L. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay, K. Park, Numerical optimal control of parabolic PDEs using DASOPT, in: M. Gro tschel, S.O. Krumke, J. Rambau (Eds.), Large Scale Optimization with Applications, Part II, vol. 93, Springer, 1997, pp. 271-- 300.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Prett, Morari (1989) Mayne, Michalska (1990) Soeterboek (1992) Clarke (1994) Muske Edgar (1997) and Sutton Bitmead (1999) These techniques are related to those used in (essentially time invariant) distributed optimization problems, such as the optimization of bioartificial arteries (Petzold et al. 1997), the prediction of bone hardening due to applied periodic loading (Jacobs et al. 1997) and the optimization of airfoils for aerodynamic design (Reuther et al. 1996) In the active feedback control setting, the predictive control technique has found broad application and popular acceptance in ....

Petzold, L.R., Rosen, J.B., Gill, P.E., Jay, L.O., & Park K. 1997 Numerical optimal control of parabolic PDEs using DASOPT. In Large Scale Optimization with Applications. Part II: Optimal Design and Control (ed. L. Biegler, T. Coleman, A. Conn & F. Santosa). Springer.

....at a portion (depending on available storage) of the time steps; iterating on the nonlinear equations that update the states can then be integrated with updates of the design variables, a la SQP. For example, one might use a multiple shooting method for solving the system of DAEs (as was done in [36] for a time dependent heat equation) or a very high order method in time. Second, with the goal of reducing the number of optimization iterations, one might pursue incorporating second order derivatives for use in a Newton method. Our experience (for a problem in optimal boundary control of ....

L. Petzold, J. B. Rosen, P. E. Gill, L. O. Jay, and K. Park, Numerical optimal control of parabolic PDEs using DASOPT, Tech. Rep. NA 96-3, Department of Mathematics, University of California, San Diego, 1996.

.... Prett, Morari (1989) Mayne, Michalska (1990) Soeterboek (1992) Clarke (1994) Muske Edgar (1997) and Sutton Bitmead (1999) These techniques are related to those used in (essentially time invariant) distributed optimization problems, such as the optimization of bioartificial arteries (Petzold et al. 1997), the prediction of bone hardening due to applied periodic loading (Jacobs et al. 1997) and the optimization of airfoils for aerodynamic design (Reuther et al. 1996) In the active feedback control setting, the predictive control technique has found broad application and popular acceptance in ....

Petzold, L.R., Rosen, J.B., Gill, P.E., Jay, L.O., & Park K. 1997 Numerical optimal control of parabolic PDEs using DASOPT. In Large Scale Optimization with Applications. Part II: Optimal Design and Control (ed. L. Biegler, T. Coleman, A. Conn & F. Santosa). Springer.

....the form (1) or (2) There are many examples of optimization algorithms and implementations which use the structure of a particular problem in the class (1) or (2) See, e. g, the papers by Betts [1997] Betts and Frank [1994] Bock [1988] Gill, Murray, and Saunders [1997] Kupfer and Sachs [1992] Petzold, Rosen, Gill, Jay, and Park [1996], and Varvarezos, Biegler, and Grossmann [1994] However, in all cases either specific optimization algorithms are implemented for a specific problem or for a specific class of problems such as optimal control of ODEs or DAEs. The exchange of the optimization algorithm or the use of the ....

Petzold, L., Rosen, J. B., Gill, P. E., Jay, L. O., and Park, K. 1996. Numerical optimal control of parabolic PDEs using DASOPT. Na--96--1, Department of Mathematics, University of california, San Diego, La Jolla, CA.

....of the objective function and constraints with respect to the optimization variables. We compute these derivatives via di#erential algebraic equation (DAE) sensitivity software DASPKSO [8] Our basic algorithm and software for the optimal control of dynamical systems are described in detail in [9]. This basic multiple shooting type of strategy can work very well for small to moderate size ODE systems, and has an additional advantage that it is inherently parallel. However, for large scale ODE systems there is a problem because the computational complexity grows rapidly with the dimension ....

L. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay, K. Park, Numerical optimal control of parabolic PDEs using DASOPT, in: L. Biegler, T. Coleman, A. Conn, F. Santosa (Eds.), Large Scale Optimization with Applications, Part II: Optimal Design and Control, IMA Volumes in Mathematics and its Applications, Vol. 93, 1997, pp. 271--300.

No context found.

PETZOLD, L.R., ROSEN, J.B., GILL, P.E., JAY, L.O., AND PARK, K. Numerical Optimal Control of Parabolic PDEs using DASOPT. In Large Scale Optimization with Applications, Part II: Optimal Design and Control (1997), Biegler, L., Coleman, T., Conn, A., and Santosa, F., Ed., vol. 93 of IMA Volumes in Mathematics and its Applications, pp. 271-300. 10

....equations form a system of di#erential algebraic equations (DAE) The final element of optimal trajectory planning is the optimization algorithm itself. Here, the optimization algorithm is designed specifically to work with large systems of DAEs or ordinary di#erential equations (ODE) [1]. The optimal control algorithm transforms the dynamic optimization problem for the process transients to one of parameter optimization, which is then solved using sequential quadratic programming (SQP) software [2] This transformation is accomplished by a shooting approach where the original ....

.... di#erential algebraic equation (DAE) sensitivity software DASPKSO [10] The sensitivity equations to be solved by DASPKSO are generated via the automatic di#erentiation software ADIFOR [11] The basic algorithms and software for the optimal control of dynamical systems are described in detail in [1]. This basic multiple shooting type of strategy can work very well for small tomoderate size DAE systems, and has an additional advantage that it is inherently parallel. However, for large scale DAE systems there is a problem because the computational complexity grows rapidly with the dimension ....

L. Petzold, J. B. Rosen, P. E. Gill, L. O. Jay and K. Park, Numerical Optimal Control of Parabolic PDEs using DASOPT, Large Scale Optimization with Applications, Part II: Optimal Design and Control, Eds. L. Biegler, T. Coleman, A. Conn and F. Santosa, IMA Volumes in Mathematics and its Applications, Vol. 93, (1997), pp. 271-300.

No context found.

Petzold, L.R., J. B. Rosen, P. E. Gill, L. O. Jay and K. Park #1997# Numerical Optimal Control of Parabolic PDEs using DASOPT, Large Scale Optimization with Applications, Part II: Optimal Design and Control, Eds. L. Biegler, T. Coleman, A. Conn and F. Santosa, IMA Volumes in Mathematics and its Applications, 93, 271#300.

....makes it easier to monitor the performance of the optimizer. 4 Implementation and numerical results In our implementation, the continuous optimization is done via DASOPT, a code for parameter estimation and optimal control of differential algebraic systems which is currently under development [22]. This code solves the class of problems find u(t) and x(t) for t 0 t t f (10) to minimize J = Z t f t 0 L(x(t) u(t) t)dt V (x(t f ) 11) subject to f(t; x(t) x 0 (t) u(t) 0 (12) g(t; x(t) u(t) 0: 13) In the above, x is the state time history vector, u is the control time ....

L. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay and K. Park, Numerical Optimal Control of Parabolic PDEs Using DASOPT, Proc. IMA Workshop on LargeScale Optimization, 1996.

....SNOPT [8] which is based on sequential quadratic programming (SQP) methods. The SQP methods require a gradient and Jacobian matrix which are derivatives of the objective function and of the constraints with respect to the optimization variables. DASPKSO has been used to compute these derivatives [14]. One of the di culties for the optimization problems is that the solution output from the optimizer does not satisfy the consistent initial conditions required by DASPK. The consistent initial conditions must be computed rst before we start the next time step. An initialization algorithm for ....

L. R. Petzold, J. B. Rosen, P. E. Gill, L. O. Jay and K. Park, Numerical optimal control of parabolic PDEs using DASOPT, In Large Scale Optimization with Applications, Part II: Optimal Design and Control, Eds. L. Biegler, T. Coleman, A. Conn and F. Santosa, IMA Volumes in Mathematics and its Applications, 93, 271-300.

....of the objective function and constraints with respect to the optimization variables. We compute these derivatives via differential algebraic equation (DAE) sensitivity software DASPKSO [9] Our basic algorithm and software for the optimal control of dynamical systems are described in detail in [10]. This basic multiple shooting type of strategy can work very well for small tomoderate size ODE systems, and has an additional advantage that it is inherently parallel. However, for large scale ODE systems there is a problem because the computational complexity grows rapidly with the dimension of ....

L. Petzold, J. B. Rosen, P. E. Gill, L. O. Jay and K. Park, Numerical Optimal Control of Parabolic PDEs using DASOPT, Large Scale Optimization with Applications, Part II: Optimal Design and Control, Eds. L. Biegler, T. Coleman, A. Conn and F. Santosa, IMA Volumes in Mathematics and its Applications, Vol. 93, (1997), pp. 271-300.

No context found.

L. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay, K. Park, Numerical optimal control of parabolic PDEs using DASOPT, in: M. Gro tschel, S.O. Krumke, J. Rambau (Eds.), Large Scale Optimization with Applications, Part II, vol. 93, Springer, 1997, pp. 271-- 300.

No context found.

Petzold, L.; Rosen, J.B.; Gill, P.E.; Jay, L.O., Park, K.: Numerical optimal control of parabolic PDEs using DASOPT. In: L.T. Biegler et al. (eds.): LargeScale Optimization with Applications, Part II (Springer, 1997) 271--299.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC