Search

Stochastic model predictive control (SMPC) provides a probabilistic framework for MPC of systems with stochastic uncertainty. A key feature of SMPC is the inclusion of chance constraints, which enables a systematic trade-off between attainable control performance and probability of state constraint violations in a stochastic setting. This paper presents an overview of core concepts in SMPC in relation to MPC and stochastic optimal control, with numerical illustrations on a typical chemical process. Estimation of stochastic disturbances as well as the impact of estimation quality of stochastic disturbances on the SMPC performance are discussed. Some avenues for future research in SMPC are suggested. [ABSTRACT FROM AUTHOR]

• Novel constrained grey-box optimization framework using Gaussian process models. • New almost everywhere differentiable acquisition function for composite functions. • Efficient moment-based approximation of chance constraints. • Tailored algorithm for enrichment sub-problem that exploits model structure. • Performance comparison with Bayesian optimization on diverse set of test problems. [Display omitted] Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems. [ABSTRACT FROM AUTHOR]

Deterministic optimization approaches have been well developed and widely used in the process industry to accomplish off-line and on-line process optimization. The challenging task for the academic research currently is to address large-scale, complex optimization problems under various uncertainties. Therefore, investigations on the development of stochastic optimization approaches are needed. In the last few years we proposed and utilized a new solution concept to deal with optimization problems under uncertain operating conditions as well as uncertain model parameters. Stochastic optimization problems are solved with the methodology of chance constrained programming. The problem is to be relaxed into an equivalent nonlinear optimization problem such that it can be solved by a nonlinear programming (NLP) solver. The major challenge towards solving chance constrained optimization problems lies in the computation of the probability and its derivatives of satisfying inequality constraints. Approaches to addressing linear, nonlinear, steady-state as well as dynamic optimization problems under uncertainty have been developed and applied to various optimization tasks with uncertainties such as optimal design and operation, optimal production planning as well as optimal control of industrial processes under uncertainty. In this paper, a comprehensive summary of our recent work on the theoretical development and practical applications is presented. [Copyright &y& Elsevier]