This issue has been shown to be important in timeseries predictions 14. Gaussian process models contain noticeably less coef. School of automation science and electrical engineering, beihang university, beijing, 100191, china email. Given any set of n points in the desired domain of your functions, take a multivariate gaussian whose covariance matrix parameter is the gram matrix of your n points with some desired kernel, and sample from that gaussian. Gaussian processes often have characteristics that can be changed by setting certain parameters and in section 2. This thesis is devoted to developing a robust model predictive control mpc strategy based on gaussian processes gp, especially for drinking water networks dwn.
We present a combination of a output feedback model predictive control scheme, which does not require full state information, and a gaussian process prediction model that is capable of. Pdf stochastic datadriven model predictive control. Gaussian process model based predictive control jus kocijan, roderick murraysmith, carl edward rasmussen, agathe girard abstract gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identifica tion of nonlinear dynamic systems. The idea of using the learned model in predictive control is conceptually similar to 5, 6, 12, with the key difference that we use a gp to predict time varying effects. We therefore propose to use the two together to obtain faulttolerant control. This paper describes model based predictive control based on gaussian processes. The predictive control principle is demonstrated on control of ph process benchmark.
Nonlinear model predictive control nmpc is one of the few control methods that can handle multivariable nonlinear control systems with constraints. Gaussian processes seem to be very promising candidates for the first of these, and model predictive control has a proven capability for the second. Gaussian process based predictive control for periodic error. Cautious nmpc with gaussian process dynamics for autonomous miniature race cars. Abstract nonlinear model predictive control nmpc algorithms are based on various nonlinear models. For solution of the multioutput prediction problem, gaussian. In predictive control, gps were successfully applied to improve control performance when learning periodic timevarying. Gaussian process based predictive control for periodic.
Gaussian process model based predictive control ju. Gaussianprocessbased demand forecasting for predictive control of drinking water networks ye wang y, carlos ocampomart nez. Model predictive control for drinking water networks based. Gaussian process model based predictive control enlighten. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other. Gaussian process model predictive control we propose to utilize the probability density function of a gaussian process trained on exemplar data as the cost function in a linear model predictive control. Gaussian process model predictive control of unknown nonlinear. A gaussian process model is parametrized by two objects. Nov 08, 2019 we present a combination of a output feedback model predictive control scheme, which does not require full state information, and a gaussian process prediction model that is capable of online. Research in the intelligent control systems group focuses on decision making, control, and learning for autonomous intelligent systems. Recently, an online optimization approach for stochastic nmpc based on a gaussian process model was proposed. The main issue in using mpc to control systems modelled by gp is the propagation of such uncertainties within the control horizon. We develop fundamental methods and algorithms that enable robots. The predictive control principle is demonstrated via the control of a ph process benchmark.
However, this process does not take into account the uncertainties introduced by each successive prediction. Gaussianprocess based demand forecasting for predictive control of drinking water networks ye wang y, carlos ocampomart nez. Fault tolerant control using gaussian processes and model predictive control, proceedings of the 2nd international conference on control and faulttolerant systems, nice, france, pp. Himmel and kai sundmacher and rolf findeisen, year2019 janine matschek, a. Pdf gaussian process model based predictive control jus. Within a gaussian process gp regression framework, we use a locally periodic covariance function to shape the hypothesis space, which allows for a structured extrapolation that is not possible with more widely used covariance functions.
The figure2 shown below indicates the principle of model predictive control. Explicit stochastic nonlinear predictive control based on gaussian. The gaussian processes can highlight areas of the input space where prediction. Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied in this paper. The predictions from a gp model take the form of a full predictive distribution. Gaussian process building models and their application in. Gaussian process model predictive control of an unmanned. In this paper, we present a model predictive control mpc approach, which improves such a nominal model description from data using gaussian processes gps. Pdf gaussian process gp regression has been widely used in supervised machine learning for its flexibility and inherent ability to describe. Pdf predictive control with gaussian process models.
