With gpmpc1, the original stochastic model predictive control. This is different from conventional models obtained through newtonian analysis. Abstractsthis paper describes modelbased predictive control based on gaussian processes. Abstract nonlinear model predictive control nmpc algorithms are based on various nonlinear models. Gaussian processes often have characteristics that can be changed by setting certain parameters and in section 2. Pdf gaussian process model based predictive control.
Gaussian process based predictive control for periodic error. These properties however can be satisfied only if the underlying model used for prediction of the controlled process is of sufficient accuracy. Gaussian process model based predictive control enlighten. Nonlinear predictive control with a gaussian process model. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox. Predictive control of a gasliquid separation plant based on. In safetycritical applications, there is always some requirement for a safe backup in case the nominal system fails. After the learning, one can use the w parameters as indicators of how important the corresponding input components dimensions are. Explicit stochastic nonlinear predictive control based on gaussian. Predictive control of a gasliquid separation plant based. Nmpc does however require a plant model to be available. Gaussian process models contain noticeably less coef.
Gaussian process models contain noticeably less coefficients to be optimized. Learning based model predictive control for autonomous racing. Results show that both gpmpc1 and gpmpc2 produce effective controls but gpmpc2 is much. The predictions from a gp model take the form of a full predictive distribution. Gaussian process model based predictive control ieee xplore.
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 nonlinear model predictive control problem based on gaussian process model will be referred to as gpnmpc problem. The predictions obtained from the gaussian process model are then used in a model predictive control framework to correct for the external effect. 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. Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied in this paper. The extra information provided within gaussian process model is used in predictive control, where optimization of control signal takes the variance. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of. Gaussian predictive process models for large spatial data sets. Online gaussian process learningbased model predictive. Gaussian process model predictive control of unknown non. Gaussian process, model predictive control, stability. Reachabilitybased safe learning with gaussian processes. Nonlinear model predictive control nmpc is an efficient control approach for multivariate nonlinear dynamic systems with process constraints.
The extra information provided within gaussian process model is used in predictive control, where optimization of control signal takes the variance information into account. Jan 19, 2007 this paper demonstrates feasibility of application and realisation of a control algorithm based on a gaussian process model. For solution of the multioutput prediction problem, gaussian. The gaussian process model is an example of a probabilistic nonparametric model that also provides in formation about prediction uncertainties which are difficult to evaluate appropriately in nonlinear parametric models. A thesis submitted in partial fulfillment of the requirements for the degree of. Zeilinger, cautious model predictive control using gaussian process regression. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic gaussian process gp models. Explicit stochastic nonlinear predictive control based on. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other. Request pdf gaussian process model based predictive control gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of nonlinear dynamic. This paper demonstrates feasibility of application and realisation of a control algorithm based on a gaussian process model.
Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied. In this paper, an echo state gaussian processbased nonlinear model predictive control esgpnmpc is designed for the pmas. This chapter illustrates possible application of gaussian process models within model predictive control. The model formed with gp regression demonstrates characteristics that make it useful in model predictive control mpc. Gaussianprocessbased demand forecasting for predictive control of drinking water networks ye wang y, carlos ocampomart nez. Pdf this paper describes modelbased predictive control based on gaussian processes. Gaussianprocess 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. The machine learning method gaussian process gp regression is used to learn the vehicle dynamics without any prior knowledge. Zeilinger abstractgaussian process gp regression has been widely used in supervised machine learning due to its. 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 core. Gaussianprocessbased demand forecasting for predictive. This paper describes modelbased predictive control based on gaussian processes. In the slowtime scale, model predictive control is adopted to plan.
Gaussian process model predictive control of an unmanned. Model predictive control of electric power systems based on. Model predictive control mpc 1 is naturally capable of deal ing with multiinput multioutput systems and constraints on the input, state, and output, already in the design process. Sep 01, 2008 the coverage, although expected to be lower given that there is less uncertainty in the predictive process than in the parent process section 2. Gaussian process model based predictive control request pdf. As a probabilistic model we use nonparametric gaussian processes gps 47. This paper describes gaussian process regression gpr models presented in predictive model markup language pmml.
Model based predictive control mbpc is a control methodology which uses online in the control computer a process model for calculating predictions of the future plant output and for optimizing future control actions. Explicit stochastic predictive control of combustion. Stochastic model predictive control based on gaussian. First, we need to study the different possible model learning architectures for robotics. Ieee transactions on control systems technology, 2019. Gaussian processes is described in section 3, where a gaussian process model of a specific combustion plant is obtained.
We propose a novel control strategy that validates the model online and becomes more conservative if its predictions account poorly for the observed dynamics. Gaussian process model based predictive control jus kocijan, roderick murraysmith, carl edward rasmussen, agathe girard abstractgaussian process models provide a probabilistic nonparametric modelling approach for blackbox identifica tion of nonlinear dynamic systems. This paper describes model based predictive control based on gaussian processes. Gaussian process model predictive control of unknown nonlinear. Pdf gaussian process model based predictive control jus. Pdf an echo state gaussian process based nonlinear model. The tracking and balancing control is designed the controller in fast and slow time scales. Pmml is an extensible markup language xml based standard language used to represent data mining and predictive analytic models, as well as pre and postprocessed data. Explicit stochastic predictive control of combustion plants.
