Computation of low-complexity control-invariant sets for systems with uncertain parameter dependence

Computation of robust control invariant sets with predefined complexity for uncertain systems

“…We allow the sets , and to be non‐symmetric, unlike References 10,11,17,18 where some or all the sets are assumed to be symmetric. The affine parameter dependence of the system, as considered in for example, References 11,18, is just a special case that corresponds to D p = 0 in (8).…”

“…Depending upon the choice of the initial set, the result of such a recursive method is the arbitrarily close outer/inner approximation of the maximal RCI set 8,9 . Although effective, the geometric approach does not guarantee finite time termination of the procedure, and also the obtained set may have a very high representational complexity 2,4,8‐11 . For polytopic systems, the computational complexity grows exponentially with each additional vertex and system dimension 1 …”

“…In this paper, we present a novel algorithm to compute an RCI set with a predefined complexity for an uncertain system with additive disturbances. Similar to References 10,22, we consider rationally parameter‐dependent systems, which are more general than other linear system descriptions discussed above in that they can be used to approximately describe many nonlinear engineering systems 23 . We start by proposing a new necessary and sufficient condition for invariance, which is a slight extension of the result in Reference 24 for the considered system.…”

“…By then using this condition along with the full block S‐procedure, 25 a sufficient linear matrix inequality (LMI) feasibility condition for invariance is derived. Also, an approach to directly maximize the volume of the RCI sets is presented, which is less conservative than using an indirect approach used in References 10,11. In contrast to References 10,11,15,17,18,22, we directly compute the RCI sets without imposing any structural restrictions on the control input so that possibly larger RCI sets can be obtained.…”

“…Also, an approach to directly maximize the volume of the RCI sets is presented, which is less conservative than using an indirect approach used in References 10,11. In contrast to References 10,11,15,17,18,22, we directly compute the RCI sets without imposing any structural restrictions on the control input so that possibly larger RCI sets can be obtained. The algorithm generates RCI sets of monotonically increasing volume at each iteration until convergence.…”