Stochastic tracking control of multivariable nonlinear systems subject to external disturbances

• Published in: International journal of robust and nonlinear control Vol. 30; no. 16; pp. 6931 - 6946
• Main Author: Ma, Tong
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 10.11.2020; Wiley Subscription Services, Inc
• Subjects: Adaptive algorithms; Adaptive control; Computing costs; Control algorithms; Control methods; Control theory; Cost function; Covariance; disturbance rejection; Disturbances; Evolution; Feasibility; Feedback control; Feedback loops; Linear matrix inequalities; linear matrix inequality; Mathematical analysis; Mathematical models; Multivariable control; Nonlinear control; Nonlinear systems; Optimization; Optimization techniques; Predictive control; Semidefinite programming; stochastic model predictive control; Terminal constraints; tracking; Tracking control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5149

By incorporating a disturbance rejection control law with receding horizon optimization technique, this paper synthesizes a stochastic tracking nonlinear model predictive control (STNMPC) framework for multivariable nonlinear systems subject to external disturbances. In the control scheme, a cancellation strategy combined with a feedforward prefilter is adopted to drive the expected value of the output to the reference signal by compensating the undesired components in the feedback loop. Given the statistics of the stochastic disturbances, covariance evolution is involved to describe the propagation of uncertainties through the system model and a time‐varying feedback control law is designed to minimize the covariance. By employing the strong optimizing property of model predictive control (MPC), a stochastic MPC (SMPC) framework is formulated. By using the Schur complement, the nonlinear dependence of covariance evolution on time‐varying feedback control gains is removed and the cost function is reformulated as a linear one with linear matrix inequalities, which resolves the implementation issue existing in the numerical problem. To guarantee the convergence and recursive feasibility of the SMPC framework, terminal constraint with some tricks are applied, for example, Lyapunov equation. The well‐established theories and tricky techniques allow to cast the SMPC framework as a semidefinite programming, which reduces the computational cost and yields a feasible numerical solution. Numerical examples are provided to demonstrate the effectiveness of the proposed control method, comparisons with some adaptive control algorithm shows the superiority of the proposed approach.