Fernando Castaños was born in Mexico City on March 1976. He received the bachelor's degree in Electric and
Electronic Engineering from Universidad Nacional Autónoma de México(UNAM). He received the master degree in Control Engineering
from UNAM and the Ph.D degree from Université Paris-Sud XI(UPS).
He was a postdoctoral fellow at McGill'sCenter for intelligent
machines(CIM) for two years. He currently works at
the Automatic Control Department, Cinvestav, México.
Passivity-based control, nonlinear control, port-Hamiltonian systems, implicit systems, neuromorphic engineering,
robust control and variable structure systems.
(very) Short Introduction to control engineering
Control theory is a field that originates from electrical and mechanical engineering
and mathematics. The field has also found its way in other technical areas such as biology,
especially in neurobiology and physiology, medical technology, agricultural science,
economics and computer science.
Control theory is concerned with problems associated with the dynamic behaviour of systems. These
problems are about open systems, that is, systems with inputs and outputs, systems interacting with
their environment. Some important problems driving modern day research in systems and control theory are:
The modelling problem: The search for suitable concepts and mathematical tools to describe dynamical systems
in interaction with their environment.
The identification problem: Developing algorithms for determining dynamic models on the basis of observations
of signals.
The filtering problem: Reconstructing the behaviour of a variable from observations of signals subject to noise.
The control problem: Devising principles and algorithms to obtain a good controller or feedback processor.
The last problem is the link with control engineering, the applied side of the research.
The control problem (classical view)
Based on the obtained measurements, how to calculate the inputs that will drive the system as desired?
Swing-up and stabilization of an inverted pendulum
Undergraduate thesis
An experimental setup was built for swinging up and stabilizing the well-known inverted
pendulum (click on the images below to download the videos). A part of the work
consisted in writing the drivers for the DAC and ADC cards and interfacing them with
Matlab's Real-Time Workshop.
Swing up
To swing up the pendulum, a heuristic algorithm that forced the pendulum to oscillate
at its resonance frequency was used. Once the pendulum reached a neighborhood of
the upright position, the controller switched to a stabilization algorithm consisting
of an observer and a friction estimator cascaded with a linear quadratic regulator.
The thesis (in Spanish) was supervised by
Rolando Carrera.
Stabilization
Sliding-mode control
Master thesis, sliding-mode control (SMC) with an H_{∞} criterion
It is well known that sliding modes are robust concerning matched
perturbations and model uncertainties. That is, they are robust in the face of perturbations
that are coupled to the control action. On the other hand, sliding modes suffer from:
An initial period of time (called the reaching phase) in which the system's
robustness is not guaranteed
Sensitivity to unmatched perturbations
Full state measurement is required
The so-called chattering phenomenon
The first problem can be solved using integral sliding modes, which has the
additional advantage of furnishing extra design parameters. The extra freedom can then
be used to minimize, e.g., using an H_{∞} criterion, the impact of the
unmatched perturbations and uncertainties [CF06a,
CXF06, REC^{+}11,
CHZF14].
By constructing a dynamic surface, it is some times possible to enforce a desired
sliding motion using only partial state information
[CF04b], regardless of any matched uncertainty (this
addresses the third problem). The input-to-state stability framework can be used to
compute the controller gains efficiently [MCF14,
MCF15, MCF16].
In the presence of unmatched uncertainties, one can also design the dynamic surface
using an H_{∞} criterion
[CF11, MCF13].
The machinery developed fits nicely in a decentralized control scenario
[CF05a].
The well-known pole-placement formula by Ackermann was modified by Utkin and Ackermann himself
to place the eigenvalues of the sliding dynamics in conventional
SMC. The formula can be further generalized to the case of
higher-order sliding modes [HZCF14, CCF16]. The formula can
be used as part of a higher-order sliding-mode control design methodology, achieving high
accuracy and robustness at the same time.
Extremum seeking
Tracking a varying maximum or minimum (extremum) of a performance (output, cost) function is
called extremum-seeking control. It usually has two layers of control. The first layer is an
algorithm able to control (stabilize) the system and drive the performance output
to its reference. The second layer sets the appropriate reference by seeking an extremum of
the performance output.
