Model predictive control in this chapter we consider model predictive control mpc, an important advanced control technique for dif. The basic ideaof the method isto considerand optimizetherelevant variables, not. Chapter 3 nonlinear model predictive control in this chapter, we introduce the nonlinear model predictive control algorithm in a rigorous way. The problem considered in this chapter is to control a vehicle drivetrain in order to minimize its oscillations while coping with the timevarying delays. Process structurebased recurrent neural network modeling. Dixon abstractmodeling and compensation for friction effects has been a topic of considerable mainstream interest in motion control research. Lyapunovbased controller for a class of stochastic chaotic. Lyapunovbased economic model predictive control of. The objective of this paper is to control the angular speed in a model of a dc motor using different control strategies like model predictive control and linear quadratic regulator for comparison. This paper addresses the problem of faulttolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensorcontroller communication. Dynamical system theory lies at the heart of mathematical sciences and engineering. The snmpc approach aims to shape multivariate probability density function pdf of the stochastic states in presence of input and joint state chance constraints. In this work, we propose a lyapunov based model predictive control design for stabilization of nonlinear systems with both state. Nonlinear model predictive control theory and algorithms.
In this study, backstepping control integrated with lyapunov based model predictive control bsmpc is proposed for nonlinear systems in a strictfeedback form. Lyapunov based model reference adaptive control for aerial. Rossiter forthcoming titles material and device characterization measurements lev i. A new idea to construct stabilizing model predictive control is studied for a constrained system based on the adaptation of an existing stabilizing controller with a. Nmpc schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different nmpc. The basic mpc concept can be summarized as follows. This book was set in lucida using latex, and printed and bound by. In this work we propose a lyapunov based model predictive control design for stabilization of nonlinear systems with state and. Lyapunov based model reference adaptive control for aerial manipulation matko orsag, christopher korpela, stjepan bogdan, and paul oh abstractthis paper presents a control scheme to achieve dynamic stability in an aerial vehicle with dual multidegree of freedom manipulators using a lyapunov based model reference adaptive control.
Model predictive control college of engineering uc santa barbara. Lyapunov based predictive control methodologies for networked control systems. Process operational safety plays an important role in designing control systems for chemical processes. In this paper we focus on the implementation of mpc for constrained pwa systems. Output feedback lyapunovbased stochastic nonlinear. A faulttolerant lyapunovbased model predictive control mpc formulation that enforces the faulttolerant stabilization objective with reduced sensorcontroller communication needs is developed.
Lyapunovbased model predictive control for tracking of. Lyapunov based predictive control provides an attractive alternative, as it results in a lowcomplexity problem due to a unitary horizon and offers a stability guarantee. Fleming sensitivity of automatic control systems efim rozenwasser and rafael yusupov model based predictive control. From lower request of modeling accuracy and robustness to complicated process plants, mpc has been widely accepted in many practical fields. Over the past few years significant progress has been achieved in the field of nonlinear model predictive control nmpc, also referred to as receding horizon control or moving horizon control. Backstepping control integrated with lyapunovbased model. Lyapunovbased model predictive control springerlink. A complete solution manual more than 300 pages is available for course instructors. A cost function of the proposed model predictive controller is designed from the system stability point of view, inspired by the lyapunov control theory. Lyapunovbased tracking control in the presence of uncertain nonlinear parameterizable friction c. Model predictive control mpc can be dated back to the 1960s, and can now be regarded as a mature control method, which has had significant impact on industrial process control. Model predictive control theory and design rawlings, james b. Pdf lyapunovbased model predictive control for dynamic.
The virtual input of the first step is designed by solving the finitehorizon optimal control problem fhocp, and the real input is designed by the backstepping method. Stabilization of nonlinear systems with state and control. This paper presents neural lyapunov mpc, an algorithm to alternately train a lyapunov neural network and a stabilising constrained model predictive controller mpc, given a neural network model. Robust adaptive model predictive control of nonlinear systems. The lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained. Output feedback lyapunov model predictive control of stochastic nonlinear systems. To be meaningful, any statement about \robustness of a particular control algorithm must make reference to a speci c uncertainty range 1 morari 1994 reports that a simple database search for \ predictive control generated 128 references for the years 19911993. In order to take optimality considerations into account while designing saturated tracking controllers, a lyapunov based predictive tracking controller is developed, in which the contractive constraint is characterized by a backup global saturated tracking controller. A control lyapunov approach to predictive control of hybrid. While the paradigm of event based communication has been analyzed in great detail in the context of networked control systems it has not been applied to distributed model predictive control. The lyapunovbased controllers define a general class of feedback control laws which result in the closedloop system achieving negative definiteness of the drift of the lyapunov function derivative over the set.
Distributed model predictive control with eventbased. Dp control, and a lyapunovbased backstepping nonlinear control law is designed. Jan 12, 2018 economic nonlinear model predictive control. A new kind of nonlinear model predictive control algorithm enhanced by control lyapunov functions. The control lyapunov function is used to test whether a system is feedback stabilizable, that is whether for any state x there exists a control, such that the system can be brought to the zero state by applying the control u. Suppose that we wish to control a multipleinput, multipleoutput process while satisfying inequality constraints on the. Abstract in this work, we propose the integration of koopman operator methodology with lyapunov. We focus on systems which are difficult to stabilize via classical model predictive control.
