Fernando Castanos

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• Ph.D. Control Theory
• Researcher at Center for Research and Advanced Studies of the National Polytechnic Institute

The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if inte...

The dynamics of many physical processes can be suitably described by Port-Hamiltonian (PH) models, where the importance of the energy function, the interconnection pattern and the dissipation of the system is underscored. To regulate the behavior of PH systems it is natural to adopt a Passivity-Based Control (PBC) perspective, where the control obj...

We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the...

The robust trajectory tracking of fully actuated Lagrange systems is studied. Exogenous perturbations as well as parameter uncertainties are taken into account. A family of set-valued passivity-based controllers is proposed, including firstorder sliding-mode schemes. The existence of solutions and the stability of the closed-loop system are establi...

We propose a set-valued controller with a signum multifunction nested inside another one. We prove that the controller is well posed and achieves robust ultimate boundedness in the presence of mismatched, non-vanishing disturbances. Even more, the selected output can be made arbitrarily small. Also, by applying an implicit/explicit Euler scheme sim...

In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters. We give simulation results of benchmark examples that illustrate the performance of the proposed adaptive obse...

This article analyzes the high‐gain prediction approach for nonlinear input‐delay systems. The problem is discussed in the light of weighted homogeneity and input‐to‐state stability. The canonical form for uniformly observable nonlinear systems allows tuning the linear‐part spectrum by multiplicity‐induced dominancy and ensuring closed‐loop system...

This article presents the prediction problem for uniformly observable nonlinear systems with input delay. The prediction problem is addressed using high-gain observer-based predictors. A modified Lyapunov-Krasovskii functional is used to analyze the exponential convergence of the prediction error. The predictor design and tuning are illustrated thr...

This article analyzes the high-gain prediction approach for nonlinear input-delay systems. The problem is discussed in the light of weighted homogeneity and input-to-state stability. The canonical form for uniformly observable nonlinear systems allows tuning the spectrum of the linear part by multiplicity-induced dominance and ensures closed-loop s...

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in dynamical control systems. Mimicking the general strategy that led to the foundation of bifurcation theory in smooth maps, we introduce a novel notion of equivalence between linear complementarity problems that sets the basis for a theory of bifurcations in...

We propose a predictor tuning method for a class of uniformly observable nonlinear time-delay systems. This method is based on the multiplicity-induced-dominancy property of quasipolynomials. The predictor gains are chosen in such a way that a dominant root is located in the left half-plane, thus the prediction error converges exponentially to zero...

This article introduces an observer-predictor that estimates the position of a quadrotor with input delay. The predictor whose aim is to compensate the delay, is tuned using multiplicity-induced dominance of the roots of the linearized prediction error. The stability of the prediction error is analyzed using a Lyapunov-Krasovskii functional. Simula...

Se plantea el uso de leyes multivaluadas para el control de sistemas hamiltonianos con puerto. Se muestra que, si el control multivaluado satisface la propiedad de monotonía creciente, entonces la acción de control es pasiva, el sistema en lazo cerrado está bien definido y se logra la regulación de salida en forma robusta. Se propone una metodologí...

We present a robust finite-time stabilising algorithm for an arbitrary-order nonholonomic system in chained form. The state feedback is locally bounded, homogeneous and discontinuous. Its design follows from a generalised circle criterion based on the theory of homogeneous Lyapunov functions and a two-stage homogeneity-preserving strategy proposed...

For mitigating the COVID-19 pandemic, much emphasis is made on implementing non-pharmaceutical interventions to keep the reproduction number below one. However, using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significant economic and...

We propose an observer for a susceptible‐infectious‐recovered epidemic model. The observer is then uplifted into a predictor to compensate for time delays in the input and the output. Tuning criteria are given for tuning gains of the predictor, while the estimation‐error stability is ensured using Lyapunov‐Krasovskii functionals. The predictor's pe...

We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power o...

We propose an observer for a SIR epidemic model. The observer is then uplifted into a predictor to compensate for time delays in the input and the output. Tuning criteria are given for tuning gains of the predictor, while the estimation-error stability is ensured using Lyapunov-Krasovskii functionals. The predictor's performance is evaluated in com...

We study a thermomechanical system comprising an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establishes a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provides a dynamic relation between the forc...

Many systems of interest to control engineering can be modeled by linear comple-mentarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools t...

To mitigate the COVID-19 pandemic, much emphasis exists on implementing non-pharmaceutical interventions to keep the reproduction number below one. But using that objective ignores that some of these interventions, like bans of public events or lockdowns, must be transitory and as short as possible because of their significative economic and societ...

Resumen de trabajos de modelado matemático para las proyecciones de COVID-19 en la CDMX y evaluación de medidas de mitigación. Con datos al 4 de mayo del 2020. Trabajo colectivo de investigadores de la UNAM y colaboradores de otras instituciones.

Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to...

We propose a sliding surface for systems on the Lie group SO(3) × R^3. The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid bodies. The close...

Recently, the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology has been extended to underactuated mechanical systems in implicit port-Hamiltonian representation. The method is not restricted to holonomic systems, does not require a positive-definite target inertia matrix and, under general conditions, avoids the...

Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to...

We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provide a dynamic relation between the forc...

We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid b...

In this paper, the PI control of first-order linear passive systems through a delayed communication channel is revisited in light of the relative stability concept called σ-stability. Treating the delayed communication channel as a transport PDE, the passivity of the overall control-loop is guaranteed, resulting in a closed-loop system of neutral n...

Unfortunate mistakes in the statements of Theorems 1 and 6 in the above paper are corrected.

Homogeneous systems are an interesting generalisation of the class of linear systems. On the one hand, many of the properties for which linear systems are useful in the analysis of more complex systems are shared by their homogeneous counterparts. On the other hand, they exhibit a considerably larger set of behaviours. In this article a generalisat...

In this paper we study the closed-loop dynamics of linear time-invariant systems with feedback control laws that are described by set-valued maximal monotone maps. The class of systems considered in this work is subject to both unknown exogenous disturbances and parameter uncertainty. It is shown how the design of conventional sliding-mode controll...

In this paper we use geometric tools to establish controllability properties of driftless systems which have less control inputs than states, but whose input vector fields span a non-involutive distribution. Our prototypical class of systems is conformed by kinematic models of non-holonomic systems such as the unicycle or a car with N trailers. We...

This paper focuses on the discrete-time sliding-mode control problem, that is, given an uncertain linear system under the effect of external matched perturbations, to design a set-valued control law that achieves the robust regulation of the plant and at the same time reduces substantially the chattering effect in both the input and the sliding var...

This contribution reports on an ongoing research project aimed in developing a unified theoretical framework for the description of interconnected thermo-mechanical systems with a particular emphasis on thermodynamic engines. We analyse from the geometrical viewpoint the structure of thermodynamic and mechanical interconnection and propose an appro...

We introduce a methodology to implement the physiological transition between distinct neuronal spiking modes in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by the same geometry and exhibiting the same input--output properties as high-dimensional electrophysiological neu...

The use of multivalued controls derived from a special maximally monotone operator are studied in this paper. Starting with a strongly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a pass...

This work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set, i.e., there exist only finitely many possible models for the plant. Uncertainty is dealt within a min–max context,...

We introduce a methodology to implement the physiological transition {between distinct neuronal spiking modes} in electronic circuits composed of resistors, capacitors and transistors. The result is a simple neuromorphic device organized by the same geometry {and exhibiting the same input--output properties as} high-dimensional electrophysiological...

Two main concepts for sliding surfaces design procedure: pole placement and optimal stabilization are generalized for the case of arbitrary order sliding modes. For the pole placement case, the formula of Ackermann-Utkin is extended allowing the design of sliding surfaces with arbitrary relative degree. The natural connection between order of singu...

The robustness properties of a first-order sliding-mode controller are combined with those of an added linear term in order to obtain a closed loop that shows input-to-state stability with respect to matched and unmatched disturbances, of which an upper bound might not be known, using only output information. The output under consideration can have...

The output regulation problem is addressed. We start with a linear passive system without feed-forward term and we look for a static set-valued output feedback control law which guarantees the regulation of the output to a desired fixed value, even in the presence of external matched and bounded perturbations. The multivalued control is taken as th...

We introduce a novel methodology to implement the physiological transition between tonic spiking and bursting in electronic circuits composed of resistors, capacitors and transistors. The result is a six-transistor neuromorphic device organized by the same geometry of high-dimensional electrophysiological neuron models and therefore exhibiting the...

In this paper we present a controller that achieves global input-to-state stabilty for a linear system of arbitrary relative degree, subjected to matched and unmatched disturbances. This controller combines the properties of a discontinous term, and a linear one, enforcing a conventional sliding mode using only partial state information. A direct a...

Implicit port-Hamiltonian representations of mechanical systems are considered from a control perspective. Energy shaping is used for the purpose of stabilizing a desired equilibrium. When using implicit models, the problem turns out to be a simple quadratic programming problem (as opposed to the partial differential equations that need to be solve...

In this paper we address the problem of establishing conditions for global asymptotic stability in output feedback sliding-mode control. The proposed methodology introduces a linear term in a first-order sliding-mode controller. This allows to characterize the closed loop with the input-to-state stability property. Also, a Lyapunov-based methodolog...

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model...

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivi...

In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the desig...

We consider the problem of robust output regulation for a class of passive linear systems. We take a 'control by interconnection of systems' approach, where the controller is defined by means of a multivalued function. The resulting closed-loop system can be cast into the form of a variable structure system with interesting properties: output feedb...

