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 model predictive control nonlinear model predictive control as it was applied with the gaussian process model can be in general described with. 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. What are some applications of gaussian process models. My phd projects deals with the optimal operation of batch processes employing nonlinear model predictive. Gaussian process based model predictive controller for imitation learning. This is different from conventional models obtained through newtonian analysis. As the number of data points increases x, fx pairs, so do the. Jan 21, 2012 gps actually arose out of an application. 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. Two issues of quadrotor control without deterministic dynamical equations are addressed in this paper by using gaussian process gp based model predictive control mpc algorithm. Specifically, the gaussian process gp is considered nonparametric because a gp represents a function i. Pdf predictive control with gaussian process models.
The central ideas underlying gaussian processes are presented in section 3, and we derive the full gaussian process regression model in section 4. Zeilinger abstractgaussian process gp regression has been widely used in supervised. Two issues of quadrotor control without deterministic dynamical equations are addressed in this paper by using gaussian process gp based model predictive. Proceedings of 58th ieee conference on decision and control cdc 2019. 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. Stochastic nonlinear model predictive control of batch processes phd description. Apr 17, 2019 an additive gaussian process simulated data. Given any set of n points in the desired domain of your functions, take a multivariate gaussian whose. They key is in choosing good values for the hyperparameters which effectively control the complexity of the model in a similar manner that regularisation does.
To save on the cost of clinical trials and potential failure, we evaluated our model on a population of virtual patients capable of emulating the inflammatory response. Gaussian process based model predictive control for linear time. The gaussian processes can highlight areas of the input. Dynamic gaussian process models for model predictive control of vehicle roll by david j. Two main issues associated with model predictive control mpc are learning the unknown dynamics of the system and handling model uncertainties. Gaussian processes often have characteristics that can be changed by setting certain parameters and in section 2. Pilco takes model uncertainties consistently into account during longterm planning to reduce model bias. We marginalize out the model parameters in closedform, using gaussian process gp priors for both the dynamics. A gaussian process model is parametrized by two objects.
Gaussian process model predictive control of unmanned quadrotors abstract. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows for direct assessment of the residual model uncertainty. The model predictive control mpc trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. The predictive control principle is demonstrated on a simulated example of nonlinear system. Systems control design relies on mathematical models and these may be developed from measurement data. A gpdm comprises a lowdimensional latent space with associated dynamics, and a map from the latent space to an observation space. This can be seen when only selecting the linear kernel, as it allows us to perform linear regression even if more than two points have been observed, and not all functions have to pass directly through the observed training data. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic gaussian process gp models. Using gp, the variances computed during the modelling and inference processes allow us to take model uncertainty into account. Gaussian process models are generally fine with high dimensional datasets i have used them with microarray data etc. Model predictive control mpc refers to a class of control algorithms in which a dynamic process model is used to predict and optimize process performance.
School of automation science and electrical engineering, beihang. The predictions from a gp model take the form of a full predictive distribution. The extra information provided by the gaussian process model is used in predictive control, where. Using gp, the variances computed during the modelling and. This paper introduces gaussian process dynamical models gpdm for nonlinear time series analysis. This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. Model predictive control linear convex optimal control. Online gaussian process learningbased model predictive. The residuals, the differences between the actual and predicted outputs, serve as the feedback signal to a. Predictive approaches for gaussian process classifier model selection optimizing expected fmeasure. Learn about the benefits of using model predictive control mpc. We proposed a novel model predictive control method that learns a. A gaussian process based model predictive controller for. Danie krige, is generally credited with the first use of a gplike model in the 1950s to model the distribution of ore content in south african mines.
In this paper, we propose a model predictive controller mpc based on gaussian process for nonlinear systems with uncertain delays and external gaussian disturbances. A process model is used to predict the current values of the output variables. Pdf gaussian process model based predictive control. The predictive control principle is demonstrated via the control of a ph process benchmark. 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. 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. Pdf this paper describes modelbased predictive control based on gaussian processes. Here an approximation to fmeasure was made so that the fmeasure is smoothed and becomes a. The gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. As the guide for researchers and engineers all over the world concerned with the latest. Gaussian process based model predictive controller for imitation. Zeilinger abstractgaussian process gp regression has been widely used in supervised machine learning due to its. Gaussian process model based predictive control 2003.
They key is in choosing good values for the hyperparameters which effectively. Important topics covered include model predictive control from an optimal control point of view, the use of state and parameter identification for implementation of optimal adaptive control, a variational. From lower request of modeling accuracy and robustness to complicated process plants, mpc has been widely accepted in many practical fields. These properties however can be satisfied only if the underlying model used for prediction of the controlled process is of sufficient accuracy. First, we introduce pilco, a fully bayesian approach for efficient rl in. The predictions obtained from the gaussian process model are then used in a model predictive control framework to correct for the external effect. We present a model predictive control mpc approach that integrates a nominal linear system with an additive nonlinear part of the dynamics. Modelling and control of dynamic systems using gaussian. A gaussian process is a stochastic process for which any finite. We consider both a classic optimal control problem, where problem. Gaussian process model predictive control of unknown nonlinear systems abstract. Gaussian process model predictive control of unknown non.