Shaping the state probability density functions edward a. A new idea to construct stabilizing model predictive control is studied for a constrained system based on the adaptation of an existing stabilizing controller with a control lyapunov function. Model predictive control mpc refers to a class of control algorithms in which a dynamic process model is used to predict and optimize process performance. Control lyapunov functions for adaptive nonlinear stabilization. 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. Lyapunov based predictive control of vehicle drivetrains.
Lyapunovbased model predictive control of nonlinear systems. Due to the optimization essential, lmpc can explicitly consider the practical constraints on the real system and generate the best possible dp control. First and foremost, the algorithms and highlevel software available for solving challenging nonlinear optimal control problems have advanced signi. In this paper a lyapunovbased model predictive control lmpc method to control knee extension during an inputdelayed neuromuscular electrical stimulation. More formally, suppose we are given an autonomous dynamical system. Lyapunovbased model predictive control of an input delayed. Pdf model predictive control with control lyapunov. In this study, backstepping control integrated with lyapunovbased model predictive control bsmpc is proposed for nonlinear systems in a strictfeedback form. Summary the challenges of strong nonlinearities, system constraints, disturbances, and uncertainty are ubiquitous in the modern control landscape, from chemical reactors to fighter jet airframes. The nonlinear sliding model dp control can be found in 7. Model predictive control with control lyapunov function support. In this work, we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty.
Model predictive control of hybrid systems of maurice heemels. Forecasttriggered model predictive control of constrained. Pdf in this work, we focus on model predictive control of nonlinear systems subject to data. In this work, we focus on model predictive control of nonlinear systems subject to data losses. In this paper, a new lyapunov based model predictive controller is proposed for a 7level packed ucell puc7 gridconnected inverter. This work presents an output feedback stochastic nonlinear model predictive control snmpc approach for a class of nonlinear systems with unbounded stochastic uncertainties. Still, the presence of hard constraints and timevarying delays makes standard lyapunov mpc approaches over conservative. Since real chaotic systems have undesired randomlike behaviors which have also been deteriorated by environmental noise, chaotic systems are modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of wiener process which. Lyapunovbased model predictive control of a puc7 grid. Nonlinear dynamical systems and control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on lyapunov based methods. This book offers readers a thorough and rigorous introduction to nonlinear model predictive control nmpc for discretetime and sampleddata systems.
Neural lyapunov model predictive control request pdf. This paper presents a novel lyapunovbased model predictive control lmpc framework for the dynamic positioning dp control of autonomous underwater vehicles auvs. Jul 20, 2017 this paper studies the tracking problem of nonholonomic wheeled robots subject to control input constraints. A stochastic lyapunov based controller is first utilized to characterize a region of the statespace. Abstractin this work, we focus on a class of general nonlinear systems and design a model predictive control mpc scheme which is capable of optimizing. Lyapunovbased model predictive control for dynamic. Preliminaries controlled dynamical system let us consider a discretetime, timeinvariant, deterministic dynamical system of the form. Nonlinear model predictive control towards new challenging. Robust control systems and genetic algorithms mo jamshidi, renato a krohling, leandro dos santos coelho, and peter j. As the guide for researchers and engineers all over the world concerned with the latest. In a recent work, we proposed a lyapunov based model predictive control formulation that provides guaranteed stability from an explicitly characterized set of initial conditions in the presence of input constraints.
This is motivated by the fact that pwa systems can model a broad class of. Many of the control schemes for hybrid systems are based on optimal control, e. Sep 01, 2012 read lyapunov based model predictive control of stochastic nonlinear systems, automatica on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In this work, physics based recurrent neural network rnn modeling approaches are proposed for a general class of nonlinear dynamic process systems t. A control lyapunov approach to predictive control of hybrid systems 1 discrete states. Lyapunovbased model predictive control of stochastic. Control solutions based on mpc are particularly powerful due to their potential to. Motivated by this, in this work, we develop a process safeness index based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. In a recent work, 17, we proposed a lyapunov based model predictive control formulation that provided guaranteed stability from an explicitly characterized set of initial conditions in the presence of input constraints. The book consists of selected papers presented at the international workshop on assessment an future directions of nonlinear model predictive control that took. This result was further relaxed in 2,3 towards using a terminal inequality constraint on the continuous states. Lyapunovbased predictive control methodologies for networked.
However, such relaxations were achieved in the absence of discrete states. Safeness indexbased economic model predictive control of. This study presents a general control law based on lyapunovs direct method for a group of wellknown stochastic chaotic systems. Pdf lyapunovbased model predictive control of nonlinear. It is applied in many control systems and has been extended to include nonlinear dynamics and nonconvex constraints. Lyapunovbased stochastic nonlinear model predictive control.
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