The motivation for considering this problem is provided by wireless networked control systems and control of nonlinear systems under asynchronous measurement sampling. Lyapunovbased model predictive control of nonlinear systems. Control lyapunovbarrier functionbased model predictive control of. Feedback linearisation, differential flatness, control lyapunov functions, output. For access to this article, please select a purchase option. It is the first monograph to cover approaches both with and without terminal constraints and end penalties, and turnpikedissipativity based settings as well as lyapunov. Model predictive control mpc is an advanced method of process control that is used to control a process while satisfying a set of constraints. The lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained. Performance and lyapunov stability of a nonlinear path following guidance method. Summary of contributions in this paper, we present neural lyapunov mpc, an algorithmic framework that obtains a singlestep horizon model predictive controller mpc for lyapunov based control of a nonlinear deterministic system with constraints. This book was set in lucida using latex, and printed and bound by.
A control lyapunov approach to predictive control of hybrid systems 1 discrete states. 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. We justify the choice of a unitary horizon by using an imperfect forward model. Enhanced stability regions for model predictive control of. The ordinary lyapunov function is used to test whether a dynamical system is stable more.
This book collates the important results which have emerged in the field of nonlinear model based predictive control. Economic machinelearningbased predictive control of. The book is geared towards researchers and practitioners in the area of control engineering and control. Lyapunovbased stochastic nonlinear model predictive. Process operational safety plays an important role in designing control systems for chemical processes. This is motivated by the fact that pwa systems can model. The problem considered in this chapter is to control a vehicle drivetrain in order to. A stochastic lyapunov based controller is first utilized to characterize a region of the statespace. 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 this work, we propose the integration of koopman operator methodology with lyapunov. Economic nonlinear model predictive control provides a concise overview of different approaches on the question of stability and optimality in different formulations of empc. Model predictive control of nonlinear parameter varying systems via receding horizon control lyapunov functions, m. This book offers readers a thorough and rigorous introduction to nonlinear model predictive control nmpc for discretetime and sampleddata systems. Lyapunovbased predictive control methodologies for networked control systems.
Lyapunov based model predictive control for dynamic positioning of autonomous underwater vehicles chao shen 1, yang shi, brad buckham abstractthis paper presents a novel lyapunov based mod. The lyapunov based mpc lmpc is briefly summarized in this subsection by referring to 23. Lyapunovbased model predictive control of nonlinear. On the stability of quadratic forms based model predictive. Robust adaptive model predictive control of nonlinear systems. Model predictive control based integral lineofsight curved path following for unmanned aerial vehicle. In this work, we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty. In this paper we focus on the implementation of mpc for constrained pwa systems. More formally, suppose we are given an autonomous dynamical system. Lyapunovbased controller for a class of stochastic chaotic. This work considers distributed predictive control of large. 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. Download economic model predictive control pdf books pdfbooks.
Independently of the type of control system architecture and type of control algorithm utilized, a common. Since real chaotic systems have undesired randomlike behaviors which. Economic model predictive control theory, formulations. The motivation for considering this problem is provided by wireless networked control systems and control of nonlinear systems under asynchronous. This result was further relaxed in 2,3 towards using a terminal inequality constraint on the continuous states. The lmpc design provides an explicitly characterized region from. This work considers the problem of predictive control of nonlinear process systems subject to input constraints. The truetime simulation results are presented in section 4, some preliminary realtime results are illustrated in section 5 and concluding remarks are summarized in section 6. Lyapunov function stability region model predictive control input constraint. Mpc model predictive control also known as dmc dynamical matrix control. Pdf in this work, we focus on model predictive control of nonlinear systems subject to data. This study presents a general control law based on lyapunov s direct method for a group of wellknown stochastic chaotic systems. Backstepping control integrated with lyapunovbased model.
Jan 12, 2018 economic nonlinear model predictive control provides a concise overview of different approaches on the question of stability and optimality in different formulations of empc. Under the assumption of stabilizability of the origin of the stochastic nonlinear system via a stochastic lyapunov. A new kind of nonlinear model predictive control algorithm enhanced by control lyapunov. Incorporating control lyapunovbarrier functions into mpc to allow for generality in defining unsafe regions. This study presents a general control law based on lyapunovs direct method for a group of wellknown stochastic chaotic systems. Performance and lyapunov stability of a nonlinear path. Mpc is a popular control strategy based on using a model to. Lyapunovbased model predictive control for dynamic.
This book presents general methods for the design of economic model predictive control empc systems for broad classes of nonlinear systems that address key theoretical and practical. Economic model predictive control of stochastic nonlinear. Lyapunovbased model predictive control of stochastic. The authors proposed solution incorporates a control lyapunov function clf into a distributed model predictive control scheme. 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. In addition to being mathematically rigorous, these methods accommodate key practical issues, for example, direct optimization of process economics, timevarying economic cost functions and computational efficiency. 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. Lyapunov based stochastic nonlinear model predictive control. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. Lyapunov based model reference adaptive control for aerial. Pdf model predictive control with control lyapunov function.
Part of the lecture notes in control and information sciences book series. 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. These properties however can be satisfied only if the underlying model used for prediction of. Lyapunovbased controller for a class of stochastic. Distributed model predictive control with saturated inputs. Mar 01, 2000 the book consists of selected papers presented at the international symposium on nonlinear model predictive control assessment and future directions, which took place from june 3 to 5, 1998, in ascona, switzerland. 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. Nonlinear model predictive control is primarily aimed at academic researchers and practitioners working in control and optimisation but the text is selfcontained featuring background material on infinitehorizon optimal control and lyapunov stability theory which makes the book accessible to graduate students of control engineering and applied. In proceedings of the 50th ieee conference on decision and control and european control. 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.
