Keywords: Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Control of Mechanical, Electrical and Process Systems, Smart Structures
Abstract: This paper considers the design of nonlinear state observers for finite-dimensional equivariant kinematics of mechanical systems. The observer design problem is approached by lifting the system kinematics onto the symmetry group and designing an observer for the lifted system. Two particular classes of lifted systems are identified, which we term type I and type II systems, that correspond to common configurations of sensor suites for mobile robotics applications. We consider type I systems in detail and define an error signal on the symmetry group using the group structure. We propose an observer structure with a pre-observer or internal model augmented by an equivariant innovation term that leads to autonomous error evolution. A control Lyapunov function construction is used to design the observer innovation that both ensures the required equivariance, and leads to strong convergence properties of the observer error dynamics.

Keywords: Filter Design, Lyapunov Stability Methods
Abstract: This paper is concerned with the problem of H-infinity filtering for continuous-time nonlinear quadratic systems. The aim is to design a full order dynamic filter that can also contain quadratic terms. The strategy relies on the use of a quadratic Lyapunov function and an inequality condition that assures an H-infinity performance bound for the augmented quadratic system, composed by the original system and the filter to be designed, in a regional (local) context. Then, by using the Finsler's lemma, an enlarged parameter space is created, where the Lyapunov matrix appears separated from the system matrices. Imposing structural constraints to the decision variables, theoretical conditions, which can be treated as linear matrix inequality conditions by fixing a grid on a scalar parameter, can be derived for the filter design. As illustrated by numerical experiments, the proposed conditions can improve the H-infinity performance provided by linear filters by including the quadratic terms in the filter dynamics.

Keywords: H-infinity Control, Aerospace and Marine Applications, Stability
Abstract: Rate and magnitude control limitations are often responsible for the apparition of undesired limit cycles in the resulting nonlinear closed-loop system. Based on the well-known describing function approach, it is shown in this paper that such limit cycles can be avoided as soon as multiple Hinfinity constraints are simultaneously satisfied by appropriately chosen linear interconnections. This result is then used to design anti-windup compensators.

Keywords: Lyapunov Methods, H-infinity Control, Robustness
Abstract: The main objective in this paper is to investigate the robust performance degradation for a class of nonlinear systems due to some dynamics that are not taken into account during the controller design stage. This is usually the case in practical applications where a simplified (nonlinear) model is used to design the controller. Therefore, it is expected some performance degradation in the application of such a controller due to the presence of the neglected dynamics. With this purpose, some convex conditions for stability analysis and energy-peak evaluation of nonlinear control systems are given. It is supposed that the nonlinear functions present in the model are subject to bounded uncertainties and that both the simplified model and the neglected dynamics model are affected by polytopic uncertainties. The theoretical conditions providing stability and energy-peak bound on the regulated output of the system despite the presence of uncertainties associated with the nonlinear functions are obtained by means of a parameter dependent Lyapunov function. The proposal is illustrated by numerical examples.

Keywords: Lyapunov Stability Methods, Optimal Control, Stability
Abstract: In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen has the value function of an optimal problem with some specific properties. We illustrate these result on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering an orbital transfer problem.

Keywords: Optimal Control, Robustness, Numerical Methods
Abstract: In this paper, a methodology based on proper orthogonal decomposition (POD) for computing approximate closed-loop optimal or robust control laws for finite-dimensional nonlinear systems is proposed. The solution can be obtained on any arbitrary domain of the state space represented by a multidimensional grid. The method only requires the computation of a limited number of well-conditioned two-point boundary value problems and a simple backwards integration of a reduced model of the Hamilton-Jacobi-Bellman or Hamilton-Jacobi- Isaacs equation associated to the control problem. Two illustrative examples demonstrate the effectiveness of the approach.

