Keywords: Networked Nonlinear Systems

Keywords: Control and analysis of Nonlinear Systems
Abstract: We present a new high-gain feedback control design ensuring finite-time input-to-state stabilization of chains of integrators of dimension n subject to additive disturbances. The proposed high-gain homogeneous controller involves only control gains of power limited to 2 regardless of the dimension of the chains of integrators in contrast to the classical high-gain controllers involving gains with powers up to n+1 which grows with the growth of the chain of integrators. The stability analysis of the closed-loop system is achieved by means of classical Lyapunov-based tools and homogeneity-based concepts. This result can be seen as the dual design of low-power high-gain observers recently extended to the homogeneous context.

Keywords: Control and analysis of Nonlinear Systems
Abstract: We consider the model-following control (MFC) scheme for a class of nonlinear minimumphase systems in Byrnes-Isidori form using the nonlinear model in the model control loop (MCL). For the control design we apply partial state feedback in the process control loop (PCL). In particular we consider a high-gain feedback of the external state in the PCL to stabilise the system globally. For the proposed MFC design the typical peaking phenomenon of the high-gain feedback can be overcome if a sufficiently accurate estimate of the initial process state is available. We further establish that the control effort of the proposed MFC design is guaranteed less than that of a comparable stabilising high-gain design using a single-loop feedback only. We demonstrate the design capability of peaking attenuation by a numerical example.

Keywords: Control and analysis of Nonlinear Systems, Stability and Complex Dynamics, Control of Networks
Abstract: Asymptotically null controllable with bounded controls (ANCBC) is a crucial prerequisite for ensuring the global performance of saturated systems. This paper addresses the challenges inherent in multi-input multi-output systems with actuator saturation, focusing on achieving global stabilization within the ANCBC framework and managing non-uniform saturation characteristics. To this end, we propose a nonlinear control algorithm that utilizes a redesigned saturation function with a dynamic saturation level, which self-adjusts based on a first-order differential strategy. This approach effectively mitigates non-uniform saturation across dimensions by appropriately selecting both constant and time-varying parameters within the differential equation related to the dynamic saturation level. Finally, numerical simulations are provided to validate the theoretical results.

Keywords: Control of Nonlinear Systems
Abstract: Using a new set of semidefinite constraints called recurrent dissipativity-based inequalities, this letter presents an iterative procedure to design polynomial feedback control laws for polynomial nonlinear systems, let it be a static state feedback or a linear static output feedback (SOF) controller one needs to determine. In addition to that, the problem of linear SOF design for linear time-invariant (LTI) systems is solved as well. In the case of polynomial systems, we use sum-of-squares (SOS) programming for controller design and to provide an estimate of the closed-loop domain of attraction. In the case of LTI models, a set of linear matrix inequalities (LMIs) is employed in an iterative strategy to determine a stabilizing gain. Numerical simulations on a few examples borrowed from literature are provided in order to emphasize the advantages of our new dissipativity-based control (DBC) method.

Keywords: Control and analysis of Nonlinear Systems, Nonlinear Systems with Time Delay, Stability and Complex Dynamics
Abstract: We consider a bilinear control system defined by a linear time-invariant system of differential equations with both lumped and distributed delay in the state variable. We study the arbitrary finite spectrum assignment problem. One needs to construct a control vector such that the characteristic function of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of bilinear systems with delay are obtained.

Keywords: Adaptive Control and Signal Processing for Nonlinear Systems, Switching Control, Systems Biology
Abstract: In this study, an original model-free stabilizing extremum seeking (STAB-ESC) strategy is applied to optimize yeast fed-batch culture productivity. To this end, the ethanol concentration is tracked at a low level, to approach the yeast growth optimal conditions. Overflow metabolism effects, resulting from the cell’s limited respiratory capacity, are considered using a macroscopic model with discontinuous kinetics. The detrimental impact of input saturation on the proposed STAB-ESC stability is overcome using a state-dependent switching control strategy. The resulting methodology is illustrated with numerical results where the robustness of the controller to measurement noise is also highlighted.

