A Toolchain for Solving Dynamic Optimization Problems Using Symbolic and Parallel Computing (original) (raw)
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IFAC-PapersOnLine, 2017
In nonlinear model predictive control (NMPC), a control task is approached by repeatedly solving an optimal control problem (OCP) over a receding horizon. Popularly, the OCP is approximated with a finite-dimensional nonlinear program (NLP). Since computing the solution of an NLP can be a complex and time-consuming task, tailored optimization algorithms have emerged to (approximately) solve the NLPs. Most methods rely on repeatedly solving a quadratic approximation of the NLP. Since computing this approximation is generally computationally demanding, it can form a bottelenck in obtaining a real-time applicable control law. This paper proposes DOPUS, a novel update scheme for the quadratic approximation of the NLP. DOPUS exploits the structure of the NLP and the repeated nature at which it is solved, to reduce the number of computations at the price of a small reduction of the convergence speed. Foreseen application areas include (economic) NMPC for fast-changing control tasks and fast time-varying systems. The convergence properties of DOPUS are studied and the performance is illustrated in a numerical case study considering a control task for a planar robot arm.
Recent Advances in Quadratic Programming Algorithms for Nonlinear Model Predictive Control
Vietnam Journal of Mathematics, 2018
Over the past decades, the advantages of optimization-based control techniques over conventional controllers inspired developments that enabled the use of model predictive control (MPC) in applications with very high sampling rates. Since at the heart of most linear and nonlinear MPC controllers resides a quadratic programming (QP) solver, the implementation of efficient algorithms that exploit the underlying problem structure drew the attention of many researchers and the progress in the field has been remarkable. The aim of this paper is to summarize the main algorithmic advances in the field and to provide a consistent benchmark between a selection of software tools that have been recently developed. The code that was used for the simulations is publicly available for readers that wish to reproduce the results or test the benchmarked solvers on their own nonlinear MPC applications. Keywords Quadratic programming • Optimal control • Numerical methods Mathematics Subject Classification (2010) 90C20 • 49J20 • 49M15 This article is dedicated to the 70th birthday of Professor Hans Georg Bock, whose seminal contributions in the field of structure-exploiting real-time optimization algorithms inspired most of the reviewed developments.
Development of efficient algorithms for model predictive control of fast systems
Nonlinear model predictive control (NMPC) has been considered as a promising control algorithm which is based on a real-time solution of a nonlinear dynamic optimization problem. Nonlinear model equations and controls as well as state restrictions are treated as equality and inequality constraints of the optimal control problem. However, NMPC has been applied mostly in relatively slow processes until now, due to its high computational expense. Therefore, computation time needed for the solution of NMPC leads to a bottleneck in its application to fast systems such as mechanical and/or electrical processes.
A software toolbox for the dynamic optimization of nonlinear processes
2005
This contribution describes the development and implementation of a novel software toolbox, NDOT, for the dynamic optimization (open loop optimal control) of nonlinear processes. This modular and flexible toolbox combines the control vector parameterization approach with a number of local and global nonlinear programming solvers and suitable dynamic simulation methods. NDOT is able to solve dynamic optimization problems for both lumped and distributed nonlinear processes. Its performance (robustness and efficiency) is illustrated considering a representative set of nonlinear (lumped and distributed) benchmark problems.
Efficient nonlinear model predictive control
2002
The growing interest in model predictive control for nonlinear systems, also called NMPC, is motivated by the fact that today's processes need to be operated under tighter performance specifications to guarantee profitable and environmentally safe production. One of the remaining essential problems for NMPC is the high on-line computational load. At each sampling instant, a nonlinear optimal control problem must be solved. In this paper, we summarize recent results showing the practical applicability of NMPC for process control. We show how recent advances in NMPC theory and dynamic optimization can be used to make the real-time application of NMPC feasible even for high dimensional problems. As an application example the real-time control of a high purity distillation column is considered.
New optimization methods in predictive control
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This thesis is mainly concerned with the efficient solution of a linear discrete-time finite horizon optimal control problem (FHOCP) with quadratic cost and linear constraints on the states and inputs. In predictive control, such a FHOCP needs to be solved online at each sampling instant. In order to solve such a FHOCP, it is necessary to solve a quadratic programming (QP) problem. Interior point methods (IPMs) have proven to be an efficient way of solving quadratic programming problems. A linear system of equations needs to be solved in each iteration of an IPM. The ill-conditioning of this linear system in the later iterations of the IPM prevents the use of an iterative method in solving the linear system due to a very slow rate of convergence; in some cases the solution never reaches the desired accuracy. A new well-conditioned IPM, which increases the rate of convergence of the iterative method is proposed. The computational advantage is obtained by the use of an inexact Newton ...
Real time optimization (RTO) with model predictive control (MPC
This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load.
Journal of Process Control, 2002
Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented. #