Keywords: Observability and Observer Design, State Estimation and Applications
Abstract: In this paper the problem of inputs in observer design for systems which are not uniformly observable is considered. It is emphasized how it amounts to a control problem, which can be solved in a general way by some appropriate optimization approach. This is illustrated on the basis of a quite general Kalman-like observer form - possibly with high gain, as well as related simulation results on an application example.

Keywords: Observability and Observer Design, Applications of Observer Design, Observer and Filter Design By Observer Error Linearization
Abstract: This paper presents a new extended output depending nonlinear observer normal form. A sufficient geometrical conditions that guarantee a change of coordinates allowing the transformation of a given nonlinear dynamical system into the proposed observer form are given. Throughout this work, it will be showed that, unlike to the existing observer normal forms, this new form enables to design an observer for the Susceptible, Exposed, Infected, and Recovered (SEIR) model of population under an infectious disease.

Keywords: Observability and Observer Design, Robotics, Nonlinear Cooperative Control
Abstract: The trajectory tracking problem for a group of unicycle-type robots is addressed and solved by means of a partial state feedback strategy based on the leader-followers scheme using an observer to estimate the orientation angle of each mobile robot. The control law is based on an extended kinematic model where the output function to be controlled is the mid-point of the wheels axis of each robot. This choice leads to an ill defined control law when the robot is at rest. To avoid such a singularity, a complementary control law is enabled when the linear velocity of each robot is close to zero. It is shown that the combination of a classical dynamic full information controller with an exponentially convergent vehicle attitude observer yields an asymptotically stable closed-loop system. Real-time experiments show the performance of the proposed control scheme.

Keywords: Applications of Observer Design, Biological and Biomedical Systems, Observer and Filter Design By Observer Error Linearization
Abstract: This paper considers the nonlinear observer normal forms and their application in an ecological Predator-Prey system. These forms allow for the design of robust observers for Predator-Prey models where full measurement is not available. Thus, from a measured population of one specie (prey or predator), one can estimate the population that is not directly measured.

Keywords: State Estimation and Applications, Lyapunov Methods, Computational Efficiency
Abstract: In this paper the application of the comparison principle for Hamilton-Jacobi equations to a particular nonlinear control system is discussed. Two classes of approximations of the reachability sets for this system are constructed. Numerical examples of the reachability set approximations and the solutions to control synthesis problem are given to illustrate the proposed approach.

Keywords: Absolute Stability, Complex Network, Anti-Control and Synchronization
Abstract: We consider consensus algorithms for multi-agent networks with high-order and delayed dynamics of agents. The topology is assumed to be fixed and undirected, however the couplings may be nonlinear and uncertain, we assume only the symmetry condition to be valid. We obtain conditions of stability for such algorithms that are similar in spirit to the celebrated Popov criterion for the stability of Lurie systems.

Keywords: Anti-Control and Synchronization, Stability, Bifurcation and Chaos
Abstract: We present an approach which allows to accurately predict both the occurrence and type of partially synchronous regimes of delay-coupled non-linear oscillators. Unlike the conventional approach, we build on an analysis of the stability properties of the synchronized equilibrium in the (coupling gain, delay) parameter space. As partially synchronous regimes are closely related to the presence of invariant manifolds, we first present necessary and sufficient conditions for the existence of forward invariant sets. Next, from the existence of these invariant sets and from the characterization of solutions in the unstable manifold of the synchronized equilibrium, we predict which (gain,delay) parameters may result in fully/partially synchronous behavior. We illustrate the approach by means of a network of delay coupled Hindmarsh-Rose neurons.

Keywords: Nonlinear Modeling of Lumped And/Or Distributed Parameter Systems, Stability, Passivity
Abstract: We consider a generic non-linear consensus model and prove convergence results to a common value together with prescribed rate of convergence. Instead of a Lyapunov approach, we consider a functional metric space and make a Fixed point theory argument using contraction mappings. We are restricted to the case of static networks.

