A receding horizon control of Markov jump linear systems with imperfect state information and probabilistic state constraints

A receding horizon control of discrete-time Markov jump linear systems with additive Gaussian measurement and process noise, and stochastic constraints is addressed. Given the availability of the underlying jump parameter, recursive equations for optimal state estimation that resemble Kalman filter equations are provided. The receding horizon control law is considered in state-feedback form. Under some detectability conditions, the overall system is pre-stabilized off-line with state-feedback gains by ensuring mean square boundedness of system states. Using a Gaussian assumption, the stochastic constraints are reposed and approximated the original problem as a tractable deterministic receding horizon control problem in terms of conditional means and covariances of the state variable, and solved it on-line with control offset terms. The overall approach is applied on a vertical take-off and landing vehicle dynamical system example.