We propose an integral sliding surface for linear time-invariant implicit systems (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability) it is possible to design a stabilizing controller that compensates the matched perturbations exactly. Higher-order sliding motions are required since, for the solutions of t...

We show that the well-known formula by Ackermann and Utkin can be generalized to the case of higher-order sliding modes. By interpreting the eigenvalue assignment of the sliding dynamics as a zero-placement problem, the generalization becomes straightforward and the proof is greatly simplified. The generalized formula retains the simplicity of the...

This work presents initial experimental results of an adaptive sliding-mode extremum seeker that minimizes the hydrogen consumption in a fuel cell based system. The extremum seeker is based on the classical steepest-descent method, the main challenge being the fact that the gradient of the objective function is unknown. The gradient is estimated by...

We present an adaptive sliding-mode extremum seeker that minimizes an unknown function that is subject to an unknown static constraint. The same algorithm can be applied when the static constraint is replaced by a dynamic one, provided that the dynamics possess strong stability properties. The application and feasibility study is focused on hydroge...

Implicit and explicit representations of smooth, finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equati...

We propose an integral sliding surface for linear time-invariant implicit descriptions (descriptor systems). We show that, under reasonable assumptions (regularity, stabilizability and a corresponding matching condition), it is possible to design a controller that drives the descriptor variables to zero, even in the presence of disturbances. Higher...

We consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state-dependent drift and input matrix. The general case of both, matched and unmatched disturbances affecting the system is addressed. It is proved that the definition of a suitable sliding manifold and the ge...

The robustness properties of sliding-mode and H ∞ controllers are exploited to produce a dynamic output feedback controller that is insensitive to matched perturbations and attenuates the unmatched ones. The assumptions on the plant differ from the standard assumptions of the Riccati state-space approach to H ∞ control. The sliding-mode controller...

The paper further elaborates on a passive output that was constructed in [3] with the purpose of providing an energy-balance (EB) interpretation for basic interconnection and damping assignment (BIDA [6, 7]). Such output has its roots in power shaping [4], an alternative method to stabilize nonlinear RLC circuits subjected to the dissipation obstac...

This paper considers the problem of using an integral sliding mode strategy to reduce the disturbance terms acting on nonlinear systems in regular form. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it can guarantee the minimization of the disturbance terms. Simulation examples shows the ef...

Passivity-based controllers (PBCs) achieve stabilization of nonlinear systems, rendering the closed-loop passive with a desired energy (storage) function. A natural question is, under which conditions is it possible to make this function equal to the difference between the plant and controller energies—when the controller is said to be energy-balan...

In this paper we identify graph-theoretic conditions which allow us to write a nonlinear RLC circuit as port-Hamiltonian with constant input matrices. We show that under additional monotonicity conditions on the network’s components, the circuit enjoys the property of relative passivity, an extended notion of classical passivity. The property of re...

We study the asymptotic properties of control by interconnection, a passivity-based controller design methodology for stabilization of port-Hamiltonian systems. It is well-known that the method, in its basic form, imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium. We propose two different ways...

We present sufficient conditions for robust relay delayed semiglobal stabilization of second order systems, which relate the upper bound to an uncertain time delay and the parameters of the plant. We also suggest an algorithm of delayed relay control gain adaptation for semiglobal stabilization, which is based on delayed information about the sign...

In this note we identify graph-theoretic conditions which allow to write an RLC circuit as port-Hamiltonian with constant input matrices. We show that under additional monotonicity conditions of the network's components, the circuit enjoys the property of relative passivity, an extended notion of classical passivity. The property of relative passiv...

It is well known that if the linear time invariant system is passive the associated incremental system , with , u⋆,y⋆ the constant input and output associated to an equilibrium state x⋆, is also passive. In this paper, we identify a class of nonlinear passive systems of the form whose incremental model is also passive. Using this result we then pro...

In this note we provide a way of designing the nominal trajectory of an integral sliding mode controller for linear multi-model uncertain systems. The nominal system is chosen using a mini-max criterion for the norm of the discontinuous, feed-forward control. The continuous feed-back control is then designed using linear matrix inequalities

The robustness properties of integral sliding mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if inte...

Se propone un esquema sencillo que lleva al pendulo del punto de equilibrio estable al punto de equilibrio inestable con un control de posicion del carro que hace entrar al pendulo en resonancia, y al entrar a la posicion vertical conmuta a un esquema de regulacion del pendulo. Para el diseno de los controles se uso LQR discreto. Se muestran los re...

The robustness properties of both, sliding mode control and H∞ design methodologies are exploited in the con-text of decentralized control, for which interconnections among subsystems are treated as perturbations. A dynamic surface is proposed for the sliding mode design. The sliding mode control successfully rejects the matched interconnections an...