1,645 research outputs found
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
The Convergent Generalized Central Paths for Linearly Constrained Convex Programming
The convergence of central paths has been a focal point of research on interior point methods. Quite detailed analyses have been made for the linear case. However, when it comes to the convex case, even if the constraints remain linear, the problem is unsettled. In [Math. Program., 103 (2005), pp. 63–94], Gilbert, Gonzaga, and Karas presented some examples in convex optimization, where the central path fails to converge. In this paper, we aim at finding some continuous trajectories which can converge for all linearly constrained convex optimization problems under some mild assumptions. We design and analyze a class of continuous trajectories, which are the solutions of certain ordinary differential equation (ODE) systems for solving linearly constrained smooth convex programming. The solutions of these ODE systems are named generalized central paths. By only assuming the existence of a finite optimal solution, we are able to show that, starting from any interior feasible point, (i) all of the generalized central paths are convergent, and (ii) the limit point(s) are indeed the optimal solution(s) of the original optimization problem. Furthermore, we illustrate that for the key example of Gilbert, Gonzaga, and Karas, our generalized central paths converge to the optimal solutions
Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization
This paper proposes an algorithmic framework for solving parametric
optimization problems which we call adjoint-based predictor-corrector
sequential convex programming. After presenting the algorithm, we prove a
contraction estimate that guarantees the tracking performance of the algorithm.
Two variants of this algorithm are investigated. The first one can be used to
solve nonlinear programming problems while the second variant is aimed to treat
online parametric nonlinear programming problems. The local convergence of
these variants is proved. An application to a large-scale benchmark problem
that originates from nonlinear model predictive control of a hydro power plant
is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure
A primal-dual flow for affine constrained convex optimization
We introduce a novel primal-dual flow for affine constrained convex
optimization problem. As a modification of the standard saddle-point system,
our primal-dual flow is proved to possesses the exponential decay property, in
terms of a tailored Lyapunov function. Then a class of primal-dual methods for
the original optimization problem are obtained from numerical discretizations
of the continuous flow, and with a unified discrete Lyapunov function,
nonergodic convergence rates are established. Among those algorithms, we can
recover the (linearized) augmented Lagrangian method and the quadratic penalty
method with continuation technique. Also, new methods with a special inner
problem, that is a linear symmetric positive definite system or a nonlinear
equation which may be solved efficiently via the semi-smooth Newton method,
have been proposed as well. Especially, numerical tests on the linearly
constrained - minimization show that our method outperforms the
accelerated linearized Bregman method
Set-valued State Estimation for Nonlinear Systems Using Hybrid Zonotopes
This paper proposes a method for set-valued state estimation of nonlinear,
discrete-time systems. This is achieved by combining graphs of functions
representing system dynamics and measurements with the hybrid zonotope set
representation that can efficiently represent nonconvex and disjoint sets.
Tight over-approximations of complex nonlinear functions are efficiently
produced by leveraging special ordered sets and neural networks, which enable
computation of set-valued state estimates that grow linearly in memory
complexity with time. A numerical example demonstrates significant reduction of
conservatism in the set-valued state estimates using the proposed method as
compared to an idealized convex approach
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