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  • CYBERNETICS  (4)
  • 1
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    Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces (1987)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
    Keywords: CYBERNETICS
    Type: NASA-CR-178302 , ICASE-87-31 , NAS 1.26:178302 , AD-A192764
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 2
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    Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case (1987)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.
    Keywords: CYBERNETICS
    Type: NASA-CR-178303 , ICASE-87-32 , NAS 1.26:178303
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  • 3
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    Optimal control of thermally coupled Navier Stokes equations (1994)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The optimal boundary temperature control of the stationary thermally coupled incompressible Navier-Stokes equation is considered. Well-posedness and existence of the optimal control and a necessary optimality condition are obtained. Optimization algorithms based on the augmented Lagrangian method with second order update are discussed. A test example motivated by control of transport process in the high pressure vapor transport (HVPT) reactor is presented to demonstrate the applicability of our theoretical results and proposed algorithm.
    Keywords: CYBERNETICS
    Type: NASA-CR-199714 , NAS 1.26:199714 , NIPS-95-06066 , Workshop on Optimal Control Design and Control; Apr 08, 1994 - Apr 09, 1994; Blacksburg, VA; United States
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  • 4
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    On nonconvergence of adjoint semigroups for control systems with delays (1988)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: The spline scheme of Banks and Kappel (1979) is used as an aproximation method for calculating optimal feedback gains for control systems governed by functional differential equations. It is shown that the adjoints of the spline-based approximation scheme for delay equations do not converge strongly.
    Keywords: CYBERNETICS
    Type: SIAM Journal on Control and Optimization (ISSN 0363-0129); 26; 1442-145
    Format: text
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