In some applications, the reference-to-output map has an extremum and the objective is to select
the set-point that keeps the output at the extremum value. The uncertainty in the reference-to-output
map makes it necessary to use some sort of adaptation to find the set point that optimizes the output.
Usually, the adaptation scheme requires a dither signal to satisfy the so-called persistence of
excitation. In [CK15], a nonsmooth ditherless extemum seeker is applied
to the problem of minimizing hydrogen consumption in fuel cells. See also
[KC13a, KC13b]
Passivity-based control
Passivity is a particular instance of dissipativity, a system-theoretic property
that relates different notions of stability (see the
diagram
for details).
PhD thesis, control by interconnection
Within a passivity framework, the control problem is approached by
using the notion of energy-shaping as the main design principle and
exploiting the physical properties of the plant.
The basic steps are:
Derive an energy-based model (e.g., Euler-Lagrange, port-Hamiltonian, Brayton-Moser,
etc). Energy-based models are simpler and intuitive. They also provide a dissipation
inequality which can be used as starting point.
Using the property of energy conservation, design a controller that
“shapes” the system's energy as required. (The requirement of having a
physical interpretation of the controller usually simplifies this task.)
Add damping to improve the transient response.
It is well known that many mechanical and electro-mechanical systems can be described
using port-Hamiltonian models. In addition, a large class or RLC nonlinear circuits can also be put
in port-Hamiltonian form, provided their graphs satisfy some conditions
[CJOGC09]. This class of systems can be asymptotically stabilized
with a nonlinear proportional-integral controller [JOGCC07].
Implicit port-Hamiltonian models are developed in [CGHM13] and
the interconnection and damping assignment (IDA) control technique is developed for implicit port-Hamiltonian
models in [CG16].
Energy shaping can be accomplished via standard passivity-based techniques like
energy-balance [CO09] or interconnection and damping
assignment [OvdSCA08, CG15]. Alternatively, one may reformulate
the control problem in a control-by-interconnection
setting [COvdSA09], where the original system and
the controller are viewed as energy ports that are interconnected in order to produce
the desired behavior.
Jan Willems' behavioral approach to systems and control is particularly well suited
for developing passivity-based control theory. The results presented in the
thesis are stated within the behavioral
framework. The thesis was supervised by
Romeo Ortega.
Passivity-based control of delayed systems
Passivity-based control (PBC) schemes usually take advantage of the following property: the interconnection of two passive
systems is again passive. This property ceases to hold when delays are part of the interconnection
structure (i.e., as in the case of two systems that are interconnected by means of a communication channel).
A linear transformation can be applied to the Telegrapher's equations (which define a passive system)
in order to obtain a pair of uncoupled transport equations (which define a pair of delays). In the context of
robot telemanipulation, Anderson and Spong proposed to modify a communication channel, modelled as
a pair of delays, by applying the inverse transformation, so that the transformed channel is passive and
the overall interconnected system is again passive.
In the context of set-point regulation, the performance of Anderson's transformation is evaluated in terms
of achievable σ-stability. Using a frequency domain approach, analytic formulae
for optimal control parameters are derived [CEMR17].
Set-valued PBC
The renown robustness of sliding-mode control can be understood in terms of the multi-valued nature of
the signum function. That is, robustness stems from the fact that, according to Filippov's theory,
a signum function appearing on the right-hand side of a differential equation takes values on the power
set of the real line (as opposed to the real line itself).
It is shown in [MC17, MC15, MC14] that it is possible to
achieve similar (or sometimes better) robust controllers with the use of other multi-valued functions. In the
above-mentioned references, the robust output regulation of passive linear systems is achieved by means
of set-valued, maximally monotone passive controllers. The results are extended to the non linear Lagrangian
systems in [MBC17]
Implicit systems
Implicit systems are described by mathematical models in which the derivative of the state is determined implicitly by a function
whose arguments are: the state, the derivative itself and the control. The class of implicit (or descriptor) models
contains the class of state-space models, in which the derivative of the state is given explicitly as a function of
the state and the control (i.e., vector fields). Implicit models can be used, e.g., to describe systems which perform a derivative
action on the input, a feature that cannot be captured by state-space models at all. In [CHZF14]
we apply integral sliding-mode control to linear descriptor systems in order to reject matched perturbations. Eigenvalue assignement
using conventional sliding-mode control is considered in [HZCF16]. In contrast with
classical state-space systems, one has to take special care on the differentiability of the control action (otherwise, a solution
to the system equations might not exist).
