Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control

• URL: http://arxiv.org/abs/2103.05441v1
• Date: Tue, 9 Mar 2021 14:25:08 GMT
• Title: Combining Gaussian processes and polynomial chaos expansions for stochastic nonlinear model predictive control
• Authors: E. Bradford and L. Imsland
• Abstract summary: We introduce a new algorithm to explicitly consider time-invariant uncertainties in optimal control problems. The main novelty in this paper is to use this combination in an efficient fashion to obtain mean and variance estimates of nonlinear transformations. It is shown how to formulate both chance-constraints and a probabilistic objective for the optimal control problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to closed-loop performance deterioration and constraint violations. In this paper we introduce a new algorithm to explicitly consider time-invariant stochastic uncertainties in optimal control problems. The difficulty of propagating stochastic variables through nonlinear functions is dealt with by combining Gaussian processes with polynomial chaos expansions. The main novelty in this paper is to use this combination in an efficient fashion to obtain mean and variance estimates of nonlinear transformations. Using this algorithm, it is shown how to formulate both chance-constraints and a probabilistic objective for the optimal control problem. On a batch reactor case study we firstly verify the ability of the new approach to accurately approximate the probability distributions required. Secondly, a tractable stochastic nonlinear model predictive control approach is formulated with an economic objective to demonstrate the closed-loop performance of the method via Monte Carlo simulations.

Related papers

• Multi-Response Heteroscedastic Gaussian Process Models and Their Inference [1.52292571922932]
  We propose a novel framework for the modeling of heteroscedastic covariance functions. We employ variational inference to approximate the posterior and facilitate posterior predictive modeling. We show that our proposed framework offers a robust and versatile tool for a wide array of applications.
  arXiv  Detail & Related papers  (2023-08-29T15:06:47Z)
• Model Predictive Control with Gaussian-Process-Supported Dynamical Constraints for Autonomous Vehicles [82.65261980827594]
  We propose a model predictive control approach for autonomous vehicles that exploits learned Gaussian processes for predicting human driving behavior. A multi-mode predictive control approach considers the possible intentions of the human drivers.
  arXiv  Detail & Related papers  (2023-03-08T17:14:57Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Model-Based Reinforcement Learning via Stochastic Hybrid Models [39.83837705993256]
  This paper adopts a hybrid-system view of nonlinear modeling and control. We consider a sequence modeling paradigm that captures the temporal structure of the data. We show that these time-series models naturally admit a closed-loop extension that we use to extract local feedback controllers.
  arXiv  Detail & Related papers  (2021-11-11T14:05:46Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Stein Variational Model Predictive Control [130.60527864489168]
  Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex distributions. We show that this framework leads to successful planning in challenging, non optimal control problems.
  arXiv  Detail & Related papers  (2020-11-15T22:36:59Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Uncertainty Modelling in Risk-averse Supply Chain Systems Using Multi-objective Pareto Optimization [0.0]
  One of the arduous tasks in supply chain modelling is to build robust models against irregular variations. We have introduced a novel methodology namely, Pareto Optimization to handle uncertainties and bound the entropy of such uncertainties by explicitly modelling them under some apriori assumptions.
  arXiv  Detail & Related papers  (2020-04-24T21:04:25Z)
• DISCO: Double Likelihood-free Inference Stochastic Control [29.84276469617019]
  We propose to leverage the power of modern simulators and recent techniques in Bayesian statistics for likelihood-free inference. The posterior distribution over simulation parameters is propagated through a potentially non-analytical model of the system. Experiments show that the controller proposed attained superior performance and robustness on classical control and robotics tasks.
  arXiv  Detail & Related papers  (2020-02-18T05:29:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.