9,273 research outputs found
On Adaptive Measurement Inclusion Rate In Real-Time Moving-Horizon Observers
This paper investigates a self adaptation mechanism regarding the rate with
which new measurements have to be incorporated in Moving-Horizon state
estimation algorithms. This investigation can be viewed as the dual of the one
proposed by the author in the context of real-time model predictive control. An
illustrative example is provided in order to assess the relevance of the
proposed updating rule.Comment: 6 pages. 4 Figure
Modeling and Estimation of Biological Plants
Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants.
After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model.
The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information
about the system can be explicitly considered in the form of constraints
and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios.
Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure
DECENTRALIZED ROBUST NONLINEAR MODEL PREDICTIVE CONTROLLER FOR UNMANNED AERIAL SYSTEMS
The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1 A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2 A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3 An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4 A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible
Modulating function based algebraic observer coupled with stable output predictor for LTV and sampled-data systems
This paper proposes an algebraic observer-based modulating function approach
for linear time-variant systems and a class of nonlinear systems with discrete
measurements. The underlying idea lies in constructing an observability
transformation that infers some properties of the modulating function approach
for designing such algebraic observers. First, we investigate the algebraic
observer design for linear time-variant systems under an observable canonical
form for continuous-time measurements. Then, we provide the convergence of the
observation error in an L2-gain stability sense. Next, we develop an
exponentially stable sampled-data observer which relies on the design of the
algebraic observer and an output predictor to achieve state estimation from
available measurements and under small inter-sampling periods. Using a
trajectory-based approach, we prove the convergence of the observation error
within a convergence rate that can be adjusted through the fixed time-horizon
length of the modulating function and the upper bound of the sampling period.
Furthermore, robustness of the sampled-data algebraic observer, which yields
input-to-state stability, is inherited by the modulating kernel and the
closed-loop output predictor design. Finally, we discuss the implementation
procedure of the MF-based observer realization, demonstrate the applicability
of the algebraic observer, and illustrate its performance through two examples
given by linear time-invariant and linear time-variant systems with nonlinear
input-output injection terms.Comment: 15 pages, 9 figures, submitted to Automatic
Estimation of biomass concentration using interval observers in an E. coli fed-batch fermentation
In bioreactors, the measurement of variables that play a key role in the quality and productivity of fermentations, is of major importance. However, their direct measurement is often expensive or even impossible considering the current sensor
technology. Therefore, on-line estimation of unmeasured variables in bioreactors can be
an interesting approach.
The objective of this work is to introduce an alternative solution for the observation of
biomass concentration in E. coli fed-batch fermentations, in cases where the kinetic model is unclear and several variables, like the concentration of the influent substrates and the initial values of the state variables are badly known, a situation that is common in many practical applications.
The simple interval observer is designed on the basis of the cooperativity properties of the
observer error dynamics (Rapaport and Dochain, 2005).
The performance of the interval observer is illustrated through numerical simulation and it
was found that the observer deal well with uncertainties up to 50% and with white noise
in the variables measured on-line. The interval obtained for the biomass estimation is also
quite narrow, indicating that it is possible to accurately predict biomass concentration
under the presence of uncertainties.Programa de Desenvolvimento Educativo para Portugal (PRODEP)Fundação para a Ciência e a Tecnologia (FCT) - Projecto recSysBio
POCI/BIO/60139/200
Optimal control and robust estimation for ocean wave energy converters
This thesis deals with the optimal control of wave energy converters and some associated
observer design problems. The first part of the thesis will investigate model
predictive control of an ocean wave energy converter to maximize extracted power.
A generic heaving converter that can have both linear dampers and active elements
as a power take-off system is considered and an efficient optimal control algorithm
is developed for use within a receding horizon control framework. The optimal
control is also characterized analytically. A direct transcription of the optimal control
problem is also considered as a general nonlinear program. A variation of
the projected gradient optimization scheme is formulated and shown to be feasible
and computationally inexpensive compared to a standard nonlinear program solver.
Since the system model is bilinear and the cost function is not convex quadratic, the
resulting optimization problem is shown not to be a quadratic program. Results are
compared with other methods like optimal latching to demonstrate the improvement
in absorbed power under irregular sea condition simulations.
In the second part, robust estimation of the radiation forces and states inherent in
the optimal control of wave energy converters is considered. Motivated by this, low
order H∞ observer design for bilinear systems with input constraints is investigated
and numerically tractable methods for design are developed. A bilinear Luenberger
type observer is formulated and the resulting synthesis problem reformulated as that
for a linear parameter varying system. A bilinear matrix inequality problem is then
solved to find nominal and robust quadratically stable observers. The performance
of these observers is compared with that of an extended Kalman filter. The robustness
of the observers to parameter uncertainty and to variation in the radiation
subsystem model order is also investigated.
This thesis also explores the numerical integration of bilinear control systems with
zero-order hold on the control inputs. Making use of exponential integrators, exact
to high accuracy integration is proposed for such systems. New a priori bounds
are derived on the computational complexity of integrating bilinear systems with a
given error tolerance. Employing our new bounds on computational complexity, we
propose a direct exponential integrator to solve bilinear ODEs via the solution of
sparse linear systems of equations. Based on this, a novel sparse direct collocation
of bilinear systems for optimal control is proposed. These integration schemes are
also used within the indirect optimal control method discussed in the first part.Open Acces
Performance Comparison of Control Schemes for Variable-Speed Wind Turbines
We analyze the performance of different control schemes when applied to the regulation problem of a variable-speed representative wind turbine. In particular, we formulate and compare a wind-scheduled PID, a LQR controller and a novel adaptive non-linear model predictive controller, equipped with observers of the tower states and wind. The simulations include gusts and turbulent winds of varying intensity in nominal as well as off-design operating conditions. The experiments highlight the possible advantages of model-based non-linear control strategies
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