Nonlinear model predictive control is a thorough and rigorous introduction to nmpc for discretetime and sampleddata systems. Model predictive control mpc, also known as receding horizon control or moving horizon control, uses the range of control methods, making the use of an explicit dynamic plant model to predict the effect of future reactions of the manipulated variables on the output and the control signal obtained by minimizing the cost function 7. Pdf an infinite horizon model predictive control for stable. Model predictive control mpc, also known as receding horizon control or moving horizon control, uses the range of control methods, making the use of an explicit dynamic plant model to predict the effect.
Online optimization is possible because this class of problems is relatively easy to solve, but may. Dual mode control infinite horizon terminal constraint set. Model predictive control certaintyequivalent control constrained linearquadratic regulator in nite horizon model predictive control mpc with disturbance prediction. Model constraints stagewise cost terminal cost openloop optimal control problem openloop optimal solution is not robust must be coupled with online state model parameter update requires online solution for each updated problem analytical solution possible only in a few cases lq control. Based on a generated model of this system, we design a set of control input sequences iteratively at successive time steps over some horizon from a. There are various control design methods based on model predictive control concepts. The infinitehorizon cost is enforced using a terminal cost function obtained from. Infinitehorizon model predictive control for periodic tasks with contacts. In model predictive control, the prediction horizon, p is also an important consideration.
Model predictive control mpc is an advanced method of process control that is used to control a process while satisfying a set of constraints. Institute of robotics and cybernetics, faculty of electrical engineering and information technology. In standard linear model predictive control, the plant is modeled as a discrete linear system 4. Extended infinite horizon mpc process model in the incremental form. Works in practice, without formal analysis theory requires large infinite prediction horizon or. This paper presents an infinitehorizon differentiable linear quadratic mpc that can be learned. In section 4, asymptotic stability of the proposed nonlinear mpc scheme is discussed and. Infinitehorizon differentiable model predictive control. Institute of robotics and cybernetics, faculty of electrical engineering and information technology, slovak university of technology in bratislava, ilkovicova 3, 812 19 bratislava. The infinitehorizon cost is enforced using a terminal cost. A quasiinfinite horizon nonlinear model predictive. Control engineering 1521 technical detail tuning of mpc feedback control performance is an issue. Model predictive control is the family of controllers, makes the explicit use of model to obtain control signal. Parametrized infinitehorizon model predictive control for.
Infinitehorizon differentiable model predictive control deepai. The fundamental formulation of the linear model predictive controller is the following infinite dimensional convex quadratic program. The quasi infinite horizon approach to nonlinear model predictive control. This paper proposes a differentiable linear quadratic model predictive control mpc framework for safe imitation learning. Igcc power plant dispatch using infinitehorizon economic model predictive control benjamin p. The reason for its popularity in industry and academia is its capability of operating without. Energyplus building model usmall office building with 3 zones uchicago weather file during winter umodel predictive control. Rawlingsexistence and computation of infinite horizon model predictive control with active steadystate input constraints ieee transactions on automatic control, 48 6 2003, pp. Application of interiorpoint methods to model predictive. Robust model predictive control nominal model of the plant. Allgower, a quasiinfinite horizon nonlinear model predictive control scheme with guaranteed stability, automatica, vol. Parametrized infinitehorizon model predictive control for linear. Nonlinear model predictive control, or nmpc, is a variant of model predictive control mpc that is characterized by the use of nonlinear system models in the prediction. Application of interiorpoint methods to model predictive control.
A quasiinfinite horizon nonlinear model predictive control scheme 1207 state feedback. Most papers on constrained infinite horizon mpc rely on the as. Model predictive control mpc principles of modeling for cps fall 2018 madhur behl madhur. Infinite horizon model predictive control for periodic tasks with contacts. Receding horizon control introduces the essentials of a successful feedback strategy that has emerged in many industrial fields. Model predictive control part i utsa college of engineering. It has been in use in the process industries in chemical. Nonlinear model predictive control technique for unmanned. This combination of an offline solution of the infinite horizon problem with an online mpc controller is known as infinite horizon model predictive control ihmpc, and has previously been applied only to simple stabilization objectives. An introduction to modelbased predictive control mpc by stanislaw h. Infinite horizon model predictive control with no terminal. The reason for its popularity in industry and academia is its capability of operating without expert intervention for long periods. Model predictive control mpc originated in the late seventies and has developed considerably since then.
Pdf the quasiinfinite horizon approach to nonlinear model. Predictive control, robust stability, infinite horizon. The infinite horizon cost is enforced using a terminal cost function obtained from the discretetime algebraic riccati equation dare, so that the learned controller can be proven to be stabilizing in closedloop. Igcc power plant dispatch using infinite horizon economic model predictive control benjamin p. Estimates on the prediction horizon length in model predictive control illustrate how this generalization can be employed in order to further tighten the estimates on the horizon length. The term model predictive control does not designate a specific control strategy but rather an ample range of control methods which make explicit use of a model of the process to obtain the control signal by minimizing an objective function. A quasiinfinite horizon nonlinear model predictive control scheme. This control technique has been successfully applied to many different dynamic systems. Chmielewski1 department of chemical and biological engineering, illinois institute of technology, chicago, il 60616 the integrated gasification combined cycle igcc possesses a number of. Receding horizon control rhc has a number of advantages over other types of control. As the name implies, the model predictive control strategy also known as the receding horizon control is control method which is based on the sound knowledge of a systems model characteristics.
