Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints

Graichen, Knut; Kugi, Andreas

doi:10.1109/tac.2010.2057912

Cited by 127 publications

(79 citation statements)

References 22 publications

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“…A convergence and stability analysis regarding the projected gradient method as well as the (prematurely stopped) MPC scheme can be found in [9] and [12], respectively.…”

Section: B Optimality Conditions and Gradient Algorithmmentioning

confidence: 99%

The gradient based nonlinear model predictive control software GRAMPC

Käpernick

Graichen

2014

2014 European Control Conference (ECC)

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Abstract-This paper presents the nonlinear model predictive control (MPC) software GRAMPC (GRAdient based MPC -[graemp si:]) which is suited for controlling nonlinear systems with input constraints in the (sub)millisecond range. GRAMPC is based on a real-time solution strategy in combination with a (projected) gradient method. It is written in plain C with an interface to MATLAB/SIMULINK and also provides a graphical user interface (GUI) in MATLAB for a convenient MPC design and tuning. The performance of GRAMPC is demonstrated by two examples from different technical fields. Additionally, some comparison results with established MPC software are provided. I. INTRODUCTIONModel predictive control (MPC) has become a popular and powerful control methodology due to its ability to handle nonlinear multiple input systems as well as constraints [1], [2]. It is based on the solution of an underlying optimal control problem (OCP) which is solved online at each sampling instance and typically requires a considerable computational effort. This drawback usually limits the applicability of model predictive control to sufficiently slow or lowdimensional processes.There exist several MPC approaches and software packages to cope with the problem of real-time applicability for linear and nonlinear systems. The presented methods in [3], [4], [5] are suited for linear, time discrete systems and use efficient solution strategies, interior point approaches tailored to convex multistage problems and first order methods. The software environment ACADO Toolkit [6] provides a module to generate optimized C code for real-time MPC which can be used to control nonlinear systems. An alternative nonlinear MPC approach developed in [7] employs a continuation method to trace the solution of the optimality conditions over a single MPC step based on a generalized minimum residual (GMRES) method. This paper presents the portable and user-friendly nonlinear MPC software GRAMPC (GRAdient based MPC -[graemp si:]). It is based on a (projected) gradient method from optimal control [8], [9] and includes a real-time solution strategy for controlling nonlinear systems with input constraints and real-time demands. GRAMPC is written in plain C without the use of external libraries resulting in a small code size and a high level of portability in view of different operating systems and platforms. It is well suited to handle fast and high-dimensional systems and also provides a user-friendly integration to MATLAB/SIMULINK with an additional graphical user interface (GUI) in MATLAB

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“…A convergence and stability analysis regarding the projected gradient method as well as the (prematurely stopped) MPC scheme can be found in [9] and [12], respectively.…”

Section: B Optimality Conditions and Gradient Algorithmmentioning

confidence: 99%

The gradient based nonlinear model predictive control software GRAMPC

Käpernick

Graichen

2014

2014 European Control Conference (ECC)

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“…The optimal feedback control gain K * P can be determined by satisfying the Hamiltonian inequality (15). In other words, the choice of K P is to be adaptively tuned to minimize the system's tracking error.…”

Section: T)mentioning

confidence: 99%

“…A large body of research work has been conducted on Model Predictive Control (MPC) schemes that rely on the solution of an open-loop optimal control problem to predict the system behavior over a time horizon [10][11][12][13][14][15]. More specifically, M. Suruz Miah and Wail Gueaieb are with the School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada (e-mail: suruz.miah@uOttawa.ca and wgueaieb@eecs.uOttawa.ca).…”

Section: Introductionmentioning

confidence: 99%

Optimal time-varying P-controller for a class of uncertain nonlinear systems

Miah

Gueaieb

2014

Int. J. Control Autom. Syst.

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In this manuscript, an optimal time-varying P-controller is presented for a class of continuous-time underactuated nonlinear systems in the presence of process noise associated with systems' inputs. This is a state feedback control strategy where the optimization is performed on a time-varying feedback operator (herein called the feedback control gain). The main goal of the current manuscript is to provide a framework for multi-input multi-output nonlinear systems which yields a satisfactory tracking performance based on the optimal time-varying feedback control gain. Unlike other feedback control techniques that perform dynamic linearization of system models, the proposed time-varying P-controller provides the full-state feedback control to the original nonlinear system model. Hence, this P-controller guarantees global asymptotic statetracking. Furthermore, the bounded system's process noise is taken into consideration to measure the controller's robustness. The proposed P-controller is tested for its nonlinear trajectory tracking and fixed-point stabilization capabilities with two nonholonomic systems in the presence of actuators' noise.

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“…In the case of a free end point formulation as it is the case in (12), stability can be shown, e. g., if the terminal cost function ||Δθ(t i,f )|| 2 P represents a (local) control Lyapunov function [1,11,8] or if the horizon length t f is sufficiently large [5]. For the error dynamics (12b), which is time-dependent due to the feedforward trajectories, the rigorous proof of stability [3] as well as the consistency of this finite-dimensional control with the original infinite-dimensional system is subject of current research. In this contribution, the stability and performance of the receding horizon tracking controller are demonstrated by means of simulation studies in the following section.…”

Section: δU Fb (T) = δū(T; δθmentioning

confidence: 99%

Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

Utz

Graichen

Kugi

2013

IFIP Advances in Information and Communication Technology

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Abstract. The tracking control design for setpoint transitions of a quasi-linear diffusion-convection-reaction system with boundary control is considered. For this a suitable model-based feedforward control is determined that relies on the flatness-based parametrization of the control input. A receding horizon feedback control is added within a two-degreesof-freedom control scheme to account for disturbances, model inaccuracies, and input constraints. The tracking performance of this control scheme is shown by means of simulation studies.A large class of chemical reactors with an interaction of diffusive, convective, and reactive effects leads to infinite-dimensional mathematical models in the form of nonlinear boundary-controlled parabolic partial differential equations (PDEs) [6]. The control design for setpoint transitions of chemical reactors, e. g., for ignition, extinction, or grade-transitions constitutes a challenging problem. In this contribution, the well-known two-degrees-of-freedom (2DOF) control scheme is applied in order to tackle this control task. The basic idea consists in first designing a feedforward control to steer the system along prescribed trajectories. The trajectory planning and feedforward control are complemented with a state feedback tracking control stabilizing the system about the desired trajectories.In the literature, there exists a variety of concepts for the design of both feedforward and feedback tracking controllers. For the feedforward control design, approaches using the flatness concept [2] have found widespread attention. The flatness property allows for a parametrization of the state and input in terms of a so-called flat output and its time derivatives and therefore provides a systematic approach for feedforward control design. Originally proposed for finitedimensional systems, generalizations of the flatness concept have been successfully carried over to certain classes of PDEs, see, e. g., [7,10,12]. In these so-called late lumping approaches the parametrization is directly solved for the underlying PDE. In contrast, the early lumping approach to control design is based on a

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Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints

Cited by 127 publications

References 22 publications

The gradient based nonlinear model predictive control software GRAMPC

The gradient based nonlinear model predictive control software GRAMPC

Optimal time-varying P-controller for a class of uncertain nonlinear systems

Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

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