Fast stochastic model predictive control of high-dimensional systems

Abstract

Probabilistic uncertainties and constraints are ubiquitous in complex dynamical systems and can lead to severe closed-loop performance degradation. This paper presents a fast algorithm for stochastic model predictive control (SMPC) of high-dimensional stable linear systems with time-invariant probabilistic uncertainties in initial conditions and system parameters. Tools and concepts from polynomial chaos theory and quadratic dynamic matrix control inform the development of an input-output formulation for SMPC with output constraints. Generalized polynomial chaos theory is used to enable efficient uncertainty propagation through the high-dimensional system model. Galerkin projection is used to construct the polynomial chaos expansion for a general class of linear differential algebraic equations (DAEs), so that the SMPC algorithm is applicable to both regular and singular/descriptor systems. The fast SMPC approach is applied for control of an endto-end continuous pharmaceutical manufacturing process with approximately 8000 states. The on-line computational cost of the proposed probabilistic input-output SMPC algorithm is independent of the state dimension and, therefore, alleviates the prohibitive computational costs of control of uncertain systems with large state dimension.

Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems

“…Needless to say, the computational cost for PSE depends on the number of uncertain parameters and the number of terms considered in the PSE, which both require the calculation of additional sensitivities to construct representative low-order models. 67,68 Adding more terms to the PSE can improve the accuracy of the PSEbased approximation 35,36,38 and the number of terms required for reasonable accuracy depends on the degree of nonlinearity of the system model. Higher-order series expansions improve the model predictions but result in higher computational costs due to the computation of additional higher-order sensitivity terms.…”

Synthesise of MPC controller for uncertain systems subject to input and output constraints: application to anthropomorphic robot arm

“…In the practice, control systems have constraints which can have damaging effects on system performances (Paulson et al, 2014). These constraints can be identified as actuator saturation, actuator magnitude and restrictions on output variables (Chen, 2010;Velosa, 2015).…”

Fast Model Predictive Control for hydrogen outflow regulation in Ethanol Steam Reformers

“…The suitability of this control scheme for SISO and MIMO plants has been highlighted by many authors, e.g., [12], [13]. When input-output models are considered for controlling high-order systems, a QDMC scheme allows to dramatically reduce the online computational complexity of an optimization-based control approach [14], [15], [16]. In the following, the QDMC formulation for the SISO case is firstly presented and then the discussion is extended to the MIMO case in Section IV-B; for more details see [10], [17], [18].…”