17 research outputs found
Parameter Estimation-Based Extended Observer for Linear Systems with Polynomial Overparametrization
We consider a class of uncertain linear time-invariant overparametrized
systems affected by bounded disturbances, which are described by a known
exosystem with unknown initial conditions. For such systems an exponentially
stable extended adaptive observer is proposed, which, unlike known solutions,
simultaneously: (i) allows one to reconstruct original (physical) states of the
system represented in arbitrarily chosen state-space form rather than virtual
states of the observer canonical form; (ii) ensures convergence of the state
observation error to zero under extremely weak requirement of the regressor
finite excitation; (iii) does not include Luenberger correction gain and forms
states estimate using algebraic rather than differential equation; (iv)
additionally reconstructs the unmeasured external disturbance. Illustrative
simulations support obtained theoretical results.Comment: 6 pages, 2 figure
Exact asymptotic estimation of unknown parameters of regression equations with additive perturbations
Most identification methods of unknown parameters of linear regression
equations (LRE) ensure only boundedness of a parametric error in the presence
of additive perturbations, which is almost always unacceptable for practical
scenarios. In this paper, a new identification law is proposed to overcome this
drawback and guarantee asymptotic convergence of the unknown parameters
estimation error to zero in case the mentioned additive perturbation meets
special averaging conditions. Theoretical results are illustrated by numerical
simulations.Comment: 6 pages, 6 figure
Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters
The method to design exponentially stable adaptive observers is proposed for
linear time-invariant systems parameterized by unknown physical parameters.
Unlike existing adaptive solutions, the system state-space matrices A, B are
not restricted to be represented in the observer canonical form to implement
the observer. The original system description is used instead, and,
consequently, the original state vector is obtained. The class of systems for
which the method is applicable is identified via three assumptions related to:
(i) the boundedness of a control signal and all system trajectories, (ii) the
identifiability of the physical parameters of A and B from the numerator and
denominator polynomials of a system input/output transfer function and (iii)
the complete observability of system states. In case they are met and the
regressor is finitely exciting, the proposed adaptive observer, which is based
on the known GPEBO and DREM procedures, ensures exponential convergence of both
system parameters and states estimates to their true values. Detailed analysis
for stability and convergence has been provided along with simulation results
to validate the developed theory.Comment: 8 pages, 2 figure
Monotonous Parameter Estimation of One Class of Nonlinearly Parameterized Regressions without Overparameterization
The estimation law of unknown parameters vector is proposed for
one class of nonlinearly parametrized regression equations . We restrict our attention
to parametrizations that are widely obtained in practical scenarios when
polynomials in are used to form . For
them we introduce a new 'linearizability' assumption that a mapping from
overparametrized vector of parameters to
original one exists in terms of standard algebraic functions. Under
such assumption and weak requirement of the regressor finite excitation, on the
basis of dynamic regressor extension and mixing technique we propose a
procedure to reduce the nonlinear regression equation to the linear
parameterization without application of singularity causing operations and the
need to identify the overparametrized parameters vector. As a result, an
estimation law with exponential convergence rate is derived, which, unlike
known solutions, (i) does not require a strict P-monotonicity condition to be
met and a priori information about to be known, (ii) ensures
elementwise monotonicity for the parameter error vector. The effectiveness of
our approach is illustrated with both academic example and 2-DOF robot
manipulator control problem.Comment: 7 pages, 2 figure
Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations
The problem of state reconstruction is considered for uncertain linear
time-invariant systems with overparametrization, arbitrary state-space matrices
and unknown additive perturbation described by an exosystem. A novel adaptive
observer is proposed to solve it, which, unlike known solutions,
simultaneously: (i) reconstructs the physical state of the original system
rather than the virtual state of its observer canonical form, (ii) ensures
exponential convergence of the reconstruction error to zero when the condition
