Control of systems with constraints on state and input - Design via duality

This paper studies a way to design constrained control systems using duality theory. Many such design problems are formulated as an optimization problem on possibly infinite-dimensional spaces. Using the primal-dual approach, it is shown that a sequence of finite dimensional optimization problems can be constructed to solve the original infinite-dimensional problem for arbitrary given error bounds. Applications of the proposed method to the constrained control problems include the ℓ₁ control problem subject to time/frequency domain constraints and the reference management problem.