(665d) Carleman Linearization-Based Analytical Model Predictive Control Actions of Nonlinear Systems
Carleman linearization-based analytical model predictive control actions of nonlinear systems
Model Predictive Control (MPC) is developed as a powerful control method applied in chemical, pharmaceutical, and petroleum industries over the past two decades. Since control signals are computed by repeatedly solving receding-horizon optimization problems, the control actions evolve as the system dynamics carry on, which enables MPC to reject external disturbances and tolerate model inaccuracy while following process constraints. The computation of MPC is more complex than that of classical controllers. Complex systems with high nonlinearity require significant amount of computation. When constraints are considered, the amount of computation is even higher and it is impossible to avoid this issue by deriving analytical solutions. Developing an advanced and systematic MPC synthesis methodology for nonlinear complex systems is motivated. 
The objective is to derive search algorithms that reduce the amount of computation and remove computational delay in resolving dynamic optimization problems for nonlinear complex systems. The search algorithm computed from an algebraic nonlinear optimization problem (NLP) with analytically computed sensitivity reduces computation and removes computational delay in online operations. Based on Carleman linearization, the method proposed enables analytical solutions to the optimal control problem, while keeping the nonlinearity of system dynamics and constraints. Control actions are designed in bilinear expressions which combine feedback control laws and constant control signals.
The proposed method was computationally efficient by allowing standard, gradient-based, search algorithms. Compared with nonlinear MPC, the proposed method takes less time to compute the optimal policy. The work is illustrated by an unstable Continuous Stirred Tank Reactor with high nonlinearity and unmeasured disturbances. With the proposed method, the closed loop system remained high practical stability under disturbances and the deviation from set-points maintained less than 1%.
 A. Armaou and A. Ataei, “Piece-wise constant predictive feedback control of nonlinear systems,” J. Process Control, vol. 24, no. 4, pp. 326–335, Apr. 2014.
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