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  • Articles  (43)
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  • optimal control  (43)
  • 2010-2014
  • 1985-1989  (22)
  • 1980-1984  (21)
  • Mathematics  (43)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 15 (1988), S. 289-311 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing system ; dynamic routing ; material handling ; robotics ; semi-Markovian decision process ; optimal control ; stochastic optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An optimal routing policy is obtained for Flexible Manufacturing Systems (FMSs) with limited buffers at the work stations. This policy is used to effectively drive a robotic material handling system. The routing decisions are made by a supervising computer on a real-time basis in order to avoid any work station running out of inputs and to control the blocking of the material handling system. Using our model, general material handling times can be assumed. The optimal policy and several key performance measures are computed, following the problem formulation as a continuous-time, semi-Markovian decision process. Fast convergence and computational stability are ensured by the ergodic solution algorithm augmented to solve the functional equations of the renewal process. The solution algorithm was implemented, tested on an extensive range of problems regarding the structure and the performance of the optimal policy. Complex environments involving diverse processing times, as well as very limited buffer storage, were examined. The interaction between the allocation of buffer spaces to work stations, the structural properties of the optimal monotone (threshold-type) policy and the system performance are also investigated.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 38 (1982), S. 83-96 
    ISSN: 1573-2878
    Keywords: Numerical methods ; multiple shooting method ; optimal control ; aircraft trajectories ; flight mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Three-dimensional minimum-time 180° turns of a fighter aircraft are computed for several initial velocitiesV 0 and altitudesh 0. It is shown that the optimum turns consist of split -S maneuvers forV 0≦V 10, three-dimensional maneuvers forV 10〈V 0〈V 20, and half-loops forV 0≧V 20, withV 10,V 20 being functions of altitude or thrust/weight ratio.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 30 (1980), S. 53-71 
    ISSN: 1573-2878
    Keywords: Parallel processing ; nonlinear two-point boundary-value problems ; optimal control ; parallel shooting ; parallel integration ; parallel minimization algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a collection of parallel optimal control algorithms which are suitable for implementation on an advanced computer with the facility for large-scale parallel processing. Specifically, a parallel nongradient algorithm and a parallel variablemetric algorithm are used to search for the initial costate vector that defines the solution to the optimal control problem. To avoid the computational problems sometimes associated with simultaneous forward integration of both the state and costate equations, a parallel shooting procedure based upon partitioning of the integration interval is considered. To further speed computations, parallel integration methods are proposed. Application of this all-parallel procedure to a forced Van der Pol system indicates that convergence time is significantly less than that required by highly efficient serial procedures.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 30 (1980), S. 137-147 
    ISSN: 1573-2878
    Keywords: Discontinuous differential equations ; optimal control ; Filippov solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract When dealing with the time-optimal problem for linear control systems, there may be a difference between optimal open-loop control and corresponding synthesized feedback control, since in the latter case one is led to allow for generalized (Filippov) solutions. In this note, it is shown that the set of two-dimensional linear control systems with a convex polyhedron as control domain, which exhibit such paradoxical behavior (completely characterized by Brunovský), has a nonempty interior, in a natural and appropriately defined topology on the space of all such linear control systems.
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  • 5
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    Electronic Resource
    Springer
    Journal of optimization theory and applications 31 (1980), S. 195-205 
    ISSN: 1573-2878
    Keywords: State-variable discontinuities ; maximum principle ; fisheries management ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consideration is given to continuous-time, parameter-dependent optimal control problems with state-variable jump discontinuities atN variable interior times. A maximum principle involving known costate jump conditions is stated and is proved by transforming the problem into a standard Mayer control problem. An illustrative example for fisheries management is included.
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  • 6
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    Electronic Resource
    Springer
    Journal of optimization theory and applications 31 (1980), S. 565-581 
    ISSN: 1573-2878
    Keywords: Boundary-value problems ; elliptic control problems ; multigrid methods ; numerical methods ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Elliptic control problems with a quadratic cost functional require the solution of a system of two elliptic boundary-value problems. We propose a fast iterative process for the numerical solution of this problem. The method can be applied to very special problems (for example, Poisson equation for a rectangle) as well as to general equations (arbitrary dimensions, general region). Also, nonlinear problems can be treated. The work required is proportional to the work taken by the numerical solution of a single elliptic equation.
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  • 7
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    Springer
    Journal of optimization theory and applications 32 (1980), S. 17-37 
    ISSN: 1573-2878
    Keywords: Sensitivity analysis ; dynamic optimization ; optimal control ; near-optimal control ; Pontryagin's minimum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract To find the optimal control of chemical processes, Pontryagin's minimum principle can be used. In practice, however, one is not only interested in the optimal solution, which satisfies the restrictions on the control, the initial and terminal conditions, and the process parameters. It is also important to known how the optimal control and the minimum value of the objective function change, due to small variations in all the restrictions and the parameters. It is shown how to determine the effect of these variations directly from the optimal solution. This saves computer time, compared with the more traditional sensitivity analysis based on computing the optimal control for every single variation considered. The theory is applied to a chemical process.
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  • 8
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    Springer
    Journal of optimization theory and applications 32 (1980), S. 327-343 
    ISSN: 1573-2878
    Keywords: Linear systems ; quadratic costs ; regulator problem ; optimal control ; partial state information
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex 0. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx 0 and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 32 (1980), S. 577-593 
    ISSN: 1573-2878
    Keywords: Numerical methods ; computing methods ; optimal control ; optimality properties ; supplementary optimality properties ; gradient methods ; gradient-restoration algorithms ; sequential gradient-restoration algorithms ; general boundary conditions ; nondifferential constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, sequential gradient-restoration algorithms for optimal control problems are considered, and attention is focused on the gradient phase. It is shown that the Lagrange multipliers associated with the gradient phase not only solve the auxiliary minimization problem of the gradient phase, but are also endowed with a supplementary optimality property: they minimize the error in the optimality conditions, subject to the multiplier differential equations and boundary conditions, for given state, control, and parameter.
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  • 10
    Electronic Resource
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    Springer
    Journal of optimization theory and applications 33 (1981), S. 121-135 
    ISSN: 1573-2878
    Keywords: Sobolev equations ; pseudo-parabolic equations ; optimal control ; Lagrange multipliers ; penalty method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the approximation by the penalty method of a control problem governed by a pseudo-parabolic equation with a noncoercive control functional and with control and state constraints. The existence of solutions to the penalized problems is established. In addition, the convergence of the penalized problems to the solution, the Lagrange multipliers, and the minimum value of the original problem is studied. The results apply to Sobolev and parabolic equations as well.
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