The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Moritz Diehl - One of the best experts on this subject based on the ideXlab platform.
-
a partially tightened real time Iteration Scheme for nonlinear model predictive control
Conference on Decision and Control, 2017Co-Authors: Andrea Zanelli, Rien Quirynen, Gianluca Frison, Moritz DiehlAbstract:In this paper, a strategy is proposed to reduce the computational burden associated with the solution of problems arising in nonlinear model predictive control. The prediction horizon is split into two sections and the constraints associated with the terminal one are tightened using a barrier formulation. In this way, when using the Real-Time Iteration Scheme, variables associated with such stages can be efficiently eliminated from the quadratic subproblems by a single backward Riccati sweep. After eliminating the tightened stages, a quadratic problem with a reduced horizon is solved where the original constraints are used. The solution is then expanded to the full horizon with a single forward Riccati sweep. By doing so, the online computational burden associated with the solution of the optimization problems can be largely reduced. Numerical results are reported where, using the proposed Scheme, a speedup of about one order of magnitude can be achieved without compromising closed-loop performance.
-
Convergence Guarantees for Moving Horizon Estimation Based on the Real-Time Iteration Scheme
IEEE Transactions on Automatic Control, 2014Co-Authors: Andrew Wynn, Milan Vukov, Moritz DiehlAbstract:In this note, conditions are proven under which a realtime implementable moving horizon estimation (MHE) Scheme is locally convergent. Specifically, the real-time Iteration Scheme of [17] is studied in which a single Gauss-Newton Iteration is applied to approximate the solution to the respective MHE optimization problem at each timestep. Convergence is illustrated by a challenging small scale example, the Lorenz attractor with an unknown parameter. It is shown that the performance of the proposed real-time MHE algorithm is nearly identical to a fully converged MHE solution, while its fixed execution time per sample would allow one to solve 30 000 MHE problems per second on current hardware.
-
nominal stability of real time Iteration Scheme for nonlinear model predictive control
IEE Proceedings - Control Theory and Applications, 2005Co-Authors: Moritz Diehl, Hans Bock, Rolf Findeisen, Frank Allgower, Johannes P SchloderAbstract:A Newton-type method is investigated for online optimisation in nonlinear model predictive control, the so-called real-time Iteration Scheme. Only one Newton-type Iteration is performed per sampling instant in this Scheme, and control of the system and the solution of the optimal control problem are performed in parallel. In the resulting combined dynamics of system and optimiser, the actual feedback control in each step is based on the current solution estimate, and the solution estimates are at each sampling instant refined and transferred to the next optimisation problem by a specially designed transition. This approach yields an efficient online optimisation algorithm that has already been successfully tested in several applications. Due to the close dovetailing of system and optimiser dynamics, however, stability of the closed-loop system is not implied by standard nonlinear model predictive control results. A proof of nominal stability of the Scheme is given which builds on concepts from both NMPC stability theory and convergence analysis of Newton-type methods. The principal result is that, under some reasonable assumptions, the combined system-optimiser dynamics can be guaranteed to converge towards the origin from significantly disturbed system-optimiser states.
-
a real time Iteration Scheme for nonlinear optimization in optimal feedback control
Siam Journal on Control and Optimization, 2005Co-Authors: Moritz Diehl, Hans Bock, Johannes P SchloderAbstract:An efficient Newton-type Scheme for the approximate on-line solution of optimization problems as they occur in optimal feedback control is presented. The Scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process. The contractivity of this real-time Iteration Scheme is proven, and a bound on the loss of optimality---compared with the theoretical optimal solution---is given. The robustness and excellent real-time performance of the method is demonstrated in a numerical experiment, the control of an unstable system, namely, an airborne kite that shall fly loops.
Christian Ebenbauer - One of the best experts on this subject based on the ideXlab platform.
-
an Iteration Scheme with stability guarantees for proximity moving horizon estimation
European Control Conference, 2020Co-Authors: Meriem Gharbi, Christian EbenbauerAbstract:In this paper, we propose and investigate an Iteration Scheme for proximity moving horizon state estimation of discrete-time linear systems subject to polytopic constraints. Based on a relaxed barrier function formulation of the underlying optimization problem, the state estimate is computed at each time instant after a limited number of optimization Iterations. We establish sufficient conditions for the stability of the resulting estimation error. A simulation example demonstrates the computational efficiency of the proposed Scheme and illustrates its satisfactory performance in comparison with fully converged proximity moving horizon estimators.
-
a stabilizing Iteration Scheme for model predictive control based on relaxed barrier functions
Automatica, 2017Co-Authors: Christian Feller, Christian EbenbauerAbstract:Abstract We propose and analyze a stabilizing Iteration Scheme for the algorithmic implementation of model predictive control for linear discrete-time systems subject to polytopic input and state constraints. The required on-line optimization makes use of a relaxed barrier function based problem formulation and performs only a limited, possibly small, number of optimization algorithm Iterations between two consecutive sampling instants. The optimization algorithm dynamics as well as the resulting suboptimality of the applied control input are taken into account explicitly in the stability analysis, and the origin of the resulting overall closed-loop system, consisting of state and optimization algorithm dynamics, is proven to be asymptotically stable. The corresponding constraint satisfaction properties are also analyzed. Both the theoretical results and a presented numerical example illustrate the fact that asymptotic stability as well as a satisfactory closed-loop performance may be achieved independently of the number of optimization algorithm Iterations, thus leading to a novel class of stabilizing MPC algorithms.