Keywords: Nonlinear Model Predictive Control, Control of Nonlinear Systems
Abstract: This paper addresses the formation path tracking for a heterogeneous system made up of a steering car and a quadcopter. System modelling is based on Nonlinear Model Predictive Control (NMPC), which is a proper solution when considering a heterogeneous fleet as not only it deals with non-linearities of the dynamic model but it is also a way to generate trajectories that can be communicated to other agents. Moreover, an Extended Kalman Filter (EKF) is employed to estimate the non-measurable ground robot state variables. Two separate simulations in Simulink for each agent have been carried out leading to promising results in terms of tracking errors. Indeed, tests show that the proposed solution allows the two vehicles to follow the reference aligned with a deviation of a few centimeters.

Keywords: Control of Nonlinear Systems, Transportation
Abstract: In this article, we are interested in the hybrid electric vehicle torque split and gear shift problem, which can be formulated as a classical Lagrange optimal control problem with fixed initial condition. The Pontryagin maximum principle gives necessary optimality conditions adjoining to the state a covector called costate. Thus, the optimal state trajectory has to be found among the projections of the lifted trajectories, called Pontryagin extremals, given by the maximum principle. The indirect simple shooting method aims to compute Pontryagin extremals reducing the resolution to the research of the initial costate. Classically, a Newtonlike solver is used to compute zeros of the so-called shooting equations. The main drawback of this method is its sensitivity to the initial guess. Indeed, a good one needs to be given to make the Newton solver converge, which is not an easy task in practice. We propose a preconditioning method of the shooting function based on a geometrical interpretation of the costate, in relation with the reachable set of the extended system and the underlying symplectic structure. We numerically show that this method reduces the number of iterations of our solver. Remarkably, in our experiments, it is better to use the preconditioner than a clever initial guess for the Newton solver.

Keywords: Networked Nonlinear Systems, Control and analysis of Nonlinear Systems, Control of Networks
Abstract: This paper addresses the distributed formation control problem of networked robot manipulators in end-effector coordinates. We propose a distributed bipartite formation controller that guarantees collision avoidance and maximum distance maintenance for cooperative and competitive manipulators' end-effectors. In the considered setting, two groups of manipulators are formed and reach bipartite consensus. On the other hand, the end-effectors in the same group achieve formation. We design a gradient-based control law using barrier-Lyapunov functions to ensure that the constraints on the end-effectors are satisfied. Moreover, we establish asymptotic stability of the bipartite formation manifold. Finally, we illustrate our theoretical results via numerical simulations.

Keywords: Modeling and Identification of Nonlinear Systems, Mechatronics and Robotics, Machine Learning
Abstract: Data-driven surrogate models of dynamical systems based on the extended dynamic mode decomposition are nowadays well-established and widely applied. Further, for non-holonomic systems exhibiting a multiplicative coupling between states and controls, the usage of bilinear surrogate models has proven beneficial. However, an analysis of the approximation quality and its dependence on different hyperparameters, including physics-motivated dictionary choices, with real-world experimental data is still missing. To close this gap and due to its high practical relevance and widespread usage in applications such as service robotics, we investigate Koopman-based surrogate modeling for a differential-drive mobile robot, also in hardware.

Keywords: Control of Nonlinear Systems, Mechatronics and Robotics, Navigation and Guidance
Abstract: Design of circular path following controllers is considered for a 4 wheeled robot with steering angle saturation. First, we use a line-of-sight (LOS) guidance algorithm to derive a tracking error dynamics. Then we design controllers from a tracking error dynamics of the attitude of the robot. In this case the closed-loop error dynamics given by the designed controllers is of a nonlinear cascade form with the disturbance input induced by steering angle saturation. Then we show that the closed-loop system is integral input-to-state stable (iISS) from the disturbance to the state. Finally, we show the effectiveness of the designed controllers by simulation and experimental results.

Keywords: Control and analysis of Nonlinear Systems, Aerospace Control Systems
Abstract: This paper proposes the study of a tailsitter, delta-wing, convertible aircraft that combines the advantages of vertical take-off and landing (VTOL) and fixed-wing aircraft. Control during the transition between VTOL and horizontal flight, as well as the design of fault detection and isolation (FDI) algorithms should be considered to ensure safe operation. The main contribution of the paper is in the analysis of the flatness property of the convertible aircraft. Flat systems have the property that their inputs and states can be written as functions of a set of variables called flat outputs and their derivatives. Thus, an inverse dynamic model can be obtained which can be used to design path planning, nonlinear feedforward control, and FDI algorithms. First, the analysis of flatness in the horizontal flight is presented. Then, it is shown that this first set of flat outputs is singular at hover flight. However, this is only an apparent singularity as a second set of flat outputs can be obtained, which defines a chart of the aircraft’s dynamical model at hover and slow aerodynamic speed.

