1998 Volume 11 Issue 6 Pages 316-323
A piecewise-linear state feedback control law for the systems with constraints, based on the theory of maximal CPI set, is derived. The control law increases the feedback gain in a piecewise constant manner as the controlled error converges toward the origin. It guarantees that input bounds are never exceeded and, as a consequence, maintains stability of the system. The sequence of feedback gains is computed off-line via quadratic and convex optimization techniques. The algorithms for gain switching need on-line computations using observed state variable. These on-line computations are simple, so they can be easily implemented. The proposed switching control law is tested for the inverted pendulum model, and its effectiveness is assured. Possibility of improving the proposed control law by using information of vertices of the maximal CPI set is also discussed. However, this extension requires terrible numerical computations of all vertices of convex polyhedral set. Their subsequent implementation is difficult for higher dimensional plants.