545 research outputs found
Sum-of-Squares approach to feedback control of laminar wake flows
A novel nonlinear feedback control design methodology for incompressible
fluid flows aiming at the optimisation of long-time averages of flow quantities
is presented. It applies to reduced-order finite-dimensional models of fluid
flows, expressed as a set of first-order nonlinear ordinary differential
equations with the right-hand side being a polynomial function in the state
variables and in the controls. The key idea, first discussed in Chernyshenko et
al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating
and optimising long-time averages of a cost are relaxed by using the
upper/lower bounds of such averages as the objective function. In this setting,
control design reduces to finding a feedback controller that optimises the
bound, subject to a polynomial inequality constraint involving the cost
function, the nonlinear system, the controller itself and a tunable polynomial
function. A numerically tractable approach to the solution of such optimisation
problems, based on Sum-of-Squares techniques and semidefinite programming, is
proposed.
To showcase the methodology, the mitigation of the fluctuation kinetic energy
in the unsteady wake behind a circular cylinder in the laminar regime at
Re=100, via controlled angular motions of the surface, is numerically
investigated. A compact reduced-order model that resolves the long-term
behaviour of the fluid flow and the effects of actuation, is derived using
Proper Orthogonal Decomposition and Galerkin projection. In a full-information
setting, feedback controllers are then designed to reduce the long-time average
of the kinetic energy associated with the limit cycle. These controllers are
then implemented in direct numerical simulations of the actuated flow. Control
performance, energy efficiency, and physical control mechanisms identified are
analysed. Key elements, implications and future work are discussed
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation
In this paper, two methods for approximating the stabilizing solution of the Hamilton–Jacobi equation are proposed using symplectic geometry and a Hamiltonian perturbation technique as well as stable manifold theory. The first method uses the fact that the Hamiltonian lifted system of an integrable system is also integrable and regards the corresponding Hamiltonian system of the Hamilton–Jacobi equation as an integrable Hamiltonian system with a perturbation caused by control. The second method directly approximates the stable flow of the Hamiltonian systems using a modification of stable manifold theory. Both methods provide analytical approximations of the stable Lagrangian submanifold from which the stabilizing solution is derived. Two examples illustrate the effectiveness of the methods.
Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions
The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler\u27s lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the efficiency of the proposed methods in terms of H-infinity performance when compared with other strategies from the literature
Multi-objective optimization framework for networked predictive controller design
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Networked Control Systems (NCSs) often suffer from random packet dropouts which deteriorate overall system's stability and performance. To handle the ill effects of random packet losses in feedback control systems, closed over communication network, a state feedback controller with predictive gains has been designed. To achieve improved performance, an optimization based controller design framework has been proposed in this paper with Linear Matrix Inequality (LMI) constraints, to ensure guaranteed stability. Different conflicting objective functions have been optimized with Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The methodology proposed in this paper not only gives guaranteed closed loop stability in the sense of Lyapunov, even in the presence of random packet losses, but also gives an optimization trade-off between two conflicting time domain control objectives
Data-driven Invariance for Reference Governors
This paper presents a novel approach to synthesizing positive invariant sets
for unmodeled nonlinear systems using direct data-driven techniques. The
data-driven invariant sets are used to design a data-driven reference governor
that selects a reference for the closed-loop system to enforce constraints.
Using kernel-basis functions, we solve a semi-definite program to learn a
sum-of-squares Lyapunov-like function whose unity level-set is a constraint
admissible positive invariant set, which determines the constraint admissible
states as well as reference inputs. Leveraging Lipschitz properties of the
system, we prove that tightening the model-based design ensures robustness of
the data-driven invariant set to the inherent plant uncertainty in a
data-driven framework. To mitigate the curse-of-dimensionality, we repose the
semi-definite program into a linear program. We validate our approach through
two examples: First, we present an illustrative example where we can
analytically compute the maximum positive invariant set and compare with the
presented data-driven invariant set. Second, we present a practical autonomous
driving scenario to demonstrate the utility of the presented method for
nonlinear systems
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