Stochastic Model Predictive Control with Integrated Experiment Design for Nonlinear Systems

The performance of predictive control strategies often degrades over time due to growing plant-model mismatch. Closed-loop performance restoration typically requires some form of model maintenance to reduce model uncertainty. This paper presents a stochastic predictive control approach with integrated experiment design for nonlinear systems with probabilistic modeling uncertainties. The integration of predictive control with experiment design enables enhancing the information content of closed-loop data for online model adaption. The presented approach considers control-oriented experiment design to ensure adequate model adaptation (in probability) in terms of an admissible control performance level. The stochastic optimal control approach is demonstrated on a continuous bioreactor case study

Development of grey box state estimators for systems subjected to time correlated unmeasured disturbances

Unmeasured disturbances, which arise from uncertainties in the physical input sources, are commonly encountered in a process operation. For the purpose of developing Bayesian state estimators, such disturbances have been traditionally treated as Gaussian white noise processes. In practice, however, such disturbances are often correlated in time and the simplistic white noise assumption may not hold. Thus, to generate accurate estimates of the states, it is essential to obtain a reasonably accurate characterisation of the dynamics associated with the unmeasured disturbances. In this work, a systematic approach has been developed for identifying discrete time stochastic disturbance models, which captures the dynamics associated with such unmeasured disturbances. Under certain simplifying assumptions, the discrete time unmeasured disturbance models are combined with a continuous time mechanistic model to derive a discrete nonlinear grey box model. The grey box model is further used to formulate a nonlinear Bayesian state estimator. A constrained optimisation problem, that maximizes the log likelihood function of the innovation sequence generated by the state estimator, is formulated and solved for estimation of the parameters of the unmeasured disturbance model and the measurement noise covariance from the input-output data. The efficacy of this approach is demonstrated by simulating a benchmark continuous fermenter system and using experimental data obtained from a heater-mixer setup. The simulation studies demonstrate that the proposed approach is able to identify correlated disturbance models that closely match the characteristics of the true unmeasured disturbance models. (C) 2012 Elsevier Ltd. All rights reserved

Maximum likelihood estimation of noise covariance matrices for state estimation of autonomous hybrid systems

A critical aspect of developing Bayesian state estimators for hybrid systems, that involve a combination of continuous and discrete state variables, is to have a reasonably accurate characterization of the stochastic disturbances affecting their dynamics. Recently, Bavdekar et al. (2011) have proposed a maximum likelihood (ML) based framework for estimation of the noise covariance matrices from operating input-output data when an EKF is used for state estimation. In this work, the ML framework is extended to estimation of the noise covariance matrices associated with autonomous hybrid systems, and, to a wider class of recursive Bayesian filters. Under the assumption that the innovations generated by an estimator form a white noise sequence, the proposed ML framework computes the noise covariance matrices such that they maximize the log-likelihood function of the estimator innovations. The efficacy of the proposed scheme is demonstrated through the simulation and experimental studies on the benchmark three-tank system. (C) 2016 Elsevier Ltd. All rights reserved

Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

The performance of Bayesian state estimators, such as the extended Kalman filter (EKE), is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. The parameters of the noise densities associated with these uncertainties are, however, often treated as 'tuning parameters' and adjusted in an ad hoc manner while carrying out state and parameter estimation. In this work, two approaches are developed for constructing the maximum likelihood estimates (MLE) of the state and measurement noise covariance matrices from operating input-output data when the states and/or parameters are estimated using the EKF. The unmeasured disturbances affecting the process are either modelled as unstructured noise affecting all the states or as structured noise entering the process predominantly through known, but unmeasured inputs. The first approach is based on direct optimisation of the ML objective function constructed by using the innovation sequence generated from the EKF. The second approach - the extended EM algorithm - is a derivative-free method, that uses the joint likelihood function of the complete data, i.e. states and measurements, to compute the next iterate of the decision variables for the optimisation problem. The efficacy of the proposed approaches is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that both the proposed approaches generate fairly accurate estimates of the noise covariances. Experimental studies on a benchmark laboratory scale heater-mixer setup demonstrate a marked improvement in the predictions of the EKE that uses the covariance estimates obtained from the proposed approaches. (C) 2011 Elsevier Ltd. All rights reserved

Stochastic predictive control with adaptive model maintenance

The closed-loop performance of model-based controllers often degrades over time due to increased model uncertainty. Some form of model maintenance must be performed to regularly adapt the system model using closed-loop data. This paper addresses the problem of control-oriented model adaptation in the context of predictive control of stochastic linear systems. A stochastic predictive control approach is presented that integrates stochastic optimal control with control-oriented input design in order to confer some degree of probing effect to the control inputs. The probing effect will enable generating informative closed-loop data for (online) control-oriented model maintenance. In a simulation study, the performance of the proposed stochastic predictive control approach with integrated input design is demonstrated on a atmospheric-pressure plasma jet with potential biomedical applications

A Moving Window Formulation for Recursive Bayesian State Estimation of Systems with Irregularly Sampled and Variable Delays in Measurements

The time delay involved between sampling and obtaining measurements of certain quality variables is a common scenario in various process applications. Further, this delay is not fixed and can vary for various reasons. Moreover, certain measurements may be sampled at irregular time intervals. The state estimation algorithms available in the literature have been developed for the scenario where the measurements are sampled regularly or are available after a fixed time delay. In this work, a recursive moving window Bayesian state estimator formulation is proposed to utilize such measurements with variable time delays to compute the state estimates. The length of the moving window ensures that the algorithm utilizes all the available measurements (delayed or otherwise) for computing the state estimates. In practice, it may also become necessary to account for the physical bounds on the states. A constrained version of the moving window recursive state estimator is also developed to yield state estimates that are consistent with their respective bounds and constraints. The efficacy of the unconstrained moving window state estimator is demonstrated by application on the benchmark Tennessee Eastman simulation case study and an experimental two-tank heater-mixer setup, while the efficacy of the constrained moving window state estimator is demonstrated by simulation of a benchmark gas-phase batch reactor system