For a restricted class of systems it is possible, by suitably eliminating some of the state variables,
to transform a given implicit model into an explicit one. Even when possible in principle, it might be preferable to work
directly with an implicit model in some cases. In the specific context of Hamiltonian systems, going from an implicit representation
to an explicit one entails an effective reduction on the number of state variables, but complicates the Hamiltonian (Energy)
function substantially. Implicit representations are of higher dimension and, depending on the particular application, may
require us to solve for variables defined implicitly. On the other hand, the corresponding Hamiltonian functions have simpler
expressions. More precisely, it is possible to split the Hamiltonian functions into two terms: one depending on the momenta only
(the kinetic energy) and one depending on the positions only (the potential energy), i.e., the Hamiltonians are separable.
This property has been largely exploited in the context of numerical simulations, resulting in self-correcting numerical simulation
algorithms and discrete-time sampled-data models. When applying the interconnection and damping assignment PBC methodology
to a Hamiltonian system, the resulting partial differential equations are simplified considerably if the kinetic energy does
not depend on the positions, so there are possible advantages in using implicit representations in a control context as well.
The relationship between implicit and explicit port-Hamiltonian models can be understood in terms of commutative diagrams.
See [CGHM13] for details and, in particular, the explicit maps for going from one representation
to the other. The interconnection and damping assignment (IDA) control technique is developed for implicit port-Hamiltonian
models in [CG16].
Neuromorphic engineering
A neuromorphic electronic circuit
While the inner-workings of the brain are still largely unknown, the behaviour of a single neuron
is relatively well understood from the perspective of dynamical-systems theory. Using the geometric properties
of a neuron's critical manifolds, we designed an electronic circuit that can smoothly transition between the two
main neuronal operating modes: tonic spiking and bursting [CF17].
The resulting circuit solely uses six transistors and passive elements. For comparison,
the simplest available neuromorphic circuit capable of transitioning between tonic
spiking and bursting uses fourteen MOSFET transistors. Another advantage of our approach
is that circuit parameters are constructively tuned by geometric inspection of its static
input-output characteristic, which avoids laborious and non-constructive parameter fitting
procedures.
Fernando Castaños, Edgar Estrada, Sabine Mondié, and Adrián
Ramírez.
Passivity-based PI control of first-order systems with I/O
communication delays: a frequency domain analysis.
Int. J. Control, Online, 2017.
[ DOI |
.pdf ]
Félix Miranda, Bernard Brogliato, and Fernando Castaños.
Multivalued robust tracking control of Lagrange systems: Continuous
and discrete-time algorithms.
IEEE Trans. Autom. Control, Online, 2017.
[ DOI |
.pdf ]
Fernando Castaños and Alessio Franci.
Implementing robust neuromodulation in neuromorphic circuits.
Neurocomputing, 233:3 - 13, April 2017.
[ DOI |
.pdf ]
Félix Miranda and Fernando Castaños.
Robust output regulation of strongly passive linear systems with
multivalued maximally monotone controls.
IEEE Trans. Autom. Control, 62:238 - 249, January 2017.
[ DOI |
.pdf ]
Debbie Hernández-Zárate, Fernando Castaños, and Leonid Fridman.
Zero-dynamics design and its application to the stabilization of
implicit systems.
Systems and Control Lett., 98:74 - 78, December 2016.
[ DOI |
.pdf ]
Andrea Aparicio Martínez, Fernando Castaños, and Leonid Fridman.
Output feedback sliding-mode control with unmatched disturbances, an
ISS approach.
Int. J. Robust Nonlinear Control, 26:4056 - 4071, December
2016.
[ DOI |
.pdf ]
Félix Miranda, Fernando Castaños, and Alexander Poznyak.
Min-max piecewise constant optimal control for multi-model linear
systems.
IMA J Math Control Info, 33:1157 - 1176, December 2016.