Keywords: Variable Structure Control and Sliding Mode, Control of Sampled Data Systems
Abstract: We consider a generalized class of relay controllers where the system input may take values in a finite set of constant vectors. A simple continuous-time design method is proposed for linear time invariant (LTI) systems. Furthermore, it is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid containing the origin. The sampling intervals may be unknown and time-varying in a given interval. Simple linear matrix inequalities (LMIs) conditions are proposed for checking (local) practical stability.

Keywords: Model Based Control, Manufacturing, Applications of Observer Design
Abstract: In the ice cream industry, the type of final desired product (large cartons (sqrounds) or ice creams on a stick) determine the viscosity at which the ice cream has to be produced. One of the objectives of the ice cream crystallization processes is therefore to produce an ice cream of specified viscosity. In this paper, a nonlinear control strategy is proposed for the control of the viscosity of the ice cream in a continuous crystallizer. It has been designed on the basis of a reduced order model obtained by application of the method of moments, on a population balance equation describing the evolution of the crystal size distribution. The control strategy is based on a linearizing control law coupled with a Smith predictor to account for the measurement delay. It has been validated on a pilot plant located at IRSTEA (Antony, France).

Keywords: Input-To-State Stability, Lyapunov Methods, Small Gain Theorems
Abstract: Decomposition of a system into smaller components sometimes allows us to analyze and design the system effectively based on properties of the components. The notion of input-to-state stability (ISS) has been widely used to characterize components that refuse linear-like properties. It is, however, still restrictive, and it cannot cover a lot of saturation mechanisms which often arise in practical systems. The notion of integral input-to-state stability (iISS) is a way to remove the limitation of ISS. This paper collects and illustrates some recent advances in the framework of iISS that allows us to broaden the class of nonlinearities we can address in analysis and design of interconnected systems by making use of Lyapunov functions.

Keywords: Complex Network, Biological and Biomedical Systems, Robustness
Abstract: Control theory has been instrumental for the analysis and design of a number of engineering systems, including aerospace and transportation systems, robotics and intelligent machines, manufacturing chains, electrical, power, and information networks. In the past several years, the ability of de novo creating biomolecular systems and of measuring key physical quantities has come to a point in which quantitative analysis and design of biological networks is now possible. While a modular approach to analyze and design networked dynamical systems has proven critical in most control theory applications, it is still subject of intense debate whether a modular approach is viable in biomolecular networks. The dynamics of these networks are highly nonlinear and therefore addressing this question requires the use of tools from nonlinear control theory. In this talk, we present a theoretical framework to quantify the extent of modularity in biomolecular networks and to establish modular analysis and design techniques. Specifically, we address the fundamental question of modularity by demonstrating that impedance-like effects are found in biomolecular systems, just like in many engineering systems. These effects, which we call retroactivity, can be severe and alter the behavior of a module upon interconnection, undermining modular behavior. Leveraging nonlinear model reduction tools, we show how one can determine interconnection rules that account for retroactivity by calculating equivalent network descriptions, just like Thevenin’s theorem does for linear electrical circuits. By merging disturbance rejection and singular perturbation techniques for nonlinear systems, we further provide an approach that exploits the distinctive structure of biomolecular networks to design biomolecular insulating amplifiers. These devices buffer systems from retroactivity and restore modular behavior, allowing a bottom-up approach to creating synthetic biological circuits. We provide experimental demonstrations of our theory and illustrate concrete biological realizations of insulating amplifiers in living cells.

Keywords: Absolute Stability, Complex Network, Anti-Control and Synchronization
Abstract: The problem of synchronization (consensus) in nonlinearly coupled network is addressed. The agents of the network are assumed to identical and linear, however, they may have arbitrary order and be unstable. The interaction topology may switch and the couplings are uncertain, assumed only to satisfy conventional quadratic constraints. We offer easily verifiable synchronization criteria, based on the Kalman-Yakubovich-Popov lemma and extending a number of known result for agents with special dynamics. Those criteria are close in spirit to the celebrated circle criterion for the stability of Lurie systems.

