No abstract

This paper considers the finite dimensional approximation of dual problems that appear in control design problems, namely the discrete-time multi-objective el control problem and the continuous-time reference management problem for constrained systems. The dual problem is constructed with the properties that it does not have the duality gap with the primal problem, and that the space of variables is separable. The results are important for the exact computation of the optimal value. They provide an effective way to find separating hyperplanes between the feasible set and the level set of the cost functional.

No abstract

This paper studies the L2 gain analysis problem of linear parameter varying systems. The primal/dual framework is exploited, and the duality theorem for an abstract linear programming problem with constraints described by an unbounded operator is established. If the system matrices are smooth in the scheduling parameter, the dual variables can be chosen from a separable space. This allows finite dimensional approximation without duality gap. Furthermore, when the system murices are piecewise affine in the scheduling parameter, the problem can be cast as finite-dimensional LMI optimization problems.

In this paper, an l1-optimal control problem with frequency and time domain constraints on a closed-loop response is considered.The problem is formulated as an infinite dimensional linear programming problem, and the primal and dual approach is exploited. This sometimes results in non-zero gap between the primal and dual costs. This paper proposes a new method to approximate the primal and dual problems without the duality gap. As a result, the method yields a sub-optimal solution with arbitrary accuracy.