Authors:
Mazen Alamir,
Volume: 1, Page 742 Paper number 1119
Abstract:
A new algorithm for computing the solutions of nonlinear optimal and
robust H_(infinity) control problems is proposed. The algorithm is
based on the use of the collocation method to transform the PDE's into
ODE's. The later can be viewed as a perturbed version of some set of
ODE's that has an invariant sub-manifold and can Therefore be solved
using the post stabilization technique. Some convergence results are
given and several examples are presented.
Authors:
J. Alexander Fax,
Richard M. Murray,
Volume: 1, Page 748 Paper number 1774
Abstract:
In this paper, we consider the optimal control of time-scalable systems.
The time-scaling property is shown to convert the PDE associated with
the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE.
Solution of this PDE yields the value function at a fixed time, and
that solution can be scaled to find the value function at any point
in time. Furthermore, in certain cases the unscaled control law stabilizes
the system, and the unscaled value function acts as a Lyapunov function
for that system. The PDE is solved for the well-known example of the
nonholonomic integrator.
Authors:
Peter D. Roberts,
Victor M. Becerra,
Volume: 1, Page 754 Paper number 1262
Abstract:
A novel iterative procedure is described for solving non-linear optimal
control problems subject to differential algebraic equations. The procedure
iterates on an integrated modified linear quadratic model based problem
with parameter updating in such a manner that the correct solution
of the original non-linear problem is achieved. The resulting algorithm
has a particular advantage in that the solution is achieved without
the need to solve the differential algebraic equations . Convergence
aspects are discussed and a simulation example is described which illustrates
the performance of the technique.
Authors:
Rob L. Tousain,
Okko H. Bosgra,
Volume: 1, Page 760 Paper number 9602
Abstract:
Nonlinear Model Predictive Control (NMPC) is believed to play an important
role in improving the quality and flexibility of the production of
many chemical plants. More widespread application can be expected when
systematic solutions are found for modeling large-scale nonlinear processes
and for efficient solution of the dynamic optimization problems NMPC
entails. The control parametrization approach to dynamic optimization
solves the dynamic optimization problem as a Nonlinear Program using
e.g. the Sequential Quadratic Program (SQP) in the outer loop optimization
problem. In the SQP approach, a reduced space Quadratic program is
set up based on a quasi-Newton method estimate of the Hessian. We propose,
based on an investigation of the structure of the Hessian of the NMPC
problem, a different Hessian update procedure: part of the Hessian
is calculated explicitly and only the part that relates to the second
derivatives of the dynamics is estimated using a Hessian update. The
proposed method shows a large improvement in computational efficiency
for a semi-large-scale Poly-Ethylene reactor NMPC problem with 27 states
and 6 inputs with 15 parameters each.
Authors:
Toshiyuki Ohtsuka,
Volume: 1, Page 766 Paper number 1567
Abstract:
This paper proposes a fast algorithm for nonlinear receding horizon
control. The control input is updated by a differential equation to
trace the solution of an associated two-point boundary-value problem.
A linear equation involved in the differential equation is solved by
the generalized minimum residual (GMRES) method, one of the Krylov
subspace methods, with Jacobians approximated by forward differences.
The error in the entire algorithm is analyzed and is shown to be bounded
under mild conditions. The proposed algorithm is applied to a two-link
arm whose dynamics is highly nonlinear.
Authors:
Francesco Bullo,
W. Todd Cerven,
Volume: 1, Page 772 Paper number 1404
Abstract:
In this paper, we present algorithms for the design of feasible and
optimal trajectories of nonlinear control systems. We focus on stable
polynomial control systems linear in the controls. We prove existence
of local solutions near the minimum energy control for the linearized
system and we investigate provably convergent iterative schemes. Finally,
we formulate the trajectory optimization problem as a low dimensional
nonlinear program.
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