80 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
Control of flexible joint robotic manipulator using tuning functions design
The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified
Nonsmooth Adaptive Control Design for a Large Class of Uncertain High-Order Stochastic Nonlinear Systems
This paper investigates the problem of the global stabilization via partial-state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns and stochastic zero dynamics. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the problem, a lot of substantial technical difficulties should be overcome since the presence of severe uncertainties/unknowns, unmeasurable zero dynamics, and stochastic noise. By introducing the suitable adaptive updated law for an unknown design parameter and appropriate control Lyapunov function, and by using the method of adding a power integrator, an adaptive continuous (nonsmooth) partial-state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with
probability one. A simulation example is provided to illustrate the effectiveness of the proposed approach
Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters
The paper extends a recently proposed indirect, certainty-equivalence,
event-triggered adaptive control scheme to the case of non-observable
parameters. The extension is achieved by using a novel Batch Least-Squares
Identifier (BaLSI), which is activated at the times of the events. The BaLSI
guarantees the finite-time asymptotic constancy of the parameter estimates and
the fact that the trajectories of the closed-loop system follow the
trajectories of the nominal closed-loop system ("nominal" in the sense of the
asymptotic parameter estimate, not in the sense of the true unknown parameter).
Thus, if the nominal feedback guarantees global asymptotic stability and local
exponential stability, then unlike conventional adaptive control, the newly
proposed event-triggered adaptive scheme guarantees global asymptotic
regulation with a uniform exponential convergence rate. The developed adaptive
scheme is tested to a well-known control problem: the state regulation of the
wing-rock model. Comparisons with other adaptive schemes are provided for this
particular problem.Comment: 29 pages, 12 figure
Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition
Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure
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
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