MIMO l1 optimal control problems via the polynomial equations approach

The general MIMO multi-block l1-optimal control problem is considered. A novel solution is derived by resorting to polynomial techniques and simple algebraic conditions on the free parameter of the YJBK parameterization. As a result, we arrive at unconstrained LP formulations, less affected by redundancy and solvable by standard LP solvers. As usual, because the optimal controller is in general infinite-dimensional, a solution scheme based on solving sequences of increasing larger finite dimensional sub/super-optimal optimization problem is proposed, viz. sequences of finite dimensional optimization problems whose solutions provide lower and, respectively, upper bounds to the optimum, monotonically converging to it. Finally, an example is presented in order to exemplify the theory and show the effectiveness of the method.