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  • Articles  (7)
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  • Optimal control
  • Springer  (7)
  • 1995-1999  (7)
  • 1985-1989
  • 1970-1974
  • 1998  (7)
  • Mathematics  (7)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • Articles  (7)
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  • Springer  (7)
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  • 1995-1999  (7)
  • 1985-1989
  • 1970-1974
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  • 1
    Electronic Resource
    Electronic Resource
    Neural network controller for a multivariable model of submarine dynamics (1998)
    Springer
    Neural computing & applications 7 (1998), S. 295-308 
    Details
    ISSN: 1433-3058
    Keywords: Adaptive ; Backpropagation ; Multivariable ; Neural networks ; Optimal control ; Submarine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, there have been many attempts to use neural networks as a feedback controller. However, most of the reported cases seek to control Single-Input Single-Output (SISO) systems using some sort of adaptive strategy. In this paper, we demonstrate that neural networks can be used for the control of complex multivariable, rather than simply SISO, systems. A modified direct control scheme using a neural network architecture is used with backpropagation as the adaptive algorithm. The proposed algorithm is designed for Multi-Input Multi-Output (MIMO) systems, and is similar to that proposed by Saerens and Soquet [1] and Goldenthal and Farrell [2] for (SISO) systems, and differs only in the form of the gradient approximation. As an example of the application of this approach, we investigate the control of the dynamics of a submarine vehicle with four inputs and four outputs, in which the differential stern, bow and rudder control surfaces are dynamically coordinated to cause the submarine to follow commanded changes in roll, yaw rate, depth rate and pitch attitude. Results obtained using this scheme are compared with those obtained using optimal linear quadratic control.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01428121
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal Control of a Chemical Vapor Deposition Reactor (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 623-644 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; bang-bang control ; free boundary problems ; parabolic equations ; homogenizations ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a simple model of chemical vapor deposition on a silicon wafer. The control is the flux of chemical species, and the objective is to grow the semiconductor film so that its surface attains a prescribed profile as nearly as possible. The surface is spatially fast oscillating due to the small feature scale, and therefore the problem is formulated in terms of its homogenized approximation. We prove that the optimal control is bang-bang, and we use this information to develop a numerical scheme for computing the optimal control.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022694210246
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  • 3
    Electronic Resource
    Electronic Resource
    Tracking Demands in Optimal Control of Managerial Systems with Continuously-Divisible, Doubly Constrained Resources (1998)
    Springer
    Journal of global optimization 13 (1998), S. 43-59 
    Details
    ISSN: 1573-2916
    Keywords: Resource constrained scheduling ; renewable and nonrenewable resources ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper addresses problems of allocating continuously divisible resources among multiple production activities. The resources are allowed to be doubly constrained, so that both usage at every point of time and cumulative consumption over a planning horizon are limited as it is often the case in project and production scheduling. The objective is to track changing in time demands for the activities as closely as possible. We propose a general continuous-time model that states the problem in a form of the optimal control problem with non-linear speed-resource usage functions. With the aid of the maximum principle, properties of the solutions are derived to characterize optimal resource usage policies. On the basis of this analytical investigation, numerical scheduling methods are suggested and computationally studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008256009222
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  • 4
    Electronic Resource
    Electronic Resource
    On a Class of Optimal Control Problems with State Jumps (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 65-82 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; switching times ; state jumps ; transformations ; optimal parameter selection problem ; automatic differentiation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022684730236
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  • 5
    Electronic Resource
    Electronic Resource
    Optimal Control Problems via Exact Penalty Functions (1998)
    Springer
    Journal of global optimization 12 (1998), S. 215-223 
    Details
    ISSN: 1573-2916
    Keywords: Optimal control ; Exact penalization ; Directional differentiability ; Subdifferentiability ; Necessary optimality conditions ; Nonsmooth analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonsmoothness is viewed by many people as at least an undesirable (if not unavoidable) property. Our aim here is to show that recent developments in Nonsmooth Analysis (especially in Exact Penalization Theory) allow one to treat successfully even some quite ‘smooth’ problems by tools of Nonsmooth Analysis and Nondifferentiable Optimization. Our approach is illustrated by one Classical Control Problem of finding optimal parameters in a system described by ordinary differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008257323671
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  • 6
    Electronic Resource
    Electronic Resource
    On Global Optimality Conditions for Nonlinear Optimal Control Problems (1998)
    Springer
    Journal of global optimization 13 (1998), S. 109-122 
    Details
    ISSN: 1573-2916
    Keywords: Optimal control ; Pontryagin maximum principle ; Global optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let a trajectory and control pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g( $$\bar x$$ (T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of $$(\bar x{\text{, }}\bar u{\text{)}}$$ turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ $$\mathop {{\text{max}}}\limits_u {\text{ }}H$$ ≢ $$\mathop {{\text{min}}}\limits_u {\text{ }}H$$ on [0,T], and if there is no another pair (x,u) such that g(x(T))=g( $$\bar x$$ (T)), then $$(\bar x{\text{, }}\bar u{\text{)}}$$ is a global maximizer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008211429313
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  • 7
    Electronic Resource
    Electronic Resource
    Near Optimization of Dynamic Systems by Decomposition and Aggregation (1998)
    Springer
    Journal of optimization theory and applications 99 (1998), S. 1-22 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; dynamical systems ; decomposition ; aggregation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the reduction of a class of optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each of the decomposed matrices has one or more dominant eigenvalues. It is shown how one can construct nearly-optimal controls for the given system from the optimal solutions of the simpler reduced problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021739925071
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