Keywords: Stabilization, Lyapunov Methods, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems
Abstract: Significant advances have taken place in the last few years in the development of control designs for nonlinear infinite-dimensional systems. Such systems typically take the form of nonlinear ODEs (ordinary differential equations) with delays and nonlinear PDEs (partial differential equations). In this article we review several representative but general results on nonlinear control in the infinite-dimensional setting. First we present designs for nonlinear ODEs with constant, time-varying or state-dependent input delays, which arise in numerous applications of control over networks. Second, we present a design for nonlinear ODEs with a wave (string) PDE at its input, which is motivated by the drilling dynamics in petroleum engineering. Third, we present a design for systems of (two) coupled nonlinear first-order hyperbolic PDEs, which is motivated by slugging flow dynamics in petroleum production in off-shore facilities. Our design and analysis methodologies are based on the concepts of nonlinear predictor feedback and nonlinear infinite-dimensional backstepping. We present several simulation examples that illustrate the design methodology.

Keywords: Dissipativity, Passivity, I/O Stability Methods
Abstract: Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity when restricting to quadratic supply rates. The paper also shows that the interconnection of differentially passive systems is differentially passive, and provides preliminary examples of differentially passive electrical systems.

Keywords: Passivity, Geometric Methods, Lyapunov Stability Methods
Abstract: Motivated by developments on differential Lyapunov functions for contraction analysis in Forni, Sepulchre (2012) we propose a definition of differential passivity, based on the geometric framework of the prolongation of a nonlinear system in Crouch, van der Schaft (1987) . We explore the ramifications of this definition and its potential uses.

Keywords: Small Gain Theorems, Lyapunov Methods, Stability
Abstract: This paper makes use of the concept of a finite–time Lyapunov function to derive a non– conservative small-gain theorem for stability analysis of interconnected discrete–time nonlinear systems. Firstly, it is shown that the existence of a global finite–time Lyapunov function is equivalent to global asymptotic stability (GAS) of the overall interconnected system. Secondly, it is indicated that existence of Lyapunov–type functions for each subsystem, together with a small-gain condition implies GAS of the interconnected system. Thirdly, the main result of this paper establishes that GAS of the interconnected system always yields a set of Lyapunov–type functions that satisfy the small-gain condition for a rather general class of GAS nonlinear systems. A simple example demonstrates the non–conservatism of the proposed small-gain theorem.

Keywords: Backstepping, Small Gain Theorems, Input-To-State Stability
Abstract: We prove that a nonlinear control system with periodic dynamics in the generalized triangular form (GTF) which is affected by external disturbances can be uniformly input-to-state stabilized by means of a periodic feedback and the gain can be chosen arbitrarily small in some sense. This allows us to stabilize such a system in presence of unmeasured dynamic uncertainties.

Keywords: Input-To-State Stability, Lyapunov Methods, Stability
Abstract: We provide partial Lyapunov characterizations for a recently proposed generalization of input-to-state and integral input-to-state stability (ISS and iISS, respectively). This generalization relies on the notion of stability with respect to two measures originally introduced by Movchan [1960]. We show that the two classical Lyapunov characterizations of ISS-type properties, i.e., decrease conditions in an implication or dissipative form, correspond to ISS and iISS, respectively. We also demonstrate via an example that, for the generalization considered here, ISS does not necessarily imply iISS.

Keywords: Aerospace and Marine Applications, Robotics
Abstract: This paper proposes a method to characterize the space explored by a mobile robot during a mission. Because of localization uncertainty, the area osculated by a sensor at a given time is uncertain too. The problem is modeled by using intervals to represent trajectory uncertainties and a “visibility function” to describe the area in view at a given time. A set-inversion method is then applied to compute a “guaranteed visible area” and a “possible visible area” with respect to positioning uncertainty. A bracketing of the actual explored area between a “guaranteed explored area” and a “possible explored area” for the whole mission is finally obtained by respectively taking the union of the guaranteed and possible areas. Results from a simulated underwater exploration mission are presented.

Keywords: Geometric Methods, Stabilization
Abstract: This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stablizing controllers. The method uses first-order Taylor approximation of the nonlinear dynamics and a conservative approximation of the Lagrange remainder. An example for illustration is included.