Gaussian process model predictive control of an unmanned quadrotor. Explicit stochastic nonlinear predictive control based on. Keywordssmodel based predictive control, nonlinear control, gaussian process models, constraint optimisation. Introduction the demand for faulttolerant control ftc comes from safety requirements and from economics. Using gp, the variances computed during the modelling and inference processes allow us to take model uncertainty into account. This paper describes gaussian process regression gpr models presented in predictive model markup language pmml. How we measure reads a read is counted each time someone views. A gaussian process based model predictive controller for. Gaussian process model predictive control of unmanned quadrotors conference paper pdf available april 2016. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic gaussian process gp models. The central ideas underlying gaussian processes are presented in section 3, and we derive the full gaussian process regression model.
Gaussian process model predictive control of unknown nonlinear systems gang cao1, edmund mk lai2, fakhrul alam1 1school of engineering and advanced technology, massey university, auckland, new zealand. Pdf gaussian process model predictive control of unknown. The predictions obtained from the gp model are then used in a model predictive control. Zeilinger, cautious model predictive control using gaussian process regression. Gaussian process based model predictive control in progress project for the course statistical learning and stochastic control at university of stuttgart for detailed information about the project, please refer to the presentation and report. Our objectives differ from gaussian process regressions for large data sets in machine learning see, for example, wahba 1990, seeger et al. Fault tolerant control using gaussian processes and model. Stability of gaussian process learning based output feedback model predictive control michael maiworm, daniel limon, jose maria manzano, rolf findeisen june3,2019 nowadays,modelpredictivecontrolmpc has established itself as a stateoftheart control. Pdf constrained gaussian process learning for model. A gaussian process model based approach xiaoke yang wolfson college, cambridge this dissertation is submitted for the degree of doctor of philosophy of university of cambridge december 2014. Broderick a dissertation submitted to the graduate faculty of auburn university in partial ful.
The appeal of using gaussian process regression for model learning stems from the fact that it requires little prior process knowledge and directly provides a measure of residual model uncertainty. Nonlinear predictive control with a gaussian process model ju. It offers more insight in variance of obtained model. This paper illustrates possible application of gaussian process models within model based predictive control. Gaussian processes, to learn a reference from noisy data, while guaranteeing trackability of the modified desired reference predictions in the framework of model predictive control. Risksensitive model predictive control with gaussian process. In particular, a gp model is adopted to give a probabilistic multiplestepahead prediction of the state. In section 4, the approximate approach to explicit stochastic nonlinear predictive control based on gaussian process. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of. This is different from conventional models obtained through newtonian analysis. In this paper, we propose a model predictive controller mpc based on gaussian process for nonlinear systems with uncertain delays and external gaussian disturbances.
Explicit stochastic predictive control of combustion. We investigate the ability of gaussian process based mpc on handling the variable delay that follows a gaussian distribution through a properly selected observation horizon. Pdf cautious model predictive control using gaussian process. The gaussian processes can highlight areas of the input space where prediction quality is poor, due. The predictions obtained from the gaussian process model are then used in a model predictive control framework to correct for the external effect. The extra information provided by the gaussian process model is used in predictive control, where optimization of the control signal takes the variance information into account. Nonlinear predictive control with a gaussian process model.
Gaussian processes is described in section 3, where a gaussian process model of a specific combustion plant is obtained. This chapter illustrates possible application of gaussian process models within model predictive control. A gaussian process can be used as a prior probability distribution over functions in bayesian inference. Gaussian process based model predictive control in progress project for the course statistical learning and stochastic control at university of stuttgart for detailed information about the project. A significant advantage of the gaussian process models is that they provide information about prediction uncertainties, which would be of help in. Gaussian process model based predictive control request pdf. A significant advantage of the gaussian process models is that they provide information. Dynamic gaussian process models for model predictive control. Gaussian process model based predictive control core. Abstract gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of nonlinear dynamic systems. The model used is fixed, identified offline, which means that used control. Learning dynamics using gaussian process regression for model predictive control was done in 19, where gaussian processes also provide additional information about the uncertainty in prediction.
Cautious model predictive control using gaussian process. Stochastic model predictive control based on gaussian. Dynamic gaussian process models for model predictive. Dynamic maximization of oxygen yield in an elevatedpressure air separation unit using multiple model predictive control priyadarshi mahapatra, stephen e zitney, b. The main issue in using mpc to control systems modelled by gp is. Version 15 jmp, a business unit of sas sas campus drive cary, nc 275 15. Applications we consider two key problems that are widely encountered in robotics and engineering. Computing science, university of glasgow, glasgow 4 hamilton institute, national university of ireland, maynooth abstract. Pdf gaussian process model based predictive control roderick murraysmith academia. Gaussian process gp regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. The gaussian processes can highlight areas of the input space where prediction quality is poor, due to the. Model predictive control of electric power systems based on. The textbook provides a general introduction to gaussian processes. Prediction under uncertainty in sparse spectrum gaussian.
