7 research outputs found
Invariant Set-based Methods for the Computation of Input and Disturbance Sets
This dissertation presents new methods to synthesize disturbance sets and input constraints set for constrained linear time-invariant systems. Broadly, we formulate and solve optimization problems that (a) compute disturbance sets such that the reachable set of outputs approximates an assigned set, and (b) compute input constraint sets guaranteeing the stabilizability of a given set of initial conditions. The proposed methods find application in the synthesis and analysis of several control schemes such as decentralized control, reduced-order control, etc., as well as in practical system design problems such as actuator selection, etc.
The key tools supporting the develpment of the aforementioned methods are Robust Positive Invariant (RPI) sets. In particular, the problems that we formulate are such that they co-synthesize disturbance/input constraint sets along with the associated RPI sets. This requires embedding existing techniques to compute RPI sets within an optimization problem framework, that we facilitate by developing new results related to properties of RPI sets, polytope representations, inclusion encoding techniques, etc.
In order to solve the resulting optimization problems, we develop specialized structure-exploiting solvers that we numerically demonstrate to outperform conventional solution methods. We also demonstrate several applications of the methods we propose for control design. Finally, we extend the methods to tackle data-driven control synthesis problems in an identification-for-control framework
Parameter Dependent Robust Control Invariant Sets for LPV Systems with Bounded Parameter Variation Rate
Real-time measurements of the scheduling parameter of linear
parameter-varying (LPV) systems enables the synthesis of robust control
invariant (RCI) sets and parameter dependent controllers inducing invariance.
We present a method to synthesize parameter-dependent robust control invariant
(PD-RCI) sets for LPV systems with bounded parameter variation, in which
invariance is induced using PD-vertex control laws. The PD-RCI sets are
parameterized as configuration-constrained polytopes that admit a joint
parameterization of their facets and vertices. The proposed sets and associated
control laws are computed by solving a single semidefinite programing (SDP)
problem. Through numerical examples, we demonstrate that the proposed method
outperforms state-of-the-art methods for synthesizing PD-RCI sets, both with
respect to conservativeness and computational load.Comment: 8 pages, 6 figure
Data-Driven Synthesis of Configuration-Constrained Robust Invariant Sets for Linear Parameter-Varying Systems
We present a data-driven method to synthesize robust control invariant (RCI)
sets for linear parameter-varying (LPV) systems subject to unknown but bounded
disturbances. A finite-length data set consisting of state, input, and
scheduling signal measurements is used to compute an RCI set and
invariance-inducing controller, without identifying an LPV model of the system.
We parameterize the RCI set as a configuration-constrained polytope whose
facets have a fixed orientation and variable offset. This allows us to define
the vertices of the polytopic set in terms of its offset. By exploiting this
property, an RCI set and associated vertex control inputs are computed by
solving a single linear programming (LP) problem, formulated based on a
data-based invariance condition and system constraints. We illustrate the
effectiveness of our approach via two numerical examples. The proposed method
can generate RCI sets that are of comparable size to those obtained by a
model-based method in which exact knowledge of the system matrices is assumed.
We show that RCI sets can be synthesized even with a relatively small number of
data samples, if the gathered data satisfy certain excitation conditions.Comment: 7 pages, 4 figures, 2 table
Computation of safe disturbance sets using implicit RPI sets
Given a stable linear time-invariant (LTI) system subject to output
constraints, we present a method to compute a set of disturbances such that the
reachable set of outputs matches as closely as possible the output constraint
set, while being included in it. This problem finds application in several
control design problems, such as the development of hierarchical control loops,
decentralized control, supervisory control, robustness-verification, etc. We
first characterize the set of disturbance sets satisfying the output constraint
inclusion using corresponding minimal robust positive invariant (mRPI) sets,
following which we formulate an optimization problem that minimizes the
distance between the reachable output set and the output constraint set. We
tackle the optimization problem using an implicit RPI set approach that
provides a priori approximation error guarantees, and adopt a novel disturbance
set parameterization that permits the encoding of the set of feasible
disturbance sets as a polyhedron. Through extensive numerical examples, we
demonstrate that the proposed approach computes disturbance sets with reduced
conservativeness improved computational efficiency than state-of-the-art
methods.Comment: 16 pages, 6 figure
Data-driven synthesis of Robust Invariant Sets and Controllers
This paper presents a method to identify an uncertain linear time-invariant
(LTI) prediction model for tube-based Robust Model Predictive Control (RMPC).
The uncertain model is determined from a given state-input dataset by
formulating and solving a Semidefinite Programming problem (SDP), that also
determines a static linear feedback gain and corresponding invariant sets
satisfying the inclusions required to guarantee recursive feasibility and
stability of the RMPC scheme, while minimizing an identification criterion. As
demonstrated through an example, the proposed concurrent approach provides less
conservative invariant sets than a sequential approach