Keywords: Parameter Estimation, Numerical Methods
Abstract: Recently, a new family of methods has been proposed for characterizing accuracy in nonlinear parameter estimation by Campi et al. These methods make it possible to obtain exact, non-asymptotic confidence regions for the parameter estimates under relatively mild assumptions on the noise distribution, namely that the noise samples are independently and symmetrically distributed.

The numerical characterization of an exact confidence region with this new approach is far from being trivial, however. The aim of this paper is to show how interval analysis, which has been used for a guaranteed characterization of confidence regions for the parameter vector in other contexts, can contribute.

Keywords: State Estimation and Applications, Numerical Methods, Chemical Process
Abstract: This work considers the computation of time-varying enclosures of the reachable sets of nonlinear control systems via the solution of an initial value problem in ordinary differential equations (ODEs) with linear programs (LPs) embedded. To ensure the numerical tractability of such a formulation, the properties of the ODEs with LPs embedded are discussed including existence and uniqueness of the solutions of the initial value problem in ODEs with LPs embedded. This formulation is then applied to the computation of rigorous componentwise time-varying bounds on the states of a nonlinear control system. The bounding theory used in this work exploits physical information to yield tight bounds on the states; this work develops a new implementation of this theory. Finally, the tightness of the bounds are demonstrated for a model of a reacting chemical system with uncertain rate parameters.

Keywords: State Estimation and Applications, Observability and Observer Design
Abstract: This work is devoted to interval observer design for Linear Parameter-Varying (LPV) systems under assumption that the vector of scheduling parameters is not available for measurements. Stability conditions are expressed in terms of matrix inequalities, which can be solved using standard numerical solvers. Robustness and estimation accuracy with respect to model uncertainty is analyzed using L_infty/L_1 framework. Two solutions are proposed for nonnegative systems and for a generic case. The efficiency of the proposed approach is demonstrated through computer simulations.

Keywords: Aeronautics, Linear Algebraic Methods
Abstract: In this paper, an image-based visual servoing scheme is presented in order to control a transport aircraft in final approach phase by overcoming the need for external information (e.g. ILS or GPS systems) and runway knowledge. Based on three decoupled visual features and inertial data, the guidance scheme is designed and validated on a simplified model and tested on a realistic nonlinear simulator. Finally simulation results are presented in order to validate the choice of the visual features and the guidance laws to land the aircraft.

Keywords: Model Based Control
Abstract: A model for a quadrotor helicopter, its flatness-based parameterization, and its control are investigated. The model is transformed by expressing the configuration in terms of a reference trajectory and the deviation from the latter. A flat output for the error system is introduced. A dynamic and a quasi-static feedback for asymptotic stabilization of reference trajectories are derived. The approach avoids introducing artificial singularities and provides the possibility for tracking ”acrobatic” trajectories. A simulation result with the quadrotor flying a loop is shown.

Keywords: Automotive Systems Marine Systems, Optimal Control, Backstepping
Abstract: This paper presents a car parking control concept for real-time application. It utilizes a two-degrees-of-freedom control scheme consisting of a feedforward and a feedback controller. The reference trajectory is constructed in two steps. First a geometric path is planned by solving a local static optimization problem, which is formulated by discretizing the path. Second a pathfollowing problem in the form of an optimal control problem considering the physical limitations is solved. The solution of this optimal control problem yields the time parametrization of the geometric path. In order to account for model uncertainties and disturbances, a Lyapunov-based feedback controller is designed for the trajectory error system. Simulation studies show the applicability and efficiency of the proposed approach.

Keywords: Lyapunov Methods, Stabilization, Robotics
Abstract: Semiconcave control Lyapunov functions for globally asymptotic stabilizing controllable systems are available.However, a semiconcave control Lyapunov function for nonholonomic systems has not been proposed yet.For a two-wheeled mobile robot, we construct a homogeneous semiconcave control Lyapunov function and a control law with the function.The advantages of the proposed method are confirmed by computer simulation.