[ DOI |
.pdf ]
Fernando Castaños and Dmitry Gromov.
Passivity-based control of implicit port-hamiltonian systems
with holonomic constraints.
Systems and Control Lett., 94:11 - 18, August 2016.
[ DOI |
.pdf ]
Fernando Castaños and Cristian Kunusch.
Ditherless extremum seeking for hydrogen minimization in PEM fuel
cells.
IEEE Trans. Ind. Electron., 62:5218 - 5226, August 2015.
[ DOI |
.pdf ]
Manuel Mera, Fernando Castaños, and Alexander Poznyak.
Quantised and sampled output feedback for nonlinear systems.
Int. J. Control, 87:2475 - 2487, December 2014.
[ DOI |
.pdf ]
Fernando Castaños, Debbie Hernández-Zárate, and Leonid Fridman.
Integral sliding-mode control for linear time-invariant implicit
systems.
Automatica, 50:971 - 975, March 2014.
[ DOI |
.pdf ]
Fernando Castaños, Dmitry Gromov, Vincent Hayward, and Hannah Michalska.
Implicit and explicit representations of continuous-time
port-Hamiltonian systems.
Systems and Control Lett., 62:324 - 330, April 2013.
[ DOI |
.pdf ]
Debbie Hernández, Fernando Castaños, and Leonid Fridman.
Pole-placement in higher-order sliding-mode control.
arXiv:1309.3317 [math.OC], 2013.
[ .pdf ]
Matteo Rubagotti, Antonio Estrada, Fernando Castaños, Antonella Ferrara,
and Leonid Fridman.
Integral sliding mode control for nonlinear systems with matched and
unmatched perturbations.
IEEE Trans. Autom. Control, 56:2699 - 2704, November 2011.
[ DOI |
.pdf ]
Fernando Castaños and Leonid Fridman.
Dynamic switching surfaces for output sliding mode control: An
H_{∞} approach.
Automatica, 47:1957-1961, September 2011.
[ DOI |
.pdf ]
Fernando Castaños.
Discussion on: “Energy shaping of port-Hamiltonian systems by
using alternate passive input-output pairs”.
European Journal of Control, 16:678 - 679, December 2010.
[ DOI |
.pdf ]
Fernando Castaños, Bayu Jayawardhana, Romeo Ortega, and Eloísa
García-Canseco.
Proportional plus integral control for set-point regulation of a
class of nonlinear RLC circuits.
Circuits Syst. Signal Process., 28:609 - 623, August 2009.
[ DOI |
.pdf ]
Fernando Castaños and Romeo Ortega.
Energy-balancing passivity-based control is equivalent to dissipation
and output invariance.
Systems and Control Lett., 58:553 - 560, August 2009.
[ DOI |
.pdf ]
Fernando Castaños, Romeo Ortega, Arjan J. van der Schaft, and Alessandro
Astolfi.
Asymptotic stabilization via control by interconnection of
port-Hamiltonian systems.
Automatica, 45:1611 - 1618, July 2009.
[ DOI |
.pdf ]
Romeo Ortega, Arjan J. van der Schaft, Fernando Castaños, and Alessandro
Astolfi.
Control by interconnection and standard passivity-based control of
port-Hamiltonian systems.
IEEE Trans. Autom. Control, 53:2527 - 2542, December 2008.
[ DOI |
.pdf ]
Eugenii Shustin, Leonid Fridman, Emilia Fridman, and Fernando Castaños.
Robust semiglobal stabilization of the second order system by relay
feedback with an uncertain variable time delay.
SIAM J. Control Optim., 47:196 - 217, January 2008.
[ DOI |
.pdf ]
Bayu Jayawardhana, Romeo Ortega, Eloísa García-Canseco, and Fernando
Castaños.
Passivity of nonlinear incremental systems: Application to PI
stabilization of nonlinear RLC circuits.
Systems and Control Lett., 56:618 - 622, September 2007.
[ DOI |
.pdf ]
Fernando Castaños and Leonid Fridman.
Analysis and design of integral sliding manifolds for systems with
unmatched perturbations.
IEEE Trans. Autom. Control, 51:853 - 858, May 2006.