Conditionbased predictive order model for a mechanical. These latent values are used to define a distribution for the target in a case. Broderick a dissertation submitted to the graduate faculty of auburn university in partial ful. 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. Using gp, the variances computed during the modelling and inference processes allow us to take model uncertainty into account. Pdf predictive control with gaussian process models. The extra information provided by the gaussian process model is used in predictive control, where optimisation of the control signal takes the variance information into account. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other models. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of nonlinear dynamic systems. Model predictive control provides high performance and safety in the form of constraint satisfaction.
The gaussian process model is a nonparametric model and the output of the model has gaussian distribution with mean and variance. An efficient conditionbased predictive spare ordering approach is the key to guarantee safe operation, improve service quality, and reduce maintenance costs under a predefined lower availability threshold. A gaussian process based model predictive controller for. 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. A significant advantage of the gaussian process models is that they provide information. K 1 g, can be defined in terms of a gaussian process model for latent values associated with each case. Abstractthis paper presents a model predictive control of electric power systems based on the multiple gaussian process predictors.
Model predictive control of electric power systems based. In this paper, we propose a model predictive controller mpc based on gaussian process for nonlinear systems with uncertain delays and external gaussian disturbances. Sequential prediction, gaussian processes, planning and control, bayesian. This paper illustrates possible application of gaussian process models within model based predictive control. Gaussian processes modelbased control of underactuated. Dynamic gaussian process models for model predictive control of vehicle roll by david j. Cautious model predictive control using gaussian process regression lukas hewing, juraj kabzan, melanie n. Nonlinear predictive control with a gaussian process model 187 for di.
The gaussian processes can highlight areas of the input space where prediction quality is poor, due to the. Pmml is an extensible markup language xmlbased standard language used to represent data mining and predictive analytic models, as well as pre and postprocessed data. Cautious model predictive control using gaussian process. Regression and classification using gaussian process priors. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identication of nonlinear dynamic systems. Index termsmodel predictive control, gaussian processes.
Recently, an online optimization approach for stochastic nmpc based on a gaussian process model was proposed. In this paper, we propose a condition based predictive order model cbpo for a mechanical component, whose degradation path is modeled as inverse gaussian ig process with covariate. One way to address this challenge is by datadriven and machine learning approaches, such as gaussian processes, that allow to refine the model online. For a given problem, the parameters are learned identi. Pdf gaussian process model predictive control of unknown. In this paper, we propose a conditionbased predictive order model cbpo for a mechanical component, whose degradation path is modeled as inverse gaussian ig process with covariate effect. A gaussian process can be used as a prior probability distribution over functions in bayesian inference. Gaussian process models provide a probabilistic nonparametric. Fault tolerant control using gaussian processes and model. Combining the predictive models we obtain a multivariate gaussian distribution over the consecutive state.
In section 4, the approximate approach to explicit stochastic nonlinear predictive control based on gaussian process models is presented. We present a method to validate the model in real time and provide an adapted control strategy, which can guarantee. Introduction the demand for faulttolerant control ftc comes from safety requirements and from economics. The coverage, although expected to be lower given that there is less uncertainty in the predictive process than in the parent process section 2. This paper illustrates possible application of gaussian process models within modelbased predictive control. Dynamic gaussian process models for model predictive. Mpc with gaussian processes institute for dynamic systems. Online gaussian process learningbased model predictive control with stability guarantees. Gpmpc gaussian process linear model predictive control. Prediction under uncertainty in sparse spectrum gaussian. The proposed strategy is comprised of an esgp, which is suitable for modeling unknown nonlinear systems as well as. The implicit daisychaining property of constrained predictive control, applied mathematics and computer science 84. Pdf constrained gaussian process learning for model. An efficient condition based predictive spare ordering approach is the key to guarantee safe operation, improve service quality, and reduce maintenance costs under a predefined lower availability threshold.
The main issue in using mpc to control systems modelled by gp is the propagation of such uncertainties within the control horizon. 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. Gaussian process based predictive control for periodic. The predictive control principle is demonstrated on control of ph process benchmark. Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the. 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. Gaussian process model based predictive control 2003. The model predictive control mpc trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. The extra information provided within gaussian process model is used in predictive control, where optimization of control signal. Predictive control with gaussian process models, proceedings of ieee region 8 eurocon 2003. Learningbased model predictive control for autonomous racing. Policy improvement is based on analytic policy gradients. Here, a model describes essential information about the behavior of the environment and the influence of an agent on this environment. Gaussian process based model predictive control massey.
The central ideas underlying gaussian processes are presented in section 3, and we derive the full. The extra information provided within gaussian process model is used in. In the context of model based learning control, we view the model from three different perspectives. Himmel and kai sundmacher and rolf findeisen, journalarxiv. Dynamic gaussian process models for model predictive control. We show that the proposed approach is particularly bene. The availability of good continuous predictions allows control at a rate higher than that of the measurements. Gaussian processes for dataefficient learning in robotics. The extra information provided by the gaussian process model is used in predictive control, where optimisation of the control.