Prediction under uncertainty in sparse spectrum gaussian processes 1. Gaussian process model predictive control of unknown. A new multimodel approach by laguerre filters on sliding. The predictive control principle is demonstrated on a simulated example of nonlinear system. Datadriven model predictive control for trajectory tracking with a robotic arm. The extra information provided within gaussian process model is used in predictive control, where optimization of control signal takes the variance information into account. Gaussian processbased predictive control for periodic. The central ideas underlying gaussian processes are presented in section 3, and we derive the full gaussian process regression model in section 4. Our proposed model, tops trees of predictors, differs from existing methods in that it constructs and applies different predictive. The extra information provided within gaussian process model is used in predictive control, where optimization of control signal. 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. The model predictive control mpc trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed.
Ems by adopting gaussian process gp timeseries modelling for predicting the energy generation and the load, and model predictive control mpc as a strategy for the optimal operation of the ess. Mpc with gaussian processes institute for dynamic systems. Gaussian process models provide a probabilistic nonparametric. Gaussian process, model predictive control, stability. Nowadays there are many different mpc strategies developed for dwn, such as certainequivalent mpc cempc and chanceconstrained mpc ccmpc. As a result, we obtain substantially improved predictive performance. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of nonlinear dynamic systems. Towards this objective we developed a data driven approach for therapy optimization where a predictive model for patients behavior is learned directly from historical data. Introduction the demand for faulttolerant control ftc comes from safety. In section 4, the approximate approach to explicit stochastic nonlinear predictive control based on gaussian process models is presented. Pdf gaussian process model based predictive control. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identication of nonlinear dynamic systems. Abstractthis paper presents a model predictive control of electric power systems based on the multiple gaussian process predictors. Gaussianprocessbased demand forecasting for predictive.
Gang cao, edmund mk lai, fakhrul alam download pdf. Department of engineering, university of cambridge, cb2 1pz, united kingdom. As such, the predictive model is incorporated into a model predictive control optimization algorithm to find optimal therapy, which will lead the patient to a healthy state. Nonlinear model predictive control nonlinear model predictive control as it was applied with the gaussian process model can be in general described with a block diagram, as depicted in figure 1. The main issue in using mpc to control systems modelled by gp is the propagation of such uncertainties within the control. The uncertainty propagation problem can be dealt with by assuming that. Explicit stochastic predictive control of combustion plants. Gaussian processes for dataefficient learning in robotics. Daosud, neural network based model predictive control for a steel picking process, journal of process control 2. Dynamic gaussian process models for model predictive control of vehicle roll by david j.
Datadriven model predictive control for trajectory. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. Gaussian process model predictive control of an unmanned quadrotor 5 mean values. Gaussian process model predictive control of unknown non. Pdf online gaussian process learningbased model predictive. In predictive control, gps were successfully applied to improve control. In safetycritical applications, there is always some requirement for a safe backup in case the nominal system fails. Model predictive control mpc is one of the most fre quently met. Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied. Model predictive control of electric power systems based. In particular, we show how offsetfree tracking can be achieved by augmenting a nominal model with both a gaussian process, which makes use of offline data, and an additive disturbance model. Gaussian process regression gpr representation in predictive model markup language pmml jinkyoo park1, david lechevalier2, ronay ak3, max ferguson4, kincho law4, yungtsun tina lee3, and sudarsan rachuri5 abstract. Stability of gaussian process learning based output.
The gaussian processes can highlight areas of the input. Pdf this paper describes modelbased predictive control based on gaussian processes. Risksensitive model predictive control with gaussian process models xiaoke yang a. A deep learning architecture for predictive control. This paper describes gaussian process regression gpr models presented in predictive model. This paper illustrates possible application of gaussian process models within modelbased predictive control. Gaussian predictive process models for large spatial data sets. The gaussian process model is a nonparametric model and the output of the model has gaussian distribution with mean and variance. Abstractsthis paper describes model based predictive control based on gaussian processes.
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