[ DOI |
.pdf ]
Yuri Orlov, Leonid Fridman, and Fernando Castaños.
Discussion on: “dynamic sliding mode control for a class of systems
with mismatched uncertainty”.
European Journal of Control, pages 11-18, 2005.
[ DOI |
.pdf ]
Ismael Castillo, Fernando Castaños, and Leonid Fridman.
Sliding surface design for higher-order sliding modes.
In Leonid Fridman, Jean-Pierre Barbot, and Franck Plestan, editors,
Recent Trends in Sliding Mode Control, chapter 1.2, pages 29 - 57. The
Institution of Engineering and Technology, Herts, United Kingdom, 2016.
[ DOI ]
Fernando Castaños, Jian-Xin Xu, and Leonid Fridman.
Integral sliding modes for systems with matched and unmatched
uncertainties.
In Christopher Edwards, Enric Fossas Colet, and Leonid Fridman,
editors, Advances in Variable Structure and Sliding Mode Control,
chapter 11, pages 227 - 246. Springer-Verlag, Berlin, 2006.
Félix Miranda and Fernando Castaños.
Robust output regulation of linear passive systems using maximally
monotone controls.
In Proc. Conference on Decision and Control, pages 6897 -
6902, Osaka, Japan, December 2015.
[ .pdf ]
Fernando Castaños and Alessio Franci.
The transition between tonic spiking and bursting in a six-transistor
neuromorphic device.
In Proc. Int. Conf. on Electrical Eng., Computing Science and
Automatic Control, pages 1 - 6, Mexico City, Mexico, December 2015.
[ .pdf ]
Andrea Aparicio Martínez, Fernando Castaños, and Leonid Fridman.
ISS properties of sliding-mode controllers for systems with matched
and unmatched disturbances.
In Proc. European Control Conference, pages 2870-2875, Linz,
Austria, July 2015.
[ .pdf ]
Fernando Castaños and Dmitry Gromov.
Interconnection and damping assignment for implicit
port-Hamiltonian systems.
In Proc. IFAC Conf. on Modelling, Identification and Control of
Nonlinear Systems, pages 1016 - 1021, Saint Petersburg, Russia, June 2015.
[ .pdf ]
Andrea Aparicio Martínez, Fernando Castaños, and Leonid Fridman.
ISS-Lyapunov functions for output feedback sliding modes.
In Proc. Conference on Decision and Control, pages 5536 -
5541, Los Angeles, California, USA, December 2014.
[ .pdf ]
Debbie Hernández-Zárate, Fernando Castaños, and Leonid Fridman.
Pole-placement in higher-order sliding-mode control.
In Proc. IFAC World Congress, pages 1386 - 1391, Cape Town,
South Africa, August 2014.
[ .pdf ]
Félix Miranda and Fernando Castaños.
Robust output regulation of variable structure systems with
multivalued controls.
In Proc. Variable Structure Systems Workshop, Nantes, Francia,
June 2014.
[ .pdf ]
Andrea Aparicio Martínez, Fernando Castaños, and Leonid Fridman.
Dynamic surface for output feedback sliding modes, the case of
relative degree two.
In Proc. Conference on Decision and Control, pages 3578 -
3583, Florence, Italy, December 2013.
[ .pdf ]
Edgar Estrada, Fernando Castaños, and Sabine Mondié.
σ-estabilidad de sistemas de control basados en pasividad con
retardos en la comunicación.
In Congreso Anual de la AMCA, pages 129 - 134, Ensenada,
Mexico, October 2013.
[ .pdf ]
Andrea Aparicio Martínez and Fernando Castaños.
Control por modos deslizantes por retroalimentación de salida con
grado relativo dos.
In Congreso Anual de la AMCA, pages 544 - 549, Ensenada,
Mexico, October 2013.
[ .pdf ]
Cristian Kunusch and Fernando Castaños.
On the implementation of an adaptive extremum seeking algorithm for
hydrogen minimization in PEM fuel cell based systems.
In Proc. European Control Conference, pages 2501 - 2506,
Zürich, Switzerland, July 2013.
[ .pdf ]
Cristian Kunusch and Fernando Castaños.
Extremum seeking algorithms for minimal hydrogen consumption in PEM
fuel cells.