The problem considered in this chapter is to control a vehicle drivetrain in order to minimize its oscillations while coping with the timevarying delays. Specifically, considering the input constraints, a constrained control lyapunov. Lyapunovbased model predictive control lmpc scheme 3335 see also 36, 37 based on uniting receding horizon control with control lyapunov functions, because it allows for an explicit characterization of the stability region and a reduced complexity optimization problem. Lyapunov based predictive control of vehicle drivetrains. It fulfills the gap between the existing centralized lyapunov. Distributed lyapunovbased model predictive control for. Lyapunov based tools are used to develop control law independent characterizations of the stability region and this characterization is exploited via the constraints handling capabilities of model. In this work, we focus on model predictive control of nonlinear systems subject to data losses. The controller synthesis method used in this work is lyapunovbased model. Model predictive control provides high performance and safety in the form of constraint satisfaction. Neural lyapunov model predictive control where v netx is a lipschitz feedforward network that produces a n v n xmatrix. Based upon the piecewise affine pwa model of closedloop model predictive control mpc system and lyapunov functions, stability analysis of the closed loop mpc system is studied. Pwa based stability analysis of model predictive control. Safe model based reinforcement learning understand model and learning dynamics algorithm to safely acquire data and optimize task define safety, analyze a model for safety rkhs gaussian processes lyapunov stability model predictive control.
In this work, a lyapunov based economic model predictive control lempc method is developed to address economic optimality and closedloop stability of nonlinear systems using machine learning based. The book consists of selected papers presented at the international symposium on nonlinear model predictive control assessment and future directions, which took place from june 3 to 5, 1998, in ascona, switzerland. 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. Lyapunovbased predictive control methodologies for. The proposed controller consists of a lyapunov based hybrid model predictive control based on mixed logical dynamical mld framework. In control theory, a controllyapunov function is a lyapunov function for a system with control inputs. Lyapunovbased model predictive control of a puc7 grid.
Lyapunovbased predictive control methodologies for networked. Lyapunovbased stochastic nonlinear model predictive control. Realtime adaptive machinelearningbased predictive control. Safeness indexbased economic model predictive control of. Shaping the state probability density functions edward a. Many of the control schemes for hybrid systems are based on model predictive control mpc, e. Distributed lyapunov based model predictive control for collision avoidance of multiagent formation. Nmpc schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different nmpc variants. In proceedings of the 50th ieee conference on decision and control and european control conference, pages 46464653, orlando, florida, 2011. In recent years it has also been used in power system balancing models and in power electronics. Chapter in bookreportconference proceeding chapter.
Lyapunov based model predictive control of nonlinear systems subject to data losses abstract. Independently of the type of control system architecture and type of control. In this paper, we propose a control lyapunov barrier function based model predictive control clbfmpc method for solving the problem of stabilization of nonlinear systems with input constraint satisfaction and guaranteed safety for all times. A control lyapunov approach to predictive control of. The book presents stateoftheart methods for the design of economic model predictive control systems for chemical processes. Nonlinear model predictive control is primarily aimed at academic researchers and practitioners working in nonlinear control but the text is selfcontained featuring background material on infinitehorizon optimal control and lyapunov stability theory which makes the book accessible to graduate and advanced undergraduate students of control. Jul 24, 2019 we present a machine learning based predictive control scheme that integrates an online update of the recurrent neural network rnn models to capture process nonlinear dynamics in the presence of model uncertainty. Download economic model predictive control pdf books. May 23, 2012 a highlevel model predictive control guidance law for unmanned aerial vehicles an iterative model predictive control algorithm for uav guidance ieee transactions on aerospace and electronic systems, vol. Lyapunov based predictive control of vehicle drivetrains over. Distributed lyapunovbased mpc eindhoven university of. The koopman operator enables global linear representations of nonlinear dynamical systems. Dynamical system theory lies at the heart of mathematical sciences and engineering. Distributed lyapunovbased model predictive control for collision avoidance of multiagent formation.
Jul 20, 2017 this paper studies the tracking problem of nonholonomic wheeled robots subject to control input constraints. Lyapunovbased economic model predictive control of nonlinear. A summary of each of these ingredients is given below. Lyapunovbased hybrid model predictive control for energy. Abstract in this work, we propose the integration of koopman operator methodology with lyapunov. Pdf lyapunovbased model predictive control of nonlinear. Control lyapunovbarrier functionbased model predictive.
Nonlinear model predictive control theory and algorithms. The main contribution of the proposed technique is the assurance of the closedloop stability and recursive feasibility, by a novel approach focused on mld models, using ellipsoidal terminal constraints and the. Among different mpc formulations, a lyapunovbased model predictive control mhaskar et al. Many of the control schemes for hybrid systems are based on optimal control, e. Abstractin this work, we focus on a class of general nonlinear systems and design a model predictive control mpc scheme which is capable of.
A cost function of the proposed model predictive controller is designed from the system stability point of view, inspired by the lyapunov control. Specifically, an ensemble of the rnn models are initially obtained for the nominal system, for which lyapunov based model predictive control lmpc is utilized to drive the state. Techniques for uniting lyapunovbased and model predictive control. This study addresses the problem of distributed formation control for a multiagent system with collision avoidance between agents and with obstacles, in the presence of various constraints. Nonlinear model predictive control is primarily aimed at academic researchers and practitioners working in nonlinear control but the text is selfcontained featuring background material on. Output feedback and tracking of nonlinear systems, l. Handling asynchronous, delayed measurements and distributed implementation. Lyapunov based economic model predictive control of nonlinear systems. The lyapunov based predictive control scheme is described in section 3 along with stability results and implementation details. Model predictive control mpc and backstepping control are among the most important nonlinear control design techniques. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. 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.