This work presents an output feedback stochastic nonlinear model predictive control snmpc approach for a class of nonlinear systems with unbounded stochastic uncertainties. Jul 20, 2017 this paper studies the tracking problem of nonholonomic wheeled robots subject to control input constraints. Lyapunovbased hybrid model predictive control for energy. This result was further relaxed in 2,3 towards using a terminal inequality constraint on the continuous states. 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. A control lyapunov approach to predictive control of. More formally, suppose we are given an autonomous dynamical system. Pdf model predictive control with control lyapunov.
Lyapunovbased model predictive control of nonlinear. 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. Lyapunov functions and feedback in nonlinear control. Shaping the state probability density functions edward a.
A lyapunovbased approach for the control of biomimetic robotic systems with periodic forcing inputs domenico campolo. Model predictive control provides high performance and safety in the form of constraint satisfaction. Output feedback lyapunovbased stochastic nonlinear. Christofidesstabilization of nonlinear systems with state and control constraints using lyapunovbased predictive control. 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. Lyapunov based model reference adaptive control for aerial. General references for lyapunov functions in control include 2 and 14.
During the past decade model predictive control mpc, also referred to as receding horizon control or moving horizon control, has become the preferred control strategy for quite a number of industrial processes. 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. Until now, no book has addressed in detail all key issues in the field including apriori stability and robust stability results. Distributed lyapunovbased model predictive control for. A control lyapunov approach to predictive control of hybrid systems 1 discrete states. Economic model predictive control theory, formulations. Control lyapunov functions for the optimal control problems that we introduce in the next section, we will make use of a terminal cost that is also a. State constraints, soft constraints, input constraints, model predictive control, bounded lyapunovbased control, stability region, feasibility region. Model predictive control control theory mathematical. Safeness indexbased economic model predictive control of. Adaptive fuzzy model predictive control for nonminimum.
N control series includes bibliographical references and index. A summary of each of these ingredients is given below. Lyapunovbased model predictive control springerlink. However, such relaxations were achieved in the absence of discrete states.
The residuals, the differences between the actual and predicted outputs, serve as the feedback signal to a. Lee school of chemical and biomolecular engineering center for process systems engineering georgia inst. Model predictive control mpc has become a widely used methodology across all engineering disciplines, yet there are few books which study this approach. Unesco eolss sample chapters control systems, robotics and automation vol. Asymptotic stability in the probabilistic sense is ensured by using a lyapunovbased control law. Christofidesstabilization of nonlinear systems with state and control constraints using lyapunov based predictive control. In this work, we design a lyapunov based model predictive controller lmpc for nonlinear systems subject to stochastic uncertainty. A control lyapunov approach to predictive control of hybrid. Mechanical engineering the focus of this research is an examination of the interplay between di.
To this end, we introduce a nonempty state constraint set x. A stochastic lyapunovbased controller is first utilized to characterize a region of the statespace. Model predictive control advanced textbooks in control and. 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. Isbn 9789533071022, pdf isbn 9789535159353, published 20100818. The book is geared towards researchers and practitioners in the area of control engineering and control theory.
Mpc model predictive control also known as dmc dynamical matrix control. These properties however can be satisfied only if the underlying model used for prediction of. The model predictive control based framework is proposed to compensate for the twochannel packet dropouts. Under the assumption of stabilizability of the origin of the stochastic nonlinear system via a stochastic lyapunov. Introduction control systems are often subject to constraints on their. The lyapunov based predictive control scheme is described in section 3 along with stability results and implementation details.
Secondly, a nonconservative stabilizing predictive control scheme is designed for the model of the closedloop can system using the concept of a flexible control lyapunov function lazar, 2009. The lmpc design provides an explicitly characterized region from where stability can be probabilistically obtained. A process model is used to predict the current values of the output variables. Networkbased predictive control for constrained nonlinear. A block diagram of a model predictive control system is shown in fig. We present a machine learningbased 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. Nonlinear model predictive control nmpc is widely used in the process and chemical industries and increasingly for applications, such as those in the automotive industry, which use higher data sampling rates. Lyapunovbased stochastic nonlinear model predictive. The nonlinear dynamic model of the process consists of 179 state variables and control manipulated inputs and features a cooled plugflow reactor, an eightstage gasliquid. In rolf findeisen, frank allgwer, and lorenz biegler, editors, assessment and future directions of nonlinear model predictive control, volume 358 of lecture notes in control and information sciences, pages 7791. For access to this article, please select a purchase option. The proposed controller consists of a lyapunovbased hybrid model predictive control based on mixed logical dynamical mld framework. Control lyapunovbarrier functionbased model predictive.
There have been many significant advances in this area over the past years, one of the most important ones being its extension to nonlinear systems. Pdf model predictive control with control lyapunov function. Pdf lyapunovbased model predictive control for dynamic. Realtime adaptive machinelearningbased predictive control. Process operational safety plays an important role in designing control systems for chemical processes. 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. Neural lyapunov model predictive control where v netx is a lipschitz feedforward network that produces a n v n xmatrix. 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. Independently of the type of control system architecture and type of control algorithm utilized, a common. Half a century after its birth, it has been widely accepted in many engineering fields and has brought much. The proposed controller consists of a lyapunov based hybrid model predictive control based on mixed logical dynamical mld framework. This paper studies the tracking problem of nonholonomic wheeled robots subject to control input constraints.