Keywords: Anti-Control and Synchronization, Nonlinear Cooperative Control, Lyapunov Methods
Abstract: We investigate the synchronization of systems with additive uncertainties. In doing so, we establish a setup of diffusively coupled nonlinear systems that are perturbed by unknown linear functions, each. By assuming bounded solutions of the nominal uncoupled systems, we derive sufficient conditions for boundedness of the solutions of the coupled systems with uncertainties. Next, using the QUAD condition, we derive conditions for the synchronization error to remain bounded. Subsequently, we investigate the impact of the coupling strength on this bound and find that the bound can be made arbitrarily small for sufficiently large gains, thus establishing criteria for practical synchronization. Finally, we consider classes of uncertainties which consist of matrices whose maximal singular value is smaller than a specific value and show practical synchronization for all uncertainties belonging to that class. Therefore, we establish conditions for robust synchronization with respect to such a class. Our theoretical results are validated with a numerical example composed of perturbed Van der Pol oscillators.

Keywords: Lyapunov Methods, Chaos Control, Applications of Observer Design
Abstract: This work presents a new technique to securely transmit and retrieve a message signal via chaotic systems. In our system, a two-valued message signal modulates the frequency of a Duffing oscillator sinusoidal term. An observer is used in the receiver side to retrieve the sinusoidal signal that contains the message and a novel frequency estimator is then used to reproduce an approximated estimation of the message signal. The performance of the system is analyzed by means of numerical simulations performed in Matlab.

Keywords: Chaos Control, Complex Network, Bifurcation and Chaos
Abstract: In this paper, we consider the synchronization problem in networks of identical nonlinear systems with delayed couplings and external inputs. We show that the existence of external inputs can generate partial synchronization in networks and the synchronization pattern based on the notion of equitable partitions. Some illustrated examples with numerical simulation are given to verify the validity of the result obtained in this paper. The result indicates that synchronization patterns can be controlled by applying external inputs.

Keywords: Fault Detection, State Estimation and Applications, Parameter Estimation
Abstract: Outlier detection and analysis is a primary step in modelling towards obtaining unbiased estimates, model validation, and coherent analysis, because outliers may contain valuable information or lead to falsely rejecting hypotheses. In this work, we describe approaches for detecting outliers in measurements due to time-dependent and possibly non-homogeneously distributed measurement uncertainties within a set-membership setting. We propose a combinatorial outlier detection approach based on a rigorous invalidity criterion using semidefinite programming relaxations. To overcome combinatorial complexity issues, we furthermore propose a reachability-based approach to identify outlier candidates, which can be easily verified thereafter.

Keywords: Bifurcation and Chaos
Abstract: In recent years, it becomes important to understand chaotic behaviors in order to analyze nonlinear dynamics because chaotic behavior can be observed in many models in the field of physics, biology, and so on. To understand chaotic behaviors, investigating mechanisms of chaos is necessary and it is meaningful to study simple models that shows chaotic behaviors. In this paper, we propose an extremely simple triangle folding map and show that the map has k-periodic points for any integer k, and show the map has sensitivity to initial conditions. Finally, we discuss the connection with the Sierpinski gasket and construct similar types of fractal geometry.

Keywords: Model Based Control, Backstepping, Control of Mechanical, Electrical and Process Systems
Abstract: This paper presents two control approaches for a linear axis with pneumatic muscles. Its guided carriage is driven by a nonlinear drive system consisting of two pulley tackles with pneumatic muscle actuators arranged at both sides. This innovative drive concept allows for an increased workspace as well as higher carriage velocities as compared to a direct actuation. Both proposed control schemes have a cascaded structure, where the control design is based on backstepping techniques. Hysteresis in the force characteristic of the pneumatic muscles is considered by an asymmetric shifted Prandtl-Ishlinskii model, while remaining uncertainties are compensated using an adaptive backstepping strategy. The main difference between both approaches is the usage of either the internal muscle pressures or the muscle forces as controlled variables of the inner control loops. Both control approaches have been implemented on a test-rig and show an excellent closed-loop performance.