of finite excitation is satisfied, (iii) is applicable to systems, in which
mentioned perturbation is generated by an exosystem with fully uncertain
constant parameters. The proposed solution uses a recently published
parametrization of uncertain linear systems with unknown additive
perturbations, the dynamic regressor extension and mixing procedure, as well as
a method of physical states reconstruction developed by the authors. Detailed
analysis for stability and convergence has been provided along with simulation
results to validate the results of the theoretical analysis.Comment: 7 pages, 3 figures. arXiv admin note: text overlap with
arXiv:2302.1370
Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence
The scope of this research is the identification of unknown piecewise
constant parameters of linear regression equation under the finite excitation
condition. Compared to the known methods, to make the computational burden
lower, only one model to identify all switching states of the regression is
used in the developed procedure with the following two-fold contribution. First
of all, we propose a new truly online estimation algorithm based on a
well-known DREM approach to detect switching time and preserve time alertness
with adjustable detection delay. Secondly, despite the fact that a switching
signal function is unknown, the adaptive law is derived that provides global
exponential convergence of the regression parameters to their true values in
case the regressor is finitely exciting somewhere inside the time interval
between two consecutive parameters switches. The robustness of the proposed
identification procedure to the influence of external disturbances is
analytically proved. Its effectiveness is demonstrated via numerical
experiments, in which both abstract regressions and a second-order plant model
are used.Comment: 31 pages, 12 figure
Regression Filtration with Resetting to Provide Exponential Convergence of MRAC for Plants with Jump Change of Unknown Parameters
This paper proposes a new method to provide the exponential convergence of
both the parameter and tracking errors of the composite adaptive control system
without the requirement of the regressor persistent excitation (PE). Instead,
the composite adaptation law obtained in this paper requires the regressor to
be finitely exciting (FE) to guarantee the above-mentioned properties. Unlike
known solutions, not only does it relax the PE requirement, but also it
functions effectively under the condition of a jump change of the plant
uncertainty parameters. To derive such an adaptation law, an integral filter of
regressor with damping and resetting is proposed. It provides the required
properties of the control system, and its output signal is bounded even when
its input is subjected to noise and disturbances. A rigorous analytical proof
of all mentioned properties of the developed adaptation law is presented. Such
law is compared with the known composite ones relaxing the PE requirement. The
wing-rock problem is used for the modeling of the developed composite MRAC
system. The obtained results fully support the theoretical analysis and
demonstrate the advantages of the proposed method.Comment: 12 pages, 3 figure
Relaxation of condition for convergence of dynamic regressor extension and mixing procedure
A generalization of the dynamic regressor extension and mixing procedure is
proposed. First of all, it relaxes the requirement of the regressor finite
excitation, which is known to be the condition for the mentioned procedure
convergence. Secondly, if the weaker requirement of the regressor
semi-finite-excitation is met, it guarantees the uniform ultimate boundedness
of the parameter error and elementwise monotonicity for transients of some
parameters to be identified.Comment: 21 pages. In Russia
Exponentially Stable Adaptive Optimal Control of Uncertain LTI Systems
A novel method of an adaptive linear quadratic (LQ) regulation of uncertain
continuous linear time-invariant systems is proposed. Such an approach is based
on the direct self-tuning regulators design framework and the exponentially
stable adaptive control technique developed earlier by the authors. Unlike the
known solutions, a procedure is proposed to obtain a non-overparametrized
regression equation (RE) with respect to the unknown controller parameters from
an initial RE of the LQ-based reference tracking control system. On the basis
of such result, an adaptive law is proposed, which under mild regressor finite
excitation condition provides monotonous convergence of the LQ-controller
parameters to an adjustable set of their true values, which bound is defined
only by the machine precision. Using the Lyapunov-based analysis, it is proved
that the mentioned law guarantees the exponential stability of the closed-loop
adaptive optimal control system. The simulation examples are provided to
validate the theoretical contributions.Comment: 37 pages, 7 figure