Keywords: Control of Nonlinear Systems, Disturbance Rejection
Abstract: This paper deals with the problem of designing an output feedback controller for the class of linear systems interconnected with a nonlinearity satisfying a monotonicity assumption. The control design objective is to ensure the incremental exponential stability of the closed loop. First, a set of sufficient conditions by relying on a design based on Linear Matrix Inequalities (LMIs) are proposed. The results are then expanded to include in the design a filter to cancel additional (unwanted) harmonics of the steady-state solution. The proposed results are validated via a simplified example of application.

Keywords: Control of Networks, Control of Bifurcations, Oscillations and Chaos, Networked Nonlinear Systems
Abstract: In remote estimation of cyber-physical systems, the sensor measurement transmitted through network may be attacked by adversaries, leading to leakage risk of privacy (e.g., the system state), and/or failure of the remote estimator. To deal with this problem, a chaotic masking protocol is proposed in this paper to secure the sensor measurement transmission. In detail, at the plant side, a chaotic dynamic system is deployed to encode the sensor measurement, and at the estimator side, an estimator estimates both states of the physical plant and the chaotic system. This protocol can deal with multiple types of attacks, i.e., eavesdropping attack, replay attack, and stealthy false data injection attack.

Keywords: Control and analysis of Nonlinear Systems
Abstract: Output regulation for non-minimum phase nonlinear systems is still a largely open problem, with only a few results in the literature covering a few specific cases. This paper explores the design of a state-feedback regulator for a basic non-minimum phase benchmark system that, nevertheless, already embodies many of the challenges and difficulties linked to the lack of minimum phase. Although the developed solution only provides local regulation guarantees for this specific benchmark, it nonetheless suggests a path for the successive development of a systematic regulation theory for non-minimum phase systems in normal form. In turn, this paper is a first step in such a direction.

Keywords: Modeling and Identification of Nonlinear Systems, Disturbance Rejection, Navigation and Guidance
Abstract: We tackle the analysis of a nonlinear navigation filter used in Magneto-Inertial Dead-Reckoning (MIDR) whose input data are provided by a home-made device. This filter takes the measurements given by the magnetic sensors as inputs and returns the velocity of the body. Therefore, any unmodeled time-varying disturbance in the measurements impacts the estimation of the velocity and yields errors that distort the estimation. For dimensioning purpose, we aim to identify the bandwidth of the linearized part of this filter. To derive a model of this bandwidth, we first simplify our filter as a time-invariant Single-Input Single-Ouput (SISO) system in the situation where the steady-state regime is reached. The Best Linear Approximation (BLA) of this nonlinear system can be described by a conventional transfer function. We justify the validity of of such a linear approximation for Extended Kalman Filters (EKF) and identify it with different methods, yielding a model for the bandwidth depending on the experimental conditions of navigation. We prove that our filter is actually suitable for pedestrian navigation. Finally, simulations in realistic physical situations are used for validation.

Keywords: Navigation and Guidance, Machine Learning
Abstract: Velocity estimation of a rigid body using measurements from low-cost inertial and magnetic sensors plays an important role in various applications. The extended Kalman filter (EKF) is widely used for this purpose. However, EKF's estimation performance relies on the knowledge of process and measurement noise covariance matrices, and this information is generally unavailable. In this work, we introduce a solution that combines two techniques: the generation of velocity pseudo-measurements using a Bidirectional Long Short-Term Memory (BiLSTM) network, and the Q-learning method for online adaptation of noise covariance matrices. The performance of the proposed solution is validated using real experimental datasets, demonstrating that Q-learning can select appropriate noise covariance matrices to enhance velocity estimation.

Keywords: Control of Nonlinear Systems, Switching Control
Abstract: In this study, we propose a design method for a locally semiconcave practical control Lyapunov function (LS-PCLF) for global asymptotic stabilization. The proposed method focuses on a cascade system that is interconnected by state in a differentiable manifold. To design an LS-PCLF, we once lift the system to an étale space of the state space. In general, the lifted system has multiple equilibrium points that correspond to a desired equilibrium point of the original system. By assigning a virtual input to one of the equilibrium points, we can employ an LS-PCLF design method analogous to backstepping. A numerical example demonstrates the effectiveness of the proposed method.

