142 research outputs found
Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances
The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes
This paper presents new methods for set-valued state estimation and active
fault diagnosis of linear descriptor systems. The algorithms are based on
constrained zonotopes, a generalization of zonotopes capable of describing
strongly asymmetric convex sets, while retaining the computational advantages
of zonotopes. Additionally, unlike other set representations like intervals,
zonotopes, ellipsoids, paralletopes, among others, linear static constraints on
the state variables, typical of descriptor systems, can be directly
incorporated in the mathematical description of constrained zonotopes.
Therefore, the proposed methods lead to more accurate results in state
estimation in comparison to existing methods based on the previous sets without
requiring rank assumptions on the structure of the descriptor system and with a
fair trade-off between accuracy and efficiency. These advantages are
highlighted in two numerical examples.Comment: This paper was accepted and presented in the 1st IFAC Virtual World
Congress, 202
Fault detection and isolation using viability theory and interval observers
This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approachPeer ReviewedPostprint (author's final draft
A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in
robotics and has a wide range of applications. There are two main families of
methods to address TOPP: Numerical Integration (NI) and Convex Optimization
(CO). NI-based methods are fast but difficult to implement and suffer from
robustness issues, while CO-based approaches are more robust but at the same
time significantly slower. Here we propose a new approach to TOPP based on
Reachability Analysis (RA). The key insight is to recursively compute reachable
and controllable sets at discretized positions on the path by solving small
Linear Programs (LPs). The resulting algorithm is faster than NI-based methods
and as robust as CO-based ones (100% success rate), as confirmed by extensive
numerical evaluations. Moreover, the proposed approach offers unique additional
benefits: Admissible Velocity Propagation and robustness to parametric
uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure
Data-driven Polytopic Output Synchronization of Heterogeneous Multi-agent Systems from Noisy Data
This paper proposes a novel approach to addressing the output synchronization
problem in unknown heterogeneous multi-agent systems (MASs) using noisy data.
Unlike existing studies that focus on noiseless data, we introduce a
distributed data-driven controller that enables all heterogeneous followers to
synchronize with a leader's trajectory. To handle the noise in the
state-input-output data, we develop a data-based polytopic representation for
the MAS. We tackle the issue of infeasibility in the set of output regulator
equations caused by the noise by seeking approximate solutions via constrained
fitting error minimization. This method utilizes measured data and a
noise-matrix polytope to ensure near-optimal output synchronization. Stability
conditions in the form of data-dependent semidefinite programs are derived,
providing stabilizing controller gains for each follower. The proposed
distributed data-driven control protocol achieves near-optimal output
synchronization by ensuring the convergence of the tracking error to a bounded
polytope, with the polytope size positively correlated with the noise bound.
Numerical tests validate the practical merits of the proposed data-driven
design and theory
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