Keywords: Nonlinear Cooperative Control, Stabilization, Robotics
Abstract: With the aim of addressing the stabilization problem of periodic trajectories in systems composed of identical interconnected subsystems, we introduce the class of "spatio-temporally symmetric" nonlinear systems. We address in detail the linear, time-varying case and present conditions for the synthesis of a static and a dynamic stabilizing controller. We show that linear spatio-temporally symmetric systems can be reduced to hybrid systems, described by a periodic linear system with periodic state jumps. As an application example, we present the stabilization of a formation of unicycle robots in cyclic pursuit.

Keywords: Robotics, Mechatronic Systems, Geometric Methods
Abstract: In this paper, we propose a robotic model of casterboard, which is a commercial variant of skateboard with twistable footplates and passive inclined caster wheels.We then derive its mathematical model in the form of nonlinear state equation; this system is of much interest from both mechanical and control points of view as a new challenging example of nonholonomic mechanics. Based on the observation on preceding works concerning locomotion control for nonholonomic systems, we propose a locomotion control method with sinusoidal periodic control to realize forwarding and turning locomotion. The proposed idea is examined by simulations and physical experiments using the prototype robot developed by the authors. Moreover, we also examine the influences on the driving of the robot of parameter in the sinusoidal reference signals.

Keywords: Robotics, System Structure Identification, Hybrid Nonlinear Systems
Abstract: This paper presents the real-time identification of different types of non-holonomic mobile robot systems. Since the robot type is unknown, the robot systems are formulated as a witched singular nonlinear system, and the problem becomes the real-time identification of the switching signal, and then the existence of the input-output functions and the distinguishability of the system are studied. We show in the simulations that the technique is implemented easily and effectively, and it is robust to the noises as well.

Keywords: Variable Structure Control and Sliding Mode, Robotics, Geometric Methods
Abstract: This paper presents a novel collision avoidance approach in formation control for Multi-agent Robots. The control strategy consists in the mix of attractive vector elds and repulsive vector elds based on a scaled unstable focus centered at the position of another robot, instead of the vector elds obtained from the negative gradient of repulsive potential functions. The analysis of the closed-loop system is presented for the case of two point robots. After that, a modication of the composite vector eld is proposed adding a discontinuity in order to avoid the undesired equilibria of the system. Real-time experiments using unicycle-type robots show that the control strategy exhibits good performance.

Keywords: Stabilization, Stability, Nonlinear Cooperative Control
Abstract: Interconnection is omnipresent in a system through the state variables and induced for multi-system interaction and shared tasks. Typically, the example of multi-agent coordination was studied as an interconnected system. The paper deals with the finite-time stability problem of a general form of interconnection presented as a perturbation term. Sufficient conditions for finite-time stability are derived. A second interest is given to the interaction of multiple controlled autonomous systems, and where the multi-system control-input is established both for finite-time stabilization. As an example of application, the finite-time tracking problem of four unicycles is studied.

Keywords: Nonlinear Model Predictive Control Theory and Applications, Feasibility and Stability Issues, Stability
Abstract: In this paper we present stability conditions for nonlinear model predictive control with cyclically varying horizons. Starting from a maximum horizon length, the horizon is reduced by one at each sampling time until a minimum horizon length is reached, at which the horizon is increased to the maximum length. The approach allows to utilize shapes and structures in the terminal constraints, which can otherwise not be handled. Examples are terminal boxconstraints, where the terminal set cannot be rendered invariant, or quadratic terminal regions and penalties of diagonal structure. Such constraints are for example of advantage for distributed predictive control problems. To underline the applicability, the approach is used to control a four tank system.