Keywords: Automotive Systems Marine Systems, Lyapunov Methods, Disturbance Atténuation
Abstract: We study the problem of straight-line path following for fully actuated marine craft. We propose a controller that adjusts the speed of the marine craft according to the geometric distance and the rate of convergence to the path. The control law is derived using the method of least squares, which is used to find an approximate solution for overdetermined systems. The conditions under which the closed-loop system is globally asymptotically stable are found. Moreover, a method to ensure zero cross-track error in the presence of ocean currents is proposed. The stability proof relies on the theory of cascaded systems. The effectiveness of the method is verified by performing computer simulations.

Keywords: Lyapunov Methods, Input-To-State Stability, I/O Stability
Abstract: The purpose of this paper is to survey and discuss recent results on norm-controllability of nonlinear systems. This notion captures the responsiveness of a nonlinear system with respect to the applied inputs in terms of the norm of an output map, and can be regarded as a certain type of gain concept and/or a weaker notion of controllability. We state several Lyapunov-like sufficient conditions for this property in a simplified formulation, and illustrate the concept with several examples.

Keywords: Robotics, Lyapunov Methods, Control of Mechanical, Electrical and Process Systems
Abstract: Inspired by the motion of biological snakes, this paper presents an overview of recent results in modelling and control of snake robots. The objective of the research underlying this paper is to contribute to the mathematical foundation of the control theory of snake robots. To this end, the paper presents two mathematical models of planar snake robot dynamics, which are employed to investigate stabilisability and controllability properties of snake robots. Furthermore, averaging theory is used to derive properties of the velocity dynamics of snake robots. Moreover, a straight line path following controller is proposed and cascaded systems theory is employed to prove that the controller K-exponentially stabilizes a snake robot to any desired straight path.

Keywords: Stabilization, Stability
Abstract: This study presents an energy level stabilization algorithm for the pendulum on a cart system with restricted cart track length. The objective is to bring the pendulum to its unstable equilibrium. To do so the energy level of the pendulum is increased or decreased by accelerating the cart in the appropriate direction while keeping within imposed limit positions. To achieve, the equation of motion of the pendulum is solved by means of elliptic integrals considering the cart is moved with constant acceleration, and all the calculations are performed numerically to obtain the bounds for elapsed time and change of the energy level of the pendulum. The algorithm is tested on the system by means of numerical simulations.

Keywords: Stability, Dissipativity, Geometric Methods
Abstract: This paper considers the problem of representing a sufficiently smooth nonlinear system as a structured potential-driven system and to exploit the obtained structure for the design of nonlinear state feedback stabilizing controllers. The problem has been studied in recent years for systems modeled as structured potential-driven systems, for example gradient systems, generalized Hamiltonian systems and systems given in Brayton–Moser form. To recover the advantages of those representations for the stabilization of general nonlinear systems, the present note proposes a geometric decomposition technique to re-express a given vector field into a desired potential-driven form. The decomposition method is based on the Hodge decomposition theorem, where a one-form associated to the given vector field is decomposed into its exact, co- exact, and harmonic parts.

Keywords: Stabilization, Lyapunov Methods, Numerical Methods
Abstract: The aim of this work is to present an entropy-like Lyapunov function based dynamic feedback design technique for quasi-polynomial and Lotka-Volterra systems. It is shown, that the dynamic feedback design problem is equivalent to the feasibility of a bilinear matrix inequality. The problem is also formulated as a control Lyapunov function based feedback design when the Lyapunov function parameters are given, the solution of this problem can be obtained by solving a linear matrix inequality.

Keywords: Passivity, Stabilization, Geometric Methods
Abstract: We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC procedure. The proposed methodology relies on an energy discretization scheme with suitable discrete conjugate port variables. The main result is illustrated on two examples: a nonlinear pendulum in order to compare with some simulation results of the literature, and the impact oscillator which requires robust discretization scheme.

Keywords: Variable Structure Control and Sliding Mode, Lyapunov Methods, Stabilization
Abstract: The Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. The new high order sliding mode (HOSM) control is derived as a particular case of the developed finite-time control algorithm. The settling time estimate is obtained using ILF method. The algorithm of practical implementation of the ILF control scheme is discussed. The theoretical results are supported by numerical simulations.

Keywords: Passivity, Optimal Control, Geometric Methods
Abstract: This paper discusses the (inverse) optimality and practical usage of passivity-based controls for distributed port-Hamiltonian systems. We first clarify that passivity-based controls, damping assignment and potential shaping can be derived from a linear quadratic type optimal control problem. Next, we describe the limitation of passivity-based boundary controls and propose a practical usage of the methods in terms of discretization. Finally, we illustrate numerical results having a similar property to the strain feedback methods derived from semigroup theory for stabilizing and stiffness controlling flexible beams.

Keywords: Biological and Biomedical Systems, Stabilization, Parameter Estimation
Abstract: We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each of the two subproblems can be solved with relatively simple algorithms. We are then free to choose any numerical optimization algorithm. We give a demonstration for two choices: one is based on slow-fast dynamics and numerical continuation, the other is a combination of golden-section and Newton iteration. The method copes with non-monotonic growth functions.

Keywords: Optimal Control, Time Optimal Control, Chemical Process
Abstract: We address the problem of finding an optimal feedback control for feeding a fed-batch bioreactor with one species and one substrate, from a given initial condition to a given target value in a minimal amount of time. Mortality rate for the biomass and nutrient recycling are taken into account in this work. The optimal synthesis (optimal feeding strategy) has been obtained by Moreno in 1999 when both mortality and recycling are considered negligible, in the case of Monod and Haldane growth function. Our objective is to study the effect of mortality and recycling on the optimal synthesis. We provide an optimal synthesis of the problem using Pontryagin maximum principle, which extends the result of Moreno in the impulsive framework with mortality and recycling effect.

Keywords: Chemical Process, Biological and Biomedical Systems, Lyapunov Methods
Abstract: The present work addresses the problem of chemostat stabilization around an optimal steady state, in the sense of enlargement of its stability region. The need for stabilization becomes imperative under conditions where the growth of biomass is subject to substrate inhibition, and the primary concern is to prevent washout of the biomass in the presence of disturbances. Inspired by the empirical concept of constant-yield control, a nonlinear state feedback control law is derived, and the stability basin of resulting closed-loop system is estimated using a Lyapunov function approach. Our analysis extends previous results in the sense that it accounts for biomass decay and endogenous metabolism and, moreover, it covers the case where the product is soluble in the effluent stream.

Keywords: Stabilization, Control of Sampled Data Systems, Biological and Biomedical Systems
Abstract: The classical model of the chemostat with one substrate, one species and a Haldane type growth rate function is considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of globally asymptotically stabilizing a positive equilibrium point of this system in the case where the measured concentrations are delayed and piecewise constant with a piecewise constant control is addressed. The result relies on the introduction of a dynamic extension of a new type.

Keywords: Biological and Biomedical Systems, Stabilization
Abstract: In this paper, we tackle the problem of microalgae selection in a continuous photobioreactor where microalgae growth is limited by light. We propose a closed-loop control for selecting, for a given range of light intensity, the strain with the maximum growth rate from the microalgae population. In particular, we are interested in strains with high growth rate for high light intensity, i.e.,strains with high resistance to photoinhibition. Firstly, we recall the framework of the light-limited chemostat. Then, we propose a nonlinear adaptive control which regulates the light intensity at the bottom of the photobioreactor in monoculture. This light is of particular interest as it defines the winner of the competition in a multispecies culture operated in open-loop mode. Finally, we show that the proposed controller allows the selection of a strain of interest in the case of a culture with n species.

Keywords: Biological and Biomedical Systems, Stability, Performance Issues
Abstract: We show how a particular spatial structure with a buffer globally stabilizes the chemostat dynamics with non-monotonic response function, while this is not possible with single, serial or parallel chemostats of the same total volume and input flow. We give a characterization of the set of such configurations that satisfy this property, as well as the configuration that ensures the best nutrient conversion. Furthermore, we characterize the minimal buffer volume to be added to a single chemostat for obtaining the global stability. These results are illustrated with the Haldane kinetic function.

