Thomas Seidman - Academia.edu (original) (raw)

Papers by Thomas Seidman

Research paper thumbnail of Time-invariance of the reachable set for linear control problems

Journal of Mathematical Analysis and Applications, Nov 1, 1979

Research paper thumbnail of Some kanban-controlled manufacturing systems: a first stability analysis

IEEE Transactions on Automatic Control, Jul 1, 1996

The blockage/starvation patterns of known instability examples suggest using local demand informa... more The blockage/starvation patterns of known instability examples suggest using local demand information-which is precisely what is provided by the widely advocated kanban approach to flow control in manufacturing systems. Therefore, we have re-analyzed for stability the examples described in the 1990 Kumar-Seidman paper when modified by introducing kanban control. It is found that this does not ensure stability and, in fact, some interesting new instability phenomena arise. Counterintuitively, it is possible that increasing some reserve supply level in a stable system may induce instability.

Research paper thumbnail of Optimal solutions for a free boundary problem for crystal growth

Birkhäuser eBooks, 1989

ABSTRACT

Research paper thumbnail of A Proposal for a Professional Program in Mathematics

American Mathematical Monthly, Feb 1, 1975

Research paper thumbnail of Continuous dependence for certain degenerate parabolic equations

Journal of Differential Equations, Dec 1, 1987

Consider time-periodic solutions of ti-V. y(IVul) Vu =A where y may have an initial interval of d... more Consider time-periodic solutions of ti-V. y(IVul) Vu =A where y may have an initial interval of degeneracy: y(r) = 0 for 0 c r d rO. It is shown that, although u need not even be unique, one has continuous dependence on the data and also on the nonlinearity y(.) for II(.) := y([Vul) Vu. This generalizes the results of T. I. Seidman (J. Differential Equations 19 (1975), 242-257) for the nondegenerate case.

Research paper thumbnail of The Method of ‘Generalized Interpolation’ for Approximate Solution of Ill-Posed Problems

Suppose we seek the solution x* ɛ X of an ill-posed problem which can be formulated as an infinit... more Suppose we seek the solution x* ɛ X of an ill-posed problem which can be formulated as an infinite system of scalar equations: λj(x) = sj (j = 1,2,…). The method of generalized interpolation defines approximants xN minimizing ‖x‖ among solutions of the finite system: λj (x) = sj (j = 1,…,N). Under quite mild conditions one has xN → x*, even when the method is modified for computational convenience.

Research paper thumbnail of Nonlinear Systems of Partial Differential Equations

ormApp, o .... •v rAiSIFICATION lb. RESTRICTIVE MARKINGS 3. DISTRIBUTION/AVAILABILITY OF REPORT D... more ormApp, o .... •v rAiSIFICATION lb. RESTRICTIVE MARKINGS 3. DISTRIBUTION/AVAILABILITY OF REPORT D-A 21 581 Approved for public release; I7 1 .E distribution unlimited. &6. rrm,. R(S) S. MONITORING ORGANIZATION REPORT NUMBEf(L, 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

Research paper thumbnail of Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems

Research paper thumbnail of Periodic solutions of a non-linear parabolic equation

Journal of Differential Equations, Nov 1, 1975

Research paper thumbnail of Transformation theorems for the integration of functionals

University Microfilms eBooks, 1958

Research paper thumbnail of Determining the Nonlinearity in a Parabolic Equation from Boundary Measurements

IFAC Proceedings Volumes, Jun 1, 1989

We consider the equation _ u = r k(u)ru for a smoothly bounded region IR m and seek to determine ... more We consider the equation _ u = r k(u)ru for a smoothly bounded region IR m and seek to determine the nonlinearity k() from boundary observations on a nite time interval. We may proceed either by imposing Dirichlet boundary conditions u = g(x) on := (0; T) @ and observing the resulting ux := k(u)ru n or, alternatively, by imposing ux boundary conditions k(u)ru n = g(x) and observing the resulting trace, := u on (part of). Under suitable assumptions we show uniqueness for the determination of k from the pair g; ]. The principal element in the argument is a stability result, showing convergence to steady state for the nonlinear equation with data constant in t. This uniqueness argument is nonconstructive but some comments are made as to the construction and convergence of approximations, e.g., by regularization.

Research paper thumbnail of Control Theory and Distributed Parameter Systems

6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

Research paper thumbnail of Boundary feedback stabilization of a parabolic equation

Springer eBooks, Oct 5, 2005

ABSTRACT

Research paper thumbnail of Control of a flexible robot arm

A flexible robot arm, supported at a prismatic joint so that the length of (the relevant part of)... more A flexible robot arm, supported at a prismatic joint so that the length of (the relevant part of) the rod is variable, is modelled. The variation in the length of the arm is taken to be the control action. The principal results are exact controllability for the consideration of purely longitudinal vibrations (wave equation) and the existence of optimal controls in the more practically interesting case of transverse vibrations (Euler-Bernoulli beam equation). In each case, a free boundary problem is considered

Research paper thumbnail of Some problems of distributed parameter control with unilateral constraints

Journal of Mathematical Analysis and Applications, Mar 1, 1990

A class of constrained LQ optimal control problems can be abstractly formulated as seeking a near... more A class of constrained LQ optimal control problems can be abstractly formulated as seeking a nearest point in a "slice" Y n V, where Y' is an afline subspace of a Hilbert space Z and V is the (possibly unbounded) closed convex set corresponding to imposition of the constraint. Subject to a slackness condition, it is shown that the optimal control must then be a "nearest point in W for Some control which would be optimal,for some unconstrained problem of similar form. In particular, this is exemplified by minimum-energy boundary control of the heat equation with a non-negativity constraint.