Keywords: Optimal Control, Nonlinear Model Predictive Control Theory and Applications
Abstract: A dual control for a nonlinear system with non-minimum phase based on the bicriterial approach is proposed and discussed. A particular class of the nonlinear input/output recursive model is composed of linear and nonlinear blocks, the latter being implemented with a multi-layered perceptron neural network. The unknown parameters of the model are estimated in real-time by the extended Kalman filter. The chosen nonlinear model with the affine structure in inputs together with the certainty equivalence principle utilization allow to obtain an analytical solution to control based on generalised minimum variance method. Behaviour of the system based on the enforcement of the certainty equivalence can negatively be affected, especially in a presence of disturbances and functional uncertainties. For that, the control action is enhanced about dual property based on the bicriterial approach that uses two separate criteria to introduce one of the opposing aspects between estimation and control.

Keywords: Computational Efficiency, Nonlinear Model Predictive Control Theory and Applications, Optimal Control
Abstract: This paper presents a comparison of gradient computation techniques required to solve a single-shooting formulation of nonlinear model predictive control (NMPC) problems. An oil production system with network structure is considered as test instance. The structure of the network is exploited to improve computational efficiency. Exact gradient sensitivity calculation methods (forward and adjoint) are compared along with the finite difference approximation. Forward and Reverse automatic differentiation for calculating Jacobians are also compared along with the finite difference approximation counterpart. Since there is a trade off involving accuracy and speed when calculating these gradients, the best combination of tools is case dependent and it is determined by the analyses of performance indexes arising when solving specific NMPC problems. A hybrid approach combining finite difference Jacobian calculations with adjoint sensitivity calculations gave the best performance for our test problems.

Keywords: Nonlinear Model Predictive Control Theory and Applications, Hybrid Nonlinear Systems, Mechatronic Systems
Abstract: Control of dynamical systems gets considerably harder with an increasing number of control variables. Especially when the control variables are restricted to integer values, the solution is of combinatorial complexity. An example of such systems are Digital Hydraulic Drives, where several cylinders contribute to the output torque independently. In this work we present an optimal control approach for torque control of Digital Hydraulic Drives using Mixed-Integer Quadratic Programming in a Model Predictive Control framework. The nonlinear behavior and discrete valued inputs resulting from the use of on-off valves, are accommodated in the control model using a Mixed Logical Dynamical System representation. With the presented approach, optimal switching sequences for the electrical valves are computed that produce the desired torque trajectory with fast tracking and minimal ripple, while keeping switching events at a minimum and respecting physical system constraints.

Keywords: Biological and Biomedical Systems, Robustness, Nonlinear Model Predictive Control Theory and Applications
Abstract: The problem of controlling the blood glucose value of a patient suffering from type 1 diabetes is considered. The proposed strategy consists in designing a robust nonlinear model predictive controller based on a minimal nonlinear model. The various uncertainties and disturbances are introduced through the use of a variational model. The control problem is then expressed as a constrained game type minimax optimization problem. The choice of a final cost which ensures good stability properties are detailed. The performances of the controller are exemplified on a virtual testing platform showing its good properties.

Keywords: Disturbance Atténuation, Robustness, Nonlinear Model Predictive Control Theory and Applications
Abstract: In this paper, intelligent control approaches are introduced to overcome the problems highlighted in the standard Smith predictor (SP). First, in order to overcome the steady state error in the Integrator Plus Dead Time (IPDT) process control due to disturbance loading, a new fuzzy logic control based SP is developed by intentionally introducing a model mismatch to improve the system performance in terms of disturbance rejection and robustness to process modelling errors. In addition, for the First Order Plus Dead Time (FOPDT) process control, a Smith predictor based neural network control scheme is proposed to deal with the process modelling errors and proved to provide a significantly improved robustness. The neural network (NN) was designed to work with different types of modelling errors. Simulation results show that this NN approach provides excellent performance in terms of robustness to modelling errors and high adaptability to the control of both IPDT and FOPDT processes.