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In this article, we propose a new method to ob-tain feedback controllers of an unknown dynamical systemdirectly from noisy input/state data. The key ingredient ofour design is a new matrix S-lemma that will be proven inthis article. We provide both strict and nonstrict versionsof this S-lemma, which are of interest in their own right.Thereafter, we will apply these results to data-driven con-trol. In particular, we will derive nonconservative designmethods for quadratic stabilization, H2 and H∞ control, allin terms of data-based linear matrix inequalities. In contrastto previous work, the dimensions of our decision variablesare independent of the time horizon of the experiment. Ourapproach, thus, enables control design from large datasets.

This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples. This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. PID2020-114244RB-I00). This work has also been partially funded by AGAUR of Generalitat de Catalunya, Spain through the Advanced Control Systems (SAC) group grant (2017 SGR 482) and by the University of Stavanger, Norway through the project IN-12267. A. Ruiz is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, Spain, the European Social Fund (ESF) and AGAUR under a FI SDUR grant (ref. 2020 FI-SDUR 00097).

The integrated energy system (IES) is the physical carrier of the Energy Internet, whose optimal operation has become a hot topic because of its effectiveness in improving energy utilization efficiency. This paper proposes an optimal operation model of integrated energy system, where the internal energy flow transmission characteristic of the heating network is modeled as virtual heating energy storage by the node method to enhance the operating flexibility of IES. The second-order cone relaxation method and the incremental formulation for the piecewise linearization method are utilized to transform the proposed nonlinear model into mixed integer quadratic constraint programming model, which can be effectively solved by the commercial solver. Case studies show that the proposed model effectively reduces the operating costs and improves the renewable energy penetration level of IES.

This paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reciprocally convex quadratic terms, we provide an improved reciprocally convex combination inequality (RCCI), which includes some existing ones as its particular cases. We construct an eligible stochastic Lyapunov–Krasovskii functional to capture more information about TDs, triggering signals, and MJPs. Based on a well-designed event-triggered control scheme, we derive several novel stability criteria for the underlying systems by employing the new RCCI and other analytical techniques. Finally, we present two numerical examples to show the validity of our methods.

International audience; Adaptive control using the -modification provides an easily implementable way to stabilize systems with uncertain or fluctuating parameters. Motivated by a specific application from neuroscience, we extend here this methodology to nonlinear time-delay systems ruled by globally Lipschitz dynamics. In order to make the result more handy in practice, we provide an explicit construction of a Lyapunov–Krasovskii functional (LKF) with linear bounds and strict dissipation rate based on the knowledge of an LKF with quadratic bounds and point-wise dissipation rate. When applied to a model of neuronal populations involved in Parkinson’s disease, the benefits with respect to a pure proportional stabilization scheme are discussed through numerical simulations.

International audience; This paper addresses the design of a sampled-data model predictive control (MPC) strategy for linear parameter-varying (LPV) systems. A continuous-time prediction model, which takes into account that the samples are not necessarily periodic and that plant parameters continuously vary with time, is considered. Moreover, it is explicitly assumed that the value of the parameters used to compute the optimal control sequence is measured only at the sampling instants. The MPC approach proposed by Kothare et al. [1], where the basic idea consists in solving an infinite horizon guaranteed cost control problem at each sampling time using linear matrix inequalities (LMI) based formulations, is adopted. In this context, conditions for computing a sampled-data stabilizing LPV control law that provides a guaranteed cost for a quadratic performance criterion under input saturation are derived. These conditions are obtained from a parameter-dependent looped-functional and a parameter-dependent generalized sector condition. A strategy that consists in solving convex optimization problems in a receding horizon policy is therefore proposed. It is shown that the proposed strategy guarantees the feasibility of the optimization problem at each step and leads to the asymptotic stability of the origin. The conservatism reduction provided by the proposed results, with respect to similar ones in the literature, is illustrated through numerical examples.

Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system's continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation., 6 pages, 1 figure, submitted to IEEE L-CSS / CDC 2021

This paper studies the performance of a feedback control loop closed via an error-free digital communication channel with transmission delay. The system comprises a discrete-time noisy linear time-invariant (LTI) plant whose single measurement output is mapped into its single control input by a causal, but otherwise arbitrary, coding and control scheme. We consider a single-input multiple-output (SIMO) channel between the encoder-controller and the decoder-controller which is lossless and imposes random time delay. We derive a lower bound on the minimum average feedback data rate that guarantees achieving a certain level of average quadratic performance over all possible realizations of the random delay. For the special case of a constant channel delay, we obtain an upper bound by proposing linear source-coding schemes that attain desired performance levels with rates that are at most 1.254 bits per sample greater than the lower bound. We supplement our results with a numerical experiment demonstrating that the obtained bounds and operational rates are increasing functions of the constant delay.

An optimal fuzzy controller design scheme is proposed to address the influence of time delay and disturbance on the control performance of nonlinear batch processes. First, a two-dimensional (2D) equivalent Takagi-Suguno (T-S) fuzzy error model is formulated. By introