presented sufficient conditions for the well-posedness of a large class of functional differential equations (NNFDE). This class contains the “standard” neutral and retarded functional differential equations and many weakly singular integro-differential equations. It appears that results in this paper can be applied to infinite delay problems by using proper weighting on the state-space.
The recent work presents the motion control of a pendulum like under—actuated service robot AC RO... more The recent work presents the motion control of a pendulum like under—actuated service robot AC ROBOT ER. This robot is designed to be applied in indoor environments, where it can perform pick and place tasks autonomously and/or with close cooperation with humans. It can also serve as a platform that carries other service robots with lower mobility. The cable suspended robot has a complex structure and its dynamics is difficult to model using conventional robotic approaches. Instead, in this paper natural (Cartesian) coordinates are used to describe the configuration of the robot, while its dynamics is modeled as a set of differential algebraic equations. The method of computed torque control with a PD controller is applied to the investigated under—actuated system. The inverse dynamics solution is obtained via direct discretization of the DAE system. Results for a real parameter case study are presented by numerical simulations.
A stochastic variational inequality is proposed to model a white noise excited elasto-plastic osc... more A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii's method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions.
We consider control problems for the variational inequality describing a single degree of freedom... more We consider control problems for the variational inequality describing a single degree of freedom elasto-plastic oscillator. We are particularly interested in finding the "critical excitation", i.e., the lowest energy input excitation that drives the system between the prescribed initial and final states within a given time span. This is a control problem for a state evolution described by a variational inequality. We obtain Pontryagin's necessary condition of optimality. An essential difficulty lies with the non continuity of adjoint variables. * Dedicated to John Baillieul on the Occasion of His 65th Birthday.
AIAA Guidance, Navigation and Control Conference and Exhibit, 2007
Assistant Professor, College Station, TX, 77843, U.S.A János Turi ‡ Professor, Dallas, Texas, 750... more Assistant Professor, College Station, TX, 77843, U.S.A János Turi ‡ Professor, Dallas, Texas, 75083, U.S.A
In this paper we deal with a class of parabolic partial differential equations containing a conti... more In this paper we deal with a class of parabolic partial differential equations containing a continuous hysteresis operator. We get an existence result by means of a technique based on an implicit time discretization scheme and we also analyse the dependence of the solution on the data. This model equation appears in the context of magnetohydrodynamics.
In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time ... more In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic) introduces a nonlinearity known as "backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results. * Mathematics Subject Classifications: 34K35, 37C75.
... To evaluate the last integral on the right hand side of (20) we substitute (16) for -y4(t,s) ... more ... To evaluate the last integral on the right hand side of (20) we substitute (16) for -y4(t,s) to get (see [l] for details) and (28) + j1 -1 xF~l l+z -1 plo 1-y -ry-l+UT r;(t + drdydx) cI(T)rb(t + r)dr, (21) where c1 and cz are constant vectors and c ~ ( T ) = $&TZ - 2Ur. ...
Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002
In the paper the dynamics of an inverted pendulum on a cart is investigated assuming backlash and... more In the paper the dynamics of an inverted pendulum on a cart is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by control force which is provided by a motor driving the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid) and the belt (elastic)
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1991
... Mf(t) + Bi(t) + Kt(t) = iF(t) + Gu(t) 'The work of this author wan supported in part by ... more ... Mf(t) + Bi(t) + Kt(t) = iF(t) + Gu(t) 'The work of this author wan supported in part by the National Science Foundation under grant DMS-6907019. ... 0 Procedure for computing C,: Given data A, b, &, &, c, IEz(s) = NkZ(s), (sIE~(s))-l = Nkl(s), follow the steps below. ...
... If p> l/(la), then Abel's equation has a unique solution for each (n,<)>( in a ... more ... If p> l/(la), then Abel's equation has a unique solution for each (n,<)>( in a dense subset of lR* t» p. However, A does not generate a CQ-semigroup on IRxLp. Theorem 1 above lead Kappel and Zhang [12, 17] to consider more general necessary conditions for well-posedness ...
ABSTRACT We have extended earlier results concerning the well-posedness of FDEs on product spaces... more ABSTRACT We have extended earlier results concerning the well-posedness of FDEs on product spaces. In particular, we have presented sufficient conditions for the well-posedness of a large class of functional differential equations (NNFDE). This class contains the “standard” neutral and retarded functional differential equations and many weakly singular integro-differential equations. It appears that results in this paper can be applied to infinite delay problems by using proper weighting on the state-space.
The recent work presents the motion control of a pendulum like under—actuated service robot AC RO... more The recent work presents the motion control of a pendulum like under—actuated service robot AC ROBOT ER. This robot is designed to be applied in indoor environments, where it can perform pick and place tasks autonomously and/or with close cooperation with humans. It can also serve as a platform that carries other service robots with lower mobility. The cable suspended robot has a complex structure and its dynamics is difficult to model using conventional robotic approaches. Instead, in this paper natural (Cartesian) coordinates are used to describe the configuration of the robot, while its dynamics is modeled as a set of differential algebraic equations. The method of computed torque control with a PD controller is applied to the investigated under—actuated system. The inverse dynamics solution is obtained via direct discretization of the DAE system. Results for a real parameter case study are presented by numerical simulations.
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