Constrained tracking control of stochastic multivariable nonlinear systems using unscented Kalman filter

Abstract

To overcome the challenges, including propagation of the stochastic uncertainties through a nonlinear model and full determination of the states over the prediction horizon for successful online implementation of the stochastic nonlinear model predictive control (SNMPC) framework, this paper proposes the utilisation of unscented Kalman filter (UKF) in the context of SNMPC for the stochastic multivariable nonlinear systems to track a given trajectory in the presence of stochastic uncertainties and system constraints. Taking advantage of the UKF which estimates and propagates the entire conditional distribution of the states along the time horizon by taking into account errors due to external disturbances and measurement noises as well as errors introduced due to the imperfect knowledge of the states through the state estimation, the proposed UKF-SNMPC framework utilises the conditional mean and conditional covariance of the states to reformulate the model cost and constraint functions, which yields a tractable framework for handling nonlinear chance-constrained tracking control problems. By employing a cancellation strategy, the control law consists of two components, that is, a tracking control law is designed to follow the desired trajectory and an uncertainty compensation control law designed to accommodate the nonlinearities in the plant. The concept of ‘robust horizon’ is introduced as the terminal constraint to prevent the covariance from the explosion and guarantee the convergence of the UKF-SNMPC framework. Performance bounds of the closed-loop system are theoretically analysed. Comparative studies on numerical examples are carried out to verify the effectiveness of the proposed UKF-SNMPC scheme.