Reference governors for linear systems with nonlinear constraints

The paper considers the application of reference governors to linear discrete-time systems with constraints on state and output variables given by functional inequalities. Properties and on-line computational procedures which facilitate the implementation of the reference governors for linear systems with convex, convex quadratic, concave, and mixed logical dynamic constraints of if-then type are discussed. Two examples are considered. The first example is a three dimensional spacecraft rendezvous and proximity maneuvering problem where constraints are imposed on thrust magnitude, velocity of approach, collision avoidance, and positioning within the line-of-sight cone. While the spacecraft relative motion dynamics in this problem can be treated as linear, two of the constraints in this problem are convex quadratic and one of the constraints is of mixed logical dynamic type. Our second example is an electromagnetically actuated mass spring damper that has linear dynamics, a linear constraint on position, and a concave nonlinear constraint on the force due to nonlinear dependence of force on the distance. The reference governor based on the developments in this paper can elegantly and effectively handle the prescribed constraints.