-
a stabilizing Iteration Scheme for model predictive control based on relaxed barrier functions
arXiv: Optimization and Control, 2016Co-Authors: Christian Feller, Christian EbenbauerAbstract:We propose and analyze a stabilizing Iteration Scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called relaxed logarithmic barrier functions. The required on-line optimization is based on warm starting and performs only a limited, possibly small, number of optimization algorithm Iterations between two consecutive sampling instants. The optimization algorithm dynamics as well as the resulting suboptimality of the applied control input are taken into account explicitly in the stability analysis, and the origin of the resulting overall closed-loop system, consisting of state and optimization algorithm dynamics, is proven to be asymptotically stable. The corresponding constraint satisfaction properties are also analyzed. The theoretical results and a presented numerical example illustrate the fact that asymptotic stability as well as a satisfactory closed-loop performance can be achieved by performing only a single optimization algorithm Iteration at each sampling step.
Johannes P Schloder - One of the best experts on this subject based on the ideXlab platform.
-
fast nonlinear model predictive control with an application in automotive engineering
Lecture Notes in Control and Information Sciences, 2009Co-Authors: Jan Albersmeyer, Hans Bock, Dorte Beigel, Christian Kirches, Leonard Wirsching, Johannes P SchloderAbstract:Although nonlinear model predictive control has become a well-established control approach, its application to time-critical systems requiring fast feedback is still a major computational challenge. In this article we investigate a new multi-level Iteration Scheme based on theory and algorithmic ideas from [2], and extending the idea of real-time Iterations as presented in [4]. This novel approach takes into account the natural hierarchy of different time scales inherent in the dynamic model. Applications from aerodynamics and chemical engineering have been successfully treated. In this contribution we apply the investigated multi-level Iteration Scheme to fast optimal control of a vehicle and discuss the computational performance of the Scheme.
-
nominal stability of real time Iteration Scheme for nonlinear model predictive control
IEE Proceedings - Control Theory and Applications, 2005Co-Authors: Moritz Diehl, Hans Bock, Rolf Findeisen, Frank Allgower, Johannes P SchloderAbstract:A Newton-type method is investigated for online optimisation in nonlinear model predictive control, the so-called real-time Iteration Scheme. Only one Newton-type Iteration is performed per sampling instant in this Scheme, and control of the system and the solution of the optimal control problem are performed in parallel. In the resulting combined dynamics of system and optimiser, the actual feedback control in each step is based on the current solution estimate, and the solution estimates are at each sampling instant refined and transferred to the next optimisation problem by a specially designed transition. This approach yields an efficient online optimisation algorithm that has already been successfully tested in several applications. Due to the close dovetailing of system and optimiser dynamics, however, stability of the closed-loop system is not implied by standard nonlinear model predictive control results. A proof of nominal stability of the Scheme is given which builds on concepts from both NMPC stability theory and convergence analysis of Newton-type methods. The principal result is that, under some reasonable assumptions, the combined system-optimiser dynamics can be guaranteed to converge towards the origin from significantly disturbed system-optimiser states.
-
a real time Iteration Scheme for nonlinear optimization in optimal feedback control
Siam Journal on Control and Optimization, 2005Co-Authors: Moritz Diehl, Hans Bock, Johannes P SchloderAbstract:An efficient Newton-type Scheme for the approximate on-line solution of optimization problems as they occur in optimal feedback control is presented. The Scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process. The contractivity of this real-time Iteration Scheme is proven, and a bound on the loss of optimality---compared with the theoretical optimal solution---is given. The robustness and excellent real-time performance of the method is demonstrated in a numerical experiment, the control of an unstable system, namely, an airborne kite that shall fly loops.
Binayak S Choudhury - One of the best experts on this subject based on the ideXlab platform.
-
random mann Iteration Scheme
Applied Mathematics Letters, 2003Co-Authors: Binayak S ChoudhuryAbstract:In the present note, a random Iteration is constructed and it is proved that if the Iteration is convergent, it will converge to a random fixed point of a random operator in Hilbert spaces provided that the random operator satisfies a certain contractive inequality. The Iteration is a random version of Mann Iteration.
-
convergence of an Iteration leading to a solution of a random operator equation
Journal of Applied Mathematics and Stochastic Analysis, 1999Co-Authors: Binayak S Choudhury, M RayAbstract:In the present paper, we define a random Iteration Scheme and consider its convergence to a solution of a random operator equation. There is also a related fixed point result.
-
convergence of a random Iteration Scheme to a random fixed point
Journal of Applied Mathematics and Stochastic Analysis, 1995Co-Authors: Binayak S ChoudhuryAbstract:This paper discusses the convergence of random Ishikawa Iteration Scheme to a random fixed point for a certain class of random operators.
C H Chang - One of the best experts on this subject based on the ideXlab platform.
-
Iteration Scheme for implicit calculations of kinetic and equilibrium chemical reactions in fluid dynamics
Journal of Computational Physics, 1995Co-Authors: John D Ramshaw, C H ChangAbstract:An Iteration Scheme for the implicit treatment of equilibrium chemical reactions in partial equilibrium flow has previously been described (J. D. Ramshaw and A. A. Amsden, J. Comput. Phys.59, 484 (1985); 71 , 224 (1987)). Here we generalize this Scheme to kinetic reactions as well as equilibrium reactions. This extends the applicability of the Scheme to problems with kinetic reactions that are fast in some regions of the flow field but slow in others. The resulting Scheme thereby provides a single unified framework for the implicit treatment of an arbitrary number of coupled equilibrium and kinetic reactions in chemically reacting fluid flow.
