Design Of Model Predictive Control Algorithms Based On Multi-Step Control Policy For Stochastic Systems With Multiplicative Uncertainty

Stochastic systems with multiplicative uncertainty are widespread inpractice. Because of the stochastic nature of the system state, optimizationand control of this kind of systems should take the effect of randomness intoconsideration for both control objective and constraint satisfaction. Modelpredictive control is an advanced control algorithm for its ability to handleconstraints. When it is applied to systems with multiplicative uncertainty, thehandling of constraint satisfaction and optimization under randomness aretherefore key factors for achieving good control performance. This paperdevelops stochastic model predictive control algorithms addressing softconstraints, i.e., probabilistic constraints and mean and variance constraints.The algorithms use stochastic information of the model to control stochasticdynamics of the state, so that soft constraints are ensured as well as thecontrol performance is optimized. The main works established are as follows.1) Design of stochastic model predictive control algorithm based onmulti-step feedback laws. To ensure satisfaction of probabilistic stateconstraints, linear matrix inequalities are given at first to computeellipsoids of probabilistic distribution of state under multi-stepfeedback laws; then sufficient conditions are obtained for thesatisfaction of probabilistic state constraints and input constraintswithin the ellipsoids. The formulation of expectation control performance under multi-step feedback laws is derived. Based onthese works, we design a stochastic model predictive controlalgorithm with recursive feasibility and stability proved.2) Design of simplified algorithm for stochastic model predictivecontrol algorithm based on multi-step feedback laws. To reduce theonline comutation load of the forgoing algorithm, we prove thatcondition of linear matrix inequalities of the forgoing algorithm canbe obtained by using convex combination. The simplified algorithmis proposed based on this proof. Offline part of the algorithmcompute matrix variables needed in the convex combination, and theonline part calculates combinational coefficients. Theorecticalanalysis and simulation results show that the simplified algorithmreduces the computing scale and ensures satisfaction of constraints.3) Design of mean-variance multi-step model predictive control. Toformulate mean and variance constraints, we first give linear matrixinequalities to estimate the state covariance matrices in the recedinghorizon, with the effectiveness of this estimation ensured; then thecovariance constraints are transformed into the constraints for thestate covariance matrices. The relationship between mean-varianceperformance function and the expectation performance function isanalysised, and the computation of the mean-variance performancefunction is derived. Based on above works, we design stochasticmodel predictive control algorithm that satisfies mean and varianceconstraints. Simulation study verifies the effectiveness of theproposed algorithm.4) A CSTR case study. Considering the parameter uncertainty of thecontinus stirred-tank reactor, we model the CSTR at its equilibrium operating point as a stochastic system with multiplicative uncertainty.Stochastic model predictive control algorithm based on multi-stepfeedback laws is applied to this model to control the CSTR, and thesimulation results verify the control performance of the algorithm.