Research paper thumbnail of Minimizing driver's irritation at a roadblock

Urban traffic is a logistic issue which can have many societal implications, especially when, due... more Urban traffic is a logistic issue which can have many societal implications, especially when, due to a too high density of cars, the network of streets of a city becomes blocked, and consequently, pedestrians, bicycles, and cars start sharing the same traffic conditions potentially leading to high irritations (of people) and therefore to chaos. In this paper we focus our attention on a simple scenario: We model the driver's irritation induced by the presence of a roadblock. As a natural generalization, we extend the model for the two one-way crossroads traffic presented in [5] to that of a roadblock. Our discrete model defines and minimizes the total waiting time. The novelty lies in introducing the (total) driver's irritation and its minimization. Finally, we apply our model to a real-world situation: rush hour traffic in Hillegom, The Netherlands. We observe that minimizing the total waiting time and minimizing the total driver's irritation lead to different traffic light strategies.

Research paper thumbnail of Event-driven discontinuities for continuous-time systems

Research paper thumbnail of Existence for minimization in Banach space with some applications

Journal of Mathematical Analysis and Applications, 1987

Existence of a minimum is shown for a coercive, kc differentiable function restricted to a finite... more Existence of a minimum is shown for a coercive, kc differentiable function restricted to a finite intersection of half spaces under a structural assumption on the GLteaux derivative. This abstract existence result is illustrated by two examples from optimal control theory for distributed systems.

Research paper thumbnail of Some problems with thermostat nonlinearities

Research paper thumbnail of A convection/reaction/switching system

Nonlinear Analysis-theory Methods & Applications, Oct 1, 2007

We consider a spatially distributed hybrid system consisting of a convection/reaction system in w... more We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching "switching threshholds." The model involves a novel formulation for evolution of the free boundary between the modal regions.

Research paper thumbnail of Time-invariance of the reachable set for linear control problems

Journal of Mathematical Analysis and Applications, Nov 1, 1979

Research paper thumbnail of Some kanban-controlled manufacturing systems: a first stability analysis

IEEE Transactions on Automatic Control, Jul 1, 1996

The blockage/starvation patterns of known instability examples suggest using local demand informa... more The blockage/starvation patterns of known instability examples suggest using local demand information-which is precisely what is provided by the widely advocated kanban approach to flow control in manufacturing systems. Therefore, we have re-analyzed for stability the examples described in the 1990 Kumar-Seidman paper when modified by introducing kanban control. It is found that this does not ensure stability and, in fact, some interesting new instability phenomena arise. Counterintuitively, it is possible that increasing some reserve supply level in a stable system may induce instability.

Research paper thumbnail of Optimal solutions for a free boundary problem for crystal growth

Birkhäuser eBooks, 1989

ABSTRACT

Research paper thumbnail of A Proposal for a Professional Program in Mathematics

American Mathematical Monthly, Feb 1, 1975

Research paper thumbnail of Continuous dependence for certain degenerate parabolic equations

Journal of Differential Equations, Dec 1, 1987

Consider time-periodic solutions of ti-V. y(IVul) Vu =A where y may have an initial interval of d... more Consider time-periodic solutions of ti-V. y(IVul) Vu =A where y may have an initial interval of degeneracy: y(r) = 0 for 0 c r d rO. It is shown that, although u need not even be unique, one has continuous dependence on the data and also on the nonlinearity y(.) for II(.) := y([Vul) Vu. This generalizes the results of T. I. Seidman (J. Differential Equations 19 (1975), 242-257) for the nondegenerate case.

Research paper thumbnail of The Method of ‘Generalized Interpolation’ for Approximate Solution of Ill-Posed Problems

Suppose we seek the solution x* ɛ X of an ill-posed problem which can be formulated as an infinit... more Suppose we seek the solution x* ɛ X of an ill-posed problem which can be formulated as an infinite system of scalar equations: λj(x) = sj (j = 1,2,…). The method of generalized interpolation defines approximants xN minimizing ‖x‖ among solutions of the finite system: λj (x) = sj (j = 1,…,N). Under quite mild conditions one has xN → x*, even when the method is modified for computational convenience.

