A convex formulation for receding horizon control of constrained discrete-time systems with guaranteed l2 gain

This paper is concerned with the control of constrained linear systems subject to bounded disturbances and mixed convex constraints on the states and inputs, using a finite horizon control policy where the input at each time is parameterized as an affine function of current and prior states. We employ a quadratic cost function where the disturbance is negatively weighted as in H-infinity control, and show that receding horizon control laws based on this combination of control policy and objective function offer two advantages. First, the finite-horizon min-max optimal control problem to be solved at each time step can be rendered convex-concave, with a number of decision variables and constraints that grows polynomially with the problem size, making its solution amenable to standard techniques in convex optimization. Second, the scheme allows one to guarantee that the l2 gain of the resulting closed-loop system is bounded, and that the achievable bound decreases with the length of the planning horizon.