Keywords: Dynamical Systems Techniques, Optimal Control
Abstract: Hyper-sensitivity to unknown boundary conditions plagues indirect methods of solving optimal control problems as a Hamiltonian boundary-value problem for both state and costate. Yet the hyper-sensitivity may imply manifold structure in the Hamiltonian flow, knowledge of which would yield insight regarding the optimal solutions and suggest a solution approximation strategy that circumvents the hyper-sensitivity. Finite-time Lyapunov exponents and vectors provide a means of diagnosing hyper- sensitivity and determining the associated manifold structure. A solution approximation approach is described that requires determining the unknown boundary conditions, such that the solution end points lie on certain invariant manifolds, and matching of forward and backward segments. The approach is applied to the optimal control of a nonlinear spring-mass-damper system. The approximate solution is shown to be accurate by comparison with a solution obtained by a collocation method.

Keywords: Optimal Control, Computational Efficiency, Mechatronic Systems
Abstract: This paper describes a constraint transformation technique for optimal control problems (OCP) with nonlinear single-input single-output (SISO) systems subject to output constraints. An input-output transformation and saturation functions are used to transform the system dynamics into a new unconstrained representation. This method allows to reformulate the original OCP into an unconstrained counterpart. The transformation technique is applied to a double pendulum on a cart in order to compute optimal trajectories for a multi-stage transition scenario. Simulation as well as experimental results with an additional feedback control demonstrate the applicability of the presented method.

Keywords: Optimal Control, Time Optimal Control
Abstract: The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the “shape” of the optimal input is in general not known. The control input can be found solving an Hamilton-Jacobi-Bellman (HJB) partial differential equation (pde): it typically consists of a combination of bang-bang arcs and singular arcs. In the paper a methodology to approximate the solution of the HJB pde arising in the finite-horizon optimal control problem with input constraints is proposed. This approximation yields a dynamic state feedback law. The theory is illustrated by means of an example: the minimum time optimal control problem for an industrial wastewater treatment plant.

Keywords: Optimal Control, Time Optimal Control
Abstract: In this paper we investigate an optimal control problem in which the objective is to decelerate a simplified vehicle model, subject to input constraints, from a given initial velocity down to zero by minimizing a quadratic cost functional. The problem is of interest because, although it involves apparently simple drift-less dynamics, a minimizing trajectory does not exist. This problem is motivated by a minimum-time problem for a fairly complex car vehicle model on a race track. Numerical computations run on the car problem provide evidence of non-existence of a minimizing trajectory and of an apparently unmotivated ripple in the steer angle. We abstract this situation to a very simple dynamics/objective setting, show that no minimizing trajectory exists, and reproduce the oscillating behavior on the steer angle as a mean to reduce the cost functional.

Keywords: Optimal Control, Time Optimal Control, Robustness
Abstract: The minimum-time problem frequently arises in the design of control for actuators, and is usually solved assuming to know the correct model of the system. In industrially important cases, however, important parts of the dynamics, like friction forces or disturbances by exosystems, are hardly known or even unknown. Against this background, this paper presents an iterative approach to achieve the minimum-time control for a nonlinear, single input second-order system with constrained input and partly unknown dynamics, effectively removing the requirement of perfect knowledge of the system and its parameters to achieve the minimum-time solution in application. First it is shown that, under reasonable assumptions about the unknown part of the dynamics, the optimal control exists for the presented class of systems and that it is a bang-bang control, with at most one switch. Then this property is exploited in the proposed algorithm, that finds the single optimal switching time by an iterative method, without involving any kind of identification of the unknown system parts.

Keywords: Hybrid Nonlinear Control Systems, Lyapunov Methods, Stability
Abstract: This paper introduces a stochastic, hybrid algorithm for global almost sure synchronization of two agents evolving on the circle. Recent results on stochastic hybrid systems are exploited and a Lyapunov-based proof of global almost sure synchronization is obtained. The same arguments establish that global almost sure practical synchronization is achieved in the presence of sufficiently small disturbances. In contrast, sure almost global algorithms are more seriously affected by adversarial disturbances. Namely, there is a set of initial conditions with nonzero measure from which the agents may not approximately synchronize.

Keywords: Hybrid Nonlinear Systems, Lyapunov Methods, Robotics
Abstract: The paper extends the notion of oscillations in the sense of Yakubovich to hybrid dynamics. Several sufficient stability and instability conditions for a forward invariant set are presented. The consideration is illustrated by analysis of a model of two-link compass-gait biped robot.

