Adaptive control of open-loop unstable systems with input and state constraints

The problem of stabilization and null controllability of open loop unstable discrete-time multi-input systems with constraints on the states and the control was addressed in a previous paper (see Proc. 32nd IEEE Conf. Decision and Control, San Antonio, TX, USA, IEEE, p.3473-8, 1994). In the present paper we analyze some of the properties of the suggested quadratically saturating control, and extend the previous results to the systems with only partial state information and/or unknown parameters. We note that the idea of adaptive control design for open-loop unstable systems with constraints was the original motivation for the analysis in the previous paper. Although the proposed solution may be more conservative, especially in the case of linear constraints, it has the advantage that the solution in analytical, and easier to compute.