Partially Observed Steering the State of Linear Stochastic Systems

The presence of terminal state constraints in terms of expectations is studied for steering the state of partially observed linear stochastic systems. Three scenarios for the observation process are considered, namely, (i) continuous-time exact observations of the state, (ii) discrete-time exact observations of the state, and (iii) discrete-time exact observations of the state accompanied by continuous-time noisy observations of the state. Closed form expressions are presented for the optimal inputs enforcing the terminal state constraint under these information structures, which are expressed in terms of controllability Gramians and solutions of Riccati and Lyapunov equations. Numerical examples are provided to illustrate the results.