Polytopic Region Research Articles

ROBUST OFFSET-FREE MODEL PREDICTIVE CONTROL

In this paper a method for designing robust offset-free MPC controllers for (possibly) nonzero targets is presented. The proposed controller is guaranteed to track the controlled variable to its target for any plant that lies in a polytopic region. First, an off-line design of a robust unconstrained offset-free controller is accomplished, and a corresponding invariant region is computed in which this controller is well defined and does not violate the constraints. Next, the online implementation requires the use of this unconstrained controller if the system state is in the invariant region or, if not, the solution of a min-max finite horizon optimization problem. An illustrative example is presented.

Robust Polynomial Assignment for Uncertain Periodic Discrete-Time Systems

In this paper the problem of the robust assignment of the closed-loop polynomial for discrete-time SISO periodic systems is investigated. It is shown that this problem can be formulated as a convex optimization problem if the coefficients of the plant and of the closed-loop polynomial belong to polytopic regions. The use of periodic controllers for time-invariant plants provides further degrees of freedom that increase the feasible uncertainty region of the plant. In the paper, the robust pole-assignment via periodic memoryless output feedback is considered.

Strong stabilization over polytopes

The problem considered consists of finding a stable controller assigning a closed-loop characteristic polynomial over a stability domain specified as a polytopic region of the space of characteristic polynomial coefficients. The controller is required to be stable with respect to the same polytopic stability region specified for the closed loop system.

A Constrained Optimization Approach for Robust D-Stability and Robust H 2 Performance Design

Abstract This paper presents a methodology for the design of robust D-stability and robust H performance controllers for systems with linear interval uncertainties in the plant parameters. We introduce a performance H index corresponding to the worst H norm of the closed-loop transfer function over the extreme uncertain parameters. We propose a constraint handling Genetic Algorithm to optimize the performance index. The search domain of the genetic algorithm is given by a poly topic region in the space of the controller parameters containing the set of all the controllers that solves the robust D-stability problem. Therefore, the genetic algorithm efficiently searches, inside the polytopic region, for the robust D-stability controller that minimizes the given H performance index.

Maximal polytopic stability domains in parameter space for uncertain systems

Abstract Some results on the stability and pole location of families of uncertain systems with characteristic polynomial coefficients affected by structured perturbations are presented. The case in which the coefficients are affine in a set of system physical parameters is considered, assuming that the parameters are subject to polytopic perturbations of a given structure. For these cases, which often arise in system stability robustness analysis, as for example in the robustification of controllers for multivariable closed-loop systems, a procedure is given to estimate maximal stability polytopic regions in the space of parameters. This result is also used to derive simple necessary and sufficient conditions for the discrete-time stability of convex combinations of two polynomials.