State constraints, soft constraints, input constraints, model predictive control, bounded lyapunov based control, stability region, feasibility region. Techniques for uniting lyapunovbased and model predictive control. Lyapunovbased predictive control methodologies for networked control systems. Lyapunovbased predictive control methodologies for networked. 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. Lyapunovbased model predictive control for tracking of. Stabilization of nonlinear systems with state and control.
A stochastic lyapunov based controller is first utilized to characterize a region of the statespace. Specifically, an ensemble of the rnn models are initially obtained for the nominal system, for which lyapunovbased model predictive control lmpc is utilized to drive the. 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. 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. In this work, we propose the integration of koopman operator methodology with lyapunov. 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 predictive control methodologies for. The author writes in laymans terms, avoiding jargon and using a style that relies upon personal insight into practical applications. Lyapunovbased controller for a class of stochastic chaotic. To this end, we introduce a nonempty state con straint set x. Jun 27, 2003 model based predictive control, a practical approach, analyzes predictive control from its base mathematical foundation, but delivers the subject matter in a readable, intuitive style. Mar 23, 2018 under the assumption of stabilizability of the origin of the stochastic nonlinear system via a stochastic lyapunov.
In control theory, a controllyapunov function is a lyapunov function for a system with control inputs. In order to take optimality considerations into account while designing saturated tracking controllers, a lyapunovbased predictive tracking controller is developed, in which the contractive constraint is characterized by a backup global saturated tracking controller. 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. Nonlinear model predictive control is a thorough and rigorous introduction to nmpc for discretetime and sampleddata systems. Lyapunov based model predictive control for dynamic positioning of autonomous underwater vehicles conference paper pdf available october 2017 with 330 reads how we measure reads. Engineers and mpc researchers now have a volume that provides a complete overview of the theory. The plant to be used as predictive model is simulated by takagisugeno fuzzy model, and the optimization problem is solved by a genetic algorithms or branch and bound. Lyapunovbased controller for a class of stochastic. Lyapunov based predictive control of vehicle drivetrains. The method to tune parameters of the model predictive controller based on lyapunov stability theorem is presented.
Lyapunovbased approach introduces advanced tools for stability analysis of nonlinear systems. In this work, we focus on the development and application of two lyapunovbased model predictive control lmpc schemes to a largescale nonlinear chemical process network used in the production of vinyl acetate. The snmpc approach aims to shape multivariate probability density function pdf of the stochastic states in presence of input and joint state chance constraints. This paper investigates the predictive control scheme and the associated stability issue for the constrained nonlinear networked control systems ncss, where both the sensortocontroller packet dropout and the controllertoactuator packet dropout are considered simultaneously. Model predictive control mpc usually refers to a class of control algorithms in which a dynamic process model is used to predict and optimize process performance, but it is can also be seen as a term denoting a natural control strategy that matches the human thought form most closely. 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.
Lyapunov based predictive control methodologies for networked control systems. Lyapunovbased model predictive control of stochastic. Among different mpc formulations, a lyapunov based model predictive control mhaskar et al. 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. Distributed lyapunov based model predictive control for collision avoidance of multiagent formation. Model predictive control of a nonlinear largescale. Nonlinear model predictive control theory and algorithms. Lyapunovbased model predictive control of nonlinear systems. Xwe introduce a nonempty control constraint set ux. Economic model predictive control of stochastic nonlinear.
Lyapunov based predictive control of vehicle drivetrains over. The resulting control algorithm has the potential to satisfy the chronometric requirements, as it can be implemented as a lowcomplexity linear. 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. Model predictive control advanced textbooks in control. Lyapunovbased model predictive control of stochastic nonlinear systems. Lyapunovbased model predictive control for dynamic. Closedloop stability is ensured by designing a stability constraint in terms of a stochastic control lyapunov function, which explicitly characterizes. Lyapunovbased robust and adaptive control of nonlinear systems using a novel feedback structure by parag patre august 2009 chair.
Economic model predictive control theory, formulations and. Lyapunovbased stochastic nonlinear model predictive control. Arts lab, scuola superiore santanna, pisa, italy department of information engineering, univ. 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. 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 problem considered in this chapter is to control a vehicle drivetrain in order to minimize its oscillations while coping with the timevarying delays. Motivated by this, in this work, we develop a process safeness indexbased economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. The second edition of model predictive control provides a thorough introduction to theoretical and practical aspects of the most commonly used mpc strategies. 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. Use the performance index j as a lyapunov function. The ordinary lyapunov function is used to test whether a dynamical system is stable more restrictively, asymptotically stable. This study presents a general control law based on lyapunovs direct method for a group of wellknown stochastic chaotic systems. The authors proposed solution incorporates a control lyapunov function clf into a distributed model predictive control scheme, which inherits the strong stability property of the clf and optimises the. It bridges the gap between the powerful but often abstract techniques of control researchers and the more empirical approach of practitioners.
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