Keywords: Hybrid Nonlinear Systems, Small Gain Theorems, Input-To-State Stability
Abstract: For interconnection of impulsive systems a relation between dwell-time and small-gain conditions is considered in this paper. In particular we show how the choice of gains or supply rates affects the restriction on time intervals between impulses to assure stability properties.

Keywords: Optimal Control, Hybrid Nonlinear Control Systems
Abstract: It is well-known that a system with linear structure subjected to bounded control inputs for optimal closed-loop control yields nonlinear feedback of discontinuous bang-bang type. This paper investigates a of nonlinear feedback in the case of optimal impulsive closed-loop control which may naturally generate discontinuous trajectories. The realization of such feedback under impulsive inputs that are allowed to use delta-functions with their higher derivatives requires physically realizable approximations. Described in this paper is a new class of realizable feedback inputs that also allows to produce smooth approximation of controls. Such approach also applies to problems in micro time scales that require so-called fast or ultra-fast controls.

Keywords: Stability, Input-To-State Stability, Lyapunov Methods
Abstract: We consider the problem of stability in a class of differential equations which are driven by a differential measure associated with the inputs of locally bounded variation. After discussing some existing notions of solution for such systems, we derive conditions on the system's vector fields for asymptotic stability under a specific class of inputs. These conditions present a trade-off between the Lebesgue-integrable and the measure-driven components of the system. In case the system is not asymptotically stable, we derive weaker conditions such that the norm of the resulting trajectory is bounded by some function of the total variation of the input, which generalizes the notion of integral input-to-state stability in measure-driven systems.

Keywords: Biological and Biomedical Systems, Model Based Control, Robustness
Abstract: In this study, a multivariable control structure is developed to simultaneously control the concentrations of cells and of one of the nutrients in an animal cell cultivation system operated in perfusion. A cascade control structure is considered consisting of (i) an inner loop with a partially linearizing feedback controller, tuned so as to ensure robustness with respect to parameter uncertainties and non-canceled nonlinearities; and (ii) an outer loop involving two linear predictive controllers. The resulting control strategy shows robustness and performance properties similar to more computationally demanding strategies (such as a multivariable nonlinear MPC strategy), while requiring less measurements and involving an easier implementation.

Keywords: Biological and Biomedical Systems, Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems
Abstract: The nonlinear nature of bioprocesses often leads to the occurrence of the self-sustained oscillations of the biomass concentration in continuous flow bioreactors. For some practical reasons, sometimes it is necessary to control the oscillatory behaviour, which is usually achieved by changing the dilution rate, but this is not always the best option. Hence, the main idea of this paper is to introduce an additional substrate, which has been previously diluted. Based on the numerical analysis of an unstructured mathematical model, it is shown that by mixing two various substrates (the main and the diluted one), it is possible to induce or eliminate the sustained oscillations. As a result, the contribution of both substrates to the mixture and the degree of dilution of the additional substrate can be treated as new control variables.

Keywords: Biological and Biomedical Systems, Robustness, Performance Issues
Abstract: In this paper, a novel approach to control end-tidal CO2 in mechanically ventilated patients is presented. Assuming a homogeneous lung model, a regulation of arterial CO2 tension in blood can be achieved non-invasively using L1 adaptive control with the aid of an extremum seeking method to set the proper respiratory rate. Using these integrated approaches, not only is end-tidal CO2 regulated at the specific level, but also muscular power for breathing is optimized to comfort the muscles involved in the respiratory system. The simulation of the control algorithms show the distinctive results based on linear and nonlinear Hammerstein models of the process. These were obtained from measurement data from a human volunteer. The algorithm is applicable under pressure-controlled ventilation and provides a practical solution in various clinical situations.

Keywords: Dynamical Systems Techniques, Biological and Biomedical Systems, Stabilization
Abstract: In this paper we propose a positive linear control law for the stabilization of positive equilibria in predator-prey systems; this problem is motivated by the introduction of predators in biological control applications, to prevent excessive levels of prey (pests). We build a linear controller that we saturate at zero and prove, under some conditions, the global asymptotic stability of the equilibrium. Without one of these conditions, the point is shown to be globally attractive but may be unstable. Finally, we discuss how the control parameters should be chosen to reduce the total control effort and the size of the transient peak in the prey population.

