15 research outputs found
Convex Optimization In Identification Of Stable Non-Linear State Space Models
A new framework for nonlinear system identification is presented in terms of
optimal fitting of stable nonlinear state space equations to input/output/state
data, with a performance objective defined as a measure of robustness of the
simulation error with respect to equation errors. Basic definitions and
analytical results are presented. The utility of the method is illustrated on a
simple simulation example as well as experimental recordings from a live
neuron.Comment: 9 pages, 2 figure, elaboration of same-title paper in 49th IEEE
Conference on Decision and Contro
Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization
Control contraction metrics (CCMs) are a new approach to nonlinear control
design based on contraction theory. The resulting design problems are expressed
as pointwise linear matrix inequalities and are and well-suited to solution via
convex optimization. In this paper, we extend the theory on CCMs by showing
that a pair of "dual" observer and controller problems can be solved using
pointwise linear matrix inequalities, and that when a solution exists a
separation principle holds. That is, a stabilizing output-feedback controller
can be found. The procedure is demonstrated using a benchmark problem of
nonlinear control: the Moore-Greitzer jet engine compressor model.Comment: Conference submissio
Input Design for System Identification via Convex Relaxation
This paper proposes a new framework for the optimization of excitation inputs
for system identification. The optimization problem considered is to maximize a
reduced Fisher information matrix in any of the classical D-, E-, or A-optimal
senses. In contrast to the majority of published work on this topic, we
consider the problem in the time domain and subject to constraints on the
amplitude of the input signal. This optimization problem is nonconvex. The main
result of the paper is a convex relaxation that gives an upper bound accurate
to within of the true maximum. A randomized algorithm is presented for
finding a feasible solution which, in a certain sense is expected to be at
least as informative as the globally optimal input signal. In the case
of a single constraint on input power, the proposed approach recovers the true
global optimum exactly. Extensions to situations with both power and amplitude
constraints on both inputs and outputs are given. A simple simulation example
illustrates the technique.Comment: Preprint submitted for journal publication, extended version of a
paper at 2010 IEEE Conference on Decision and Contro
Contracting Nonlinear Observers: Convex Optimization and Learning from Data
A new approach to design of nonlinear observers (state estimators) is
proposed. The main idea is to (i) construct a convex set of dynamical systems
which are contracting observers for a particular system, and (ii) optimize over
this set for one which minimizes a bound on state-estimation error on a
simulated noisy data set. We construct convex sets of continuous-time and
discrete-time observers, as well as contracting sampled-data observers for
continuous-time systems. Convex bounds for learning are constructed using
Lagrangian relaxation. The utility of the proposed methods are verified using
numerical simulation.Comment: conference submissio
Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle
This paper derives a differential contraction condition for the existence of
an orbitally-stable limit cycle in an autonomous system. This transverse
contraction condition can be represented as a pointwise linear matrix
inequality (LMI), thus allowing convex optimization tools such as
sum-of-squares programming to be used to search for certificates of the
existence of a stable limit cycle. Many desirable properties of contracting
dynamics are extended to this context, including preservation of contraction
under a broad class of interconnections. In addition, by introducing the
concepts of differential dissipativity and transverse differential
dissipativity, contraction and transverse contraction can be established for
large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio
Stable Nonlinear Identification From Noisy Repeated Experiments via Convex Optimization
This paper introduces new techniques for using convex optimization to fit
input-output data to a class of stable nonlinear dynamical models. We present
an algorithm that guarantees consistent estimates of models in this class when
a small set of repeated experiments with suitably independent measurement noise
is available. Stability of the estimated models is guaranteed without any
assumptions on the input-output data. We first present a convex optimization
scheme for identifying stable state-space models from empirical moments. Next,
we provide a method for using repeated experiments to remove the effect of
noise on these moment and model estimates. The technique is demonstrated on a
simple simulated example
Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness
This paper introduces recurrent equilibrium networks (RENs), a new class of
nonlinear dynamical models for applications in machine learning, system
identification and control. The new model class has ``built in'' guarantees of
stability and robustness: all models in the class are contracting - a strong
form of nonlinear stability - and models can satisfy prescribed incremental
integral quadratic constraints (IQC), including Lipschitz bounds and
incremental passivity. RENs are otherwise very flexible: they can represent all
stable linear systems, all previously-known sets of contracting recurrent
neural networks and echo state networks, all deep feedforward neural networks,
and all stable Wiener/Hammerstein models. RENs are parameterized directly by a
vector in R^N, i.e. stability and robustness are ensured without parameter
constraints, which simplifies learning since generic methods for unconstrained
optimization can be used. The performance and robustness of the new model set
is evaluated on benchmark nonlinear system identification problems, and the
paper also presents applications in data-driven nonlinear observer design and
control with stability guarantees.Comment: Journal submission, extended version of conference paper (v1 of this
arxiv preprint