In Proc. of the American Control Conference, pages 1146 -
1151, Washington, DC, USA, June 2013.
[ .pdf ]
Fernando Castaños, Debbie Hernández-Zárate, and Leonid Fridman.
Integral sliding-mode control for linear time-invariant implicit
descriptions.
In Proc. Conference on Decision and Control, pages 6442 -
6447, Maui, Hawaii, December 2012.
[ .pdf ]
Matteo Rubagotti, Antonio Estrada, Fernando Castaños, Antonella Ferrara,
and Leonid Fridman.
Optimal disturbance rejection by integral sliding mode control for
systems in regular form.
In Proc. of the Variable Structure Systems Workshop, pages 78
- 82, Mexico City, Mexico, June 2010.
[ .pdf ]
Fernando Castaños and Romeo Ortega.
Energy-balancing passivity-based control is equivalent to dissipation
and output invariance.
In Proc. European Control Conference, page WeC2.4, Budapest,
Hungary, August 2009.
[ .pdf ]
Eugenii Shustin, Leonid Fridman, Emilia Shustin, and Fernando Castaños.
Robust semiglobal stabilization of the second order system by relay
feedback with an uncertain variable time delay.
In Proc. Conference on Decision and Control, pages 2716 -
2721, Cancún, México, December 2008.
[ .pdf ]
Fernando Castaños, Romeo Ortega, Arjan J. van der Schaft, and Alessandro
Astolfi.
Asymptotic stabilization via control by interconnection of
port-hamiltonian systems.
In Congreso Latinoamericano de Control Automático,
Mérida, Venezuela, November 2008.
[ .pdf ]
Fernando Castaños, Bayu Jayawardhana, Romeo Ortega, and Eloísa
García-Canseco.
A class of nonlinear RLC circuits globally stabilizable by
proportional plus integral controllers.
In Proc. of the IFAC World Congress, pages 6202 - 6207, Seoul,
Korea, June 2008.
[ .pdf ]
Romeo Ortega, Arjan J. van der Schaft, Fernando Castaños, and Alessandro
Astolfi.
Control by (state-modulated) interconnection of port-Hamiltonian
systems.
In Proc. IFAC Symposium on Nonlinear Control Systems, pages 47
- 54, Pretoria, South Africa, August 2007.
[ .pdf ]
Bayu Jayawardhana, Romeo Ortega, Eloísa García-Canseco, and Fernando
Castaños.
Passivity of nonlinear incremental systems: Application to PI
stabilization of nonlinear RLC circuits.
In Proc. Conference on Decision and Control, page ThIP2.17, San
Diego, December 2006.
[ .pdf ]
Fernando Castaños and Leonid Fridman.
Design of integral sliding manifolds for multi-model uncertain
systems via LMI.
In Proc. of the Variable Structure Systems Workshop, pages
63-67, Alghero, Italy, June 2006.
[ .pdf ]
Fernando Castaños and Leonid Fridman.
Robust design criteria for integral sliding surfaces.
In Proc. Conference on Decision and Control, and European
Control Conference, pages 1976-1981, Seville, Spain, December 2005.
[ .pdf ]
Fernando Castaños and Leonid Fridman.
Integral sliding surface design using an H_{∞}
criterion for decentralized control.
In Proc. of the IFAC World Congress, pages Th-A09-T0/2,
Prague, July 2005.
[ .pdf ]
Fernando Castaños and Leonid Fridman.
Measurement sliding mode-H_{∞} control with
application to decentralized systems.
In Proc. of the Variable Structure Systems Workshop, Vilanova i
la Geltrú, Spain, September 2004.
[ .pdf ]
Leonid Fridman, Fernando Castaños, N. M'Sirdi, and Khraef.
Decomposition and robustness properties of integral sliding mode
controllers.
In Proc. of the Variable Structure Systems Workshop, Vilanova i
la Geltrú, Spain, September 2004.
[ .pdf ]
Fernando Castaños and Leonid Fridman.
Control descentralizado por modos deslizantes.
In Congreso Anual de la AMCA, ISBN: 970-32-2137-8, pages
253-258, México, D.F., 2004.
[ .pdf ]
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