The textbook provides a general introduction to gaussian processes. Gaussian process dynamic programming sciencedirect. Mpc with gaussian process a framework for using gaussian process together with model predictive control for optimal control. Gaussian process, model predictive control, stability. May 15, 2018 learn about the benefits of using model predictive control mpc. Dynamic gaussian process models for model predictive.
In this article, we introduce gaussian process dynamic programming gpdp, an approximate value functionbased rl algorithm. 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. Cautious model predictive control using gaussian process. 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 model predictive control of an unmanned.
Cautious model predictive control using gaussian process regression lukas hewing, juraj kabzan, melanie n. This book examines gaussian processes in both modelbased reinforcement learning rl and inference in nonlinear dynamic systems. Gaussian process model predictive control prediction horizon internal. A gaussian process is a stochastic process for which any finite set of yvariables has a joint multivariate gaussian distribution. Introduction the demand for faulttolerant control ftc comes from safety requirements and from economics. Gaussian process gp regression has been widely used in supervised machine learning for its flexibility and inherent ability to describe uncertainty in the prediction. A block diagram of a model predictive control system is shown in fig.
Pdf efficient reinforcement learning using gaussian. Learning a gaussian process model with uncertain inputs. This paper illustrates possible application of gaussian process models within model based predictive control. First, we introduce pilco, a fully bayesian approach for efficient rl in continuousvalued state and action spaces when no expert knowledge is available. Gaussian process models provide a probabilistic nonparametric. The extra information provided within gaussian process model is used in predictive control, where optimization of control signal. The gaussian process can highlight areas of the input space where prediction quality is poor, due to the lack of data, by indicating the higher variance around the predicted mean. In safetycritical applications, there is always some requirement for a safe backup in case the nominal system fails. Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied. Gaussian processes gps provide a principled, practical, probabilistic approach to learning in kernel machines. This monograph opens up new horizons for engineers and researchers in academia and in industry dealing.
As the number of data points increases x, fx pairs, so do the number of model parameters restricting the shape of the function. Nonlinear predictive control with a gaussian process model. Dynamic gaussian process models for model predictive control. Gaussian predictive process models for large spatial data sets. Nonlinear predictive control with a gaussian process model ju. Modelling and control of dynamic systems using gaussian process models jus kocijan auth. Apr 02, 2019 as discussed in the section about gps, a gaussian process can model uncertain observations. A gaussian process can be used as a prior probability distribution over functions in bayesian inference. Model predictive control mpc of an unknown system that is modelled by gaussian process gp techniques is studied in this paper. Gaussian process models provide a probabilistic nonparametric modelling approach for blackbox identification of nonlinear dynamic systems. 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 models contain noticeably less coef.
Broderick a dissertation submitted to the graduate faculty of auburn university in partial ful. Risksensitive model predictive control with gaussian. Gaussian process model predictive control of unknown nonlinear. Pdf cautious model predictive control using gaussian process. Model predictive control provides high performance and safety in the form of constraint satisfaction. The gaussian processes can highlight areas of the input space where prediction quality is poor, due to the. Gaussian process based predictive control for periodic. This paper describes modelbased predictive control based on gaussian processes. Introduction the demand for faulttolerant control ftc comes from safety.
Gaussian process model predictive control of unmanned. Part of the lecture notes in computer science book series lncs, volume 3355. This paper proposes the use of risksensitive costs in a model predictive controller mpc with gaussian process gp models, for more effective online learning. Gps have received increased attention in the machinelearning community over the past decade, and this book. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other models. Introduction model predictive control mpc is an industry accepted technology for advanced control of many processes.
Gps have received increased attention in the machinelearning community over the past decade, and this book provides a longneeded systematic and unified treatment of theoretical and practical aspects of gps in machine learning. This process of system identification, when based on gp models, can play an. This process of system identification, when based on gp models, can play an integral part of control design in databased control and its description as such is an essential aspect of the text. Keywordssmodel based predictive control, nonlinear control, gaussian process models, constraint optimisation. Gaussian process based predictive control for periodic error. Proceeding of the 2004 american control conference boston, massachuselts june 30 july 2,2004 tha08. In particular, a gp model is adopted to give a probabilistic multiplestepahead prediction of the state. 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.
This chapter illustrates possible application of gaussian process models within model predictive control. The xaxis is age by default except for the third figure in the top panel, which is the disease age. Risksensitive model predictive control with gaussian process. One way to address this challenge is by datadriven and machine learning approaches, such as gaussian processes, that allow to refine the model online.
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