Model predictive control mpc has received widespread interest in both industry and academia since the technique was first proposed in the late 1970s by several researchers including. Based on these results, a procedure for systematically determining a terminal region and a terminal penalty matrix offline is sum marized. The idea behind this approach can be explained using an example of driving a car. If one chooses to hold the prediction horizon duration the product pt s constant, p must vary inversely with t s.
The term model predictive control does not designate a specific control strategy but rather an. Receding horizon control model predictive control for. Pdf an infinite horizon model predictive control for. Nonlinear model predictive control theory and algorithms. Finally, we use this quadratic approximation as the terminal cost of an online mpc. The infinite horizon cost is enforced using a terminal cost function obtained from the discretetime algebraic riccati equation dare, so that the learned controller can be. An introduction to modelbased predictive control mpc. Infinite horizon model predictive control robotics. Introduction model predictive control mpc is the most popular advanced control technique in the process industry. This combination of an offline solution of the infinitehorizon problem with an online mpc controller is known as infinite. Stability 2 of mpc 1 consider the system where f is continuously differentiable with respect to itsis continuously differentiable with respect to its arguments and f0,00.
The quasiinfinite horizon approach to nonlinear model predictive control. If n is large, the part of the problem for t n can be neglected. Igcc power plant dispatch using infinitehorizon economic. In practice, this is often intractable and therefore the prediction horizon is typically truncated leading to the standard finitehorizon mpc formulation, 1, where the.
Model predictive control receding horizon control implicitly defines the feedback law uk hxk analogy to chess playing my move the opponents move new state my move his move my move. Pdf we present a method that combines offline trajectory optimization and online model predictive control mpc, generating robust. At each time step, a finite horizon forecast is made from a predictive model of the system and the optimal. Introduct ion vac controllers generally do not use information on electricity price changes 1. Pdf infinitehorizon model predictive control for periodic tasks. In contrast to the standard, discretetime nitehorizon model. Chmielewski1 department of chemical and biological engineering, illinois institute of. Nmpc is interpreted as an approximation of infinite horizon optimal control so that important properties like closedloop stability, inverse optimality and suboptimality can be derived in a uniform manner.
This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. In section 2 mpc is introduced and the methodology proposed in 7, 9 is concisely summarized. The understanding of mpc properties has reached to a new level and has now built a framework that is. Model predictive control control theory mathematical. Pdf an overview of model predictive control semantic. Pdf infinitehorizon differentiable model predictive control. Works in practice, without formal analysis theory requires large infinite prediction horizon or terminal constraint additional tricks for a separate static optimization step integrating and unstable dynamics. An infinite horizon model predictive control for stable and integrating processes. The consequences of applying the parametric description to receding horizon control model predictive control are. Infinitehorizon model predictive control for periodic tasks. Estimates on the prediction horizon length in model predictive control illustrate how this generalization can be employed in order to further tighten the estimates on the horizon length from 7. In particular, recursive feasibility and closedloop stability are shown.
Index terms control system synthesis, model predictive control, infinite horizon optimal control, thermal variables control, energy management, optimization, linear matrix inequalities. Index termscontrol system synthesis, model predictive control, infinite horizon optimal control, thermal variables control, energy management, optimization, linear matrix inequalities. Existence and computation of infinite horizon model predictive. As in linear mpc, nmpc requires the iterative solution of optimal control problems on a finite prediction horizon. Introduction model predictive control refers to a control strategy in which a model of. Nmpc is interpreted as an approximation of infinitehorizon optimal control so. Introduction to model predictive control springerlink. The infinitehorizon cost is enforced using a terminal. Receding horizon control model predictive control for state. The fundamental formulation of the linear model predictive controller is the following infinitedimensional convex quadratic program. A quasiinfinite horizon nonlinear model predictive control scheme with.
Mpc model predictive control also known as dmc dynamical matrix control gpc generalized predictive control rhc receding horizon control control algorithms based on numerically solving an optimization problem at each step constrained optimization typically qp or lp receding horizon control. Pdf an overview of model predictive control semantic scholar. A quasiinfinite horizon nonlinear model predictive control. Implementation of a parametrized infinitehorizon model. Pdf the quasiinfinite horizon approach to nonlinear.
The vector xj represents the current estimate of the state at discrete time j, whereas xk represents the state at k sampling steps along the future. Based on these results, a procedure for systematically determining a terminal region and a terminal penalty matrix off. The infinite horizon cost is enforced using a terminal cost function. Jan 07, 2020 this paper proposes a differentiable linear quadratic model predictive control mpc framework for safe imitation learning. Infinitehorizon model predictive control for periodic. Model predictive control with linear models muske 1993. Index termsmodel predictive control mpc, optimal control, steady state constraints. Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial commercial activities on model predictive control mpc.