Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer

Abstract

ABSTRACT Lower and upper state bounds can be computed independently for cooperative ordinary differential equations (ODEs) with interval-valued initial conditions. Then, all reachable states are enclosed by two decoupled, point-valued initial value problems (IVPs). This evaluation, however, becomes more challenging if the IVPs are, furthermore, subject to uncertain parameters. In the simplest case, to which this paper is restricted, the ODEs are linear with uncertain system and input matrices. Besides actually linear dynamics, also nonlinear input-affine state-space representations can be accounted for after embedded them into a polytopic uncertainty model representing a conservative convex combination of extremal system realisations. To perform the reachability analysis for closed-loop control structures without significant computational effort, it is reasonable to impose constraints during control synthesis so that the closed-loop ODEs remain cooperative. Suitable design procedures based on linear matrix inequalities are derived in this paper together with a validation for a prototypical heat transfer process.