Keywords: Hybrid Nonlinear Systems, Biological and Biomedical Systems, Stability
Abstract: In this paper we propose a novel qualitative formalism to model gene expression dynamics dependent on dilution due to growth rate of the cell. We extend the piecewise linear (PL) systems by keeping the use of step functions to model the interactions between the elements and adding a growth rate expression to model the dilution effect. Focusing on the global gene expression machinery in bacteria, we model the growth rate as the minimum of two limiting factors: RNA polymerase (RNAP) and ribosomes. The resulting system is a switched system with two piecewise quadratic (PQ) modes. We study the stability of such switched piecewise quadratic (SPQ) system starting from the stability analysis of the (PQ) modes. We also present and analyze by means of phase-planes a bidimensional SPQ model involving RNAP and ribosomes concentrations, which brings out the important differences with respect to PL systems. Finally, we qualitatively show that our growth rate expression acts well in different biological conditions.

Keywords: Lyapunov Methods, Stabilization, Observability and Observer Design
Abstract: In this paper, global stabilization by output feedback is investigated for a class of non-minimum-phase nonlinear systems previously considered by Marino and Tomei [4]. It is shown that it is possible to construct, via a new design method that involves no filter transformation, a globally stabilizing dynamic output feedback controller of order n, instead of n + 2(ρ − 1), for the non-minimum phase nonlinear system in output feedback form [4], under a slightly general condition (i.e., Assumption 2.2) together with the assumption that the nonlinear system is non-minimum-phase with respect to the original output, but minimum-phase with respect to a virtual linear output. Two examples are given to illustrate the simplicity of the new design approach and its effectiveness.

Keywords: Stabilization, Lyapunov Methods, Adaptive Observers
Abstract: This paper focuses on the design of robust internal model-based regulators for a class of nonlinear systems and exosystems such that the desired steady state control law fulfills a nonlinear regression formula affine in possible uncertainties. The design methodology builds upon the ideas presented in a paper by the authors on Automatica in the context of linear adaptive output regulation. The design methodology relies upon an assumption of left invertibility of a matrix. Through numerical analysis we show how the design methodology succeeds in relevant cases, such as the cases in which the desired steady state is generated by uncertain Van der Pol, Duffing, and Lorentz oscillators.

Keywords: Nonlinear Cooperative Control, Network Routing, Necessary Conditions
Abstract: This paper studies the problem of output agreement in networks of nonlinear dynamical systems under time-varying disturbances. Necessary and sufficient conditions for output agreement are derived for the class of incrementally passive systems. Following this, it is shown that the optimal distribution problem in dynamic inventory systems with time-varying supply and demand can be cast as a special version of the output agreement problem. We show in particular that the time-varying optimal distribution problem can be solved by applying an internal model controller to the dual variables of a certain convex network optimization problem.

Keywords: Stabilization, Robustness, Lyapunov Methods
Abstract: The paper deals with the problem of output regulation for the class of multi-input multi-output square nonlinear systems satisfying a minimum-phase assumption and a ``positivity" condition on the high-frequency gain matrix. By following a design paradigm proposed in [12] for single-input single-output nonlinear systems, it is shown how an internal model-based controller can be obtained, whose dimension depends on the number of regulated outputs and on the dimension of the exosystem. Thanks a scalability property of the regulator structure highlighted in [12], it is shown how a ``pre-processing" internal model can be shifted from input to output, yielding in this way a ``post-processing" internal model. This makes it possible to run a high-gain asymptotic analysis that bypasses the need of finding a normal form, as it would normally be the case.

Keywords: Model Based Control
Abstract: Active control of the production choke valve is the recommended solution to prevent severe slugging flow conditions at offshore oilfields. The slugging flow constitutes an unstable and highly nonlinear system; the gain of the system changes drastically for different operating points. Although PI and PID controllers are the most widely used controllers in the industry, they need to be re-tuned for different operating conditions. The focus of this paper is designing a model-based nonlinear controller in order to counteract nonlinearities of the system. The feedback linearization based on the riser-base pressure and the topside pressure was used for the control design. Stability and convergence of the closed-loop system was verified in theory as well as by experiments on a test rig.