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