Keywords: Control and analysis of Nonlinear Systems, Nonlinear Systems with Time Delay, Control with Limited Information
Abstract: We revisit the forwarding approach for the feedback stabilization of discrete-time systems in feedforward form. We show that the resulting feedback design is parametrized by a change of coordinate which is defined via a Sylvester equation. Moreover, we investigate the optimality of such a feedback by explicitly computing a quadratic cost which is minimized by the closed loop trajectories. Finally, we apply the forwarding approach to solve the problem of global stabilization of feedforward form systems which are simply stable in the presence of input saturations. The proposed approach is also shown to be effective in tackling the stabilization of systems with input saturation and time-delays.

Keywords: Control and analysis of Nonlinear Systems, Mechatronics and Robotics, Disturbance Rejection
Abstract: Safe trajectory tracking, which follows the target trajectory while avoiding obstacles is crucial for mobile robots. In this paper, we propose an robust safety trajectory tracking　controller with respect to disturbances. To achieve obstacle avoidance in the presence of disturbances, we design a safety assist input based on the input-to-state constrained safety control barrier function (ISCSf-CBF). We combine the designed assist input with a disturbance-attenuation trajectory　tracking controller based on the input-to-state stable　tracking control Lyapunov function (ISS-TCLF). The　effectiveness of the proposed controller is confirmed by numerical simulations.

Keywords: Adaptive Control and Signal Processing for Nonlinear Systems, Switching Control, Control of Bifurcations, Oscillations and Chaos
Abstract: Power-based output feedback compensator for oscillatory systems is proposed. The average input-output power of an oscillatory signal serves as an equivalent control effort, while the unknown amplitude and frequency of oscillations are detected at each half-period. This makes the compensator adaptive and discrete, while the measured oscillatory output is the single available signal in use. The resulting discrete control scheme enables a drastic reduction of communication efforts in the control loop. The compensator is designed for 2nd order systems, while an extension to higher-order dynamics, like e.g. in case of two-inertia systems, is also provided. Illustrative experimental case study of the 5th order oscillatory system is provided.

Keywords: Nonlinear Model Predictive Control, Power and Energy Control, Control and analysis of Distributed Systems
Abstract: Modular multilevel converters (MMCs) are novel voltage source converters (VSCs) with the capacity to achieve higher efficiency and lower total harmonics distortion, but more challenging to control. MMCs can be modeled using a hierarchical structure comprising a model predictive controller (MPC) that controls the current in the top layer and sends signals to capacitor voltage modules in the lower layer (which can run in open-loop or closed-loop with a simple local controller). Typically, the prediction model used in the MPC current controller does not take into account the capacitor voltage dynamics in the lower layer, which reduces the efficiency of the hierarchical control scheme and MMC circuit. Therefore, in this paper we develop an extended prediction model for current control that includes the capacitor voltage dynamics for the modules in the lower layer. This results in a nonlinear MPC control problem of higher complexity, but with improved performance. To reduce the complexity of the nonlinear MPC problem for MMCs we make use of a linear parameter varying embedding of the nonlinear prediction model, which allows solving a sequence of quadratic programs online, instead of a nonlinear program. The proposed control scheme shows better performance while decreasing the computation load. Furthermore, compared to classical hierarchical control schemes, the proposed control scheme reduces in 20% the capacitor voltage ripple.

Keywords: Power and Energy Control, Control and analysis of Nonlinear Systems
Abstract: In this work the problem of regulation of the Root Mean Square (RMS) value of the current for Series Resonant Converter (SRC) is addressed. The self-oscillating behavior is ensured by an amplitude modulation like control law and the RMS value is estimated with a proposed hybrid system. The closed-loop regulation is done with a Proportional-Integral PI controller with anti-windup scheme, and a set of Linear Matrix Inequalities (LMIs) is introduced to tune the gains. The knowledge of a reference trajectory is not needed to implement the controller, and it is shown to be effective in simulation considering uncertain parameters.

Keywords: Control and analysis of Nonlinear Systems