Research paper thumbnail of Nonlinear Systems of Partial Differential Equations

ormApp, o .... •v rAiSIFICATION lb. RESTRICTIVE MARKINGS 3. DISTRIBUTION/AVAILABILITY OF REPORT D... more ormApp, o .... •v rAiSIFICATION lb. RESTRICTIVE MARKINGS 3. DISTRIBUTION/AVAILABILITY OF REPORT D-A 21 581 Approved for public release; I7 1 .E distribution unlimited. &6. rrm,. R(S) S. MONITORING ORGANIZATION REPORT NUMBEf(L, 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

Research paper thumbnail of Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems

Research paper thumbnail of Periodic solutions of a non-linear parabolic equation

Journal of Differential Equations, Nov 1, 1975

Research paper thumbnail of Transformation theorems for the integration of functionals

University Microfilms eBooks, 1958

Research paper thumbnail of Determining the Nonlinearity in a Parabolic Equation from Boundary Measurements

IFAC Proceedings Volumes, Jun 1, 1989

We consider the equation _ u = r k(u)ru for a smoothly bounded region IR m and seek to determine ... more We consider the equation _ u = r k(u)ru for a smoothly bounded region IR m and seek to determine the nonlinearity k() from boundary observations on a nite time interval. We may proceed either by imposing Dirichlet boundary conditions u = g(x) on := (0; T) @ and observing the resulting ux := k(u)ru n or, alternatively, by imposing ux boundary conditions k(u)ru n = g(x) and observing the resulting trace, := u on (part of). Under suitable assumptions we show uniqueness for the determination of k from the pair g; ]. The principal element in the argument is a stability result, showing convergence to steady state for the nonlinear equation with data constant in t. This uniqueness argument is nonconstructive but some comments are made as to the construction and convergence of approximations, e.g., by regularization.

Research paper thumbnail of Control Theory and Distributed Parameter Systems

6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

Research paper thumbnail of Boundary feedback stabilization of a parabolic equation

Springer eBooks, Oct 5, 2005

ABSTRACT

Research paper thumbnail of Control of a flexible robot arm

A flexible robot arm, supported at a prismatic joint so that the length of (the relevant part of)... more A flexible robot arm, supported at a prismatic joint so that the length of (the relevant part of) the rod is variable, is modelled. The variation in the length of the arm is taken to be the control action. The principal results are exact controllability for the consideration of purely longitudinal vibrations (wave equation) and the existence of optimal controls in the more practically interesting case of transverse vibrations (Euler-Bernoulli beam equation). In each case, a free boundary problem is considered

Research paper thumbnail of Some problems of distributed parameter control with unilateral constraints

Journal of Mathematical Analysis and Applications, Mar 1, 1990

A class of constrained LQ optimal control problems can be abstractly formulated as seeking a near... more A class of constrained LQ optimal control problems can be abstractly formulated as seeking a nearest point in a "slice" Y n V, where Y' is an afline subspace of a Hilbert space Z and V is the (possibly unbounded) closed convex set corresponding to imposition of the constraint. Subject to a slackness condition, it is shown that the optimal control must then be a "nearest point in W for Some control which would be optimal,for some unconstrained problem of similar form. In particular, this is exemplified by minimum-energy boundary control of the heat equation with a non-negativity constraint.

Research paper thumbnail of Minimizing driver's irritation at a roadblock

Urban traffic is a logistic issue which can have many societal implications, especially when, due... more Urban traffic is a logistic issue which can have many societal implications, especially when, due to a too high density of cars, the network of streets of a city becomes blocked, and consequently, pedestrians, bicycles, and cars start sharing the same traffic conditions potentially leading to high irritations (of people) and therefore to chaos. In this paper we focus our attention on a simple scenario: We model the driver's irritation induced by the presence of a roadblock. As a natural generalization, we extend the model for the two one-way crossroads traffic presented in [5] to that of a roadblock. Our discrete model defines and minimizes the total waiting time. The novelty lies in introducing the (total) driver's irritation and its minimization. Finally, we apply our model to a real-world situation: rush hour traffic in Hillegom, The Netherlands. We observe that minimizing the total waiting time and minimizing the total driver's irritation lead to different traffic light strategies.

Research paper thumbnail of Event-driven discontinuities for continuous-time systems

Research paper thumbnail of Existence for minimization in Banach space with some applications

Journal of Mathematical Analysis and Applications, 1987

Existence of a minimum is shown for a coercive, kc differentiable function restricted to a finite... more Existence of a minimum is shown for a coercive, kc differentiable function restricted to a finite intersection of half spaces under a structural assumption on the GLteaux derivative. This abstract existence result is illustrated by two examples from optimal control theory for distributed systems.

Research paper thumbnail of Some problems with thermostat nonlinearities

Research paper thumbnail of A convection/reaction/switching system

Nonlinear Analysis-theory Methods & Applications, Oct 1, 2007

We consider a spatially distributed hybrid system consisting of a convection/reaction system in w... more We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching "switching threshholds." The model involves a novel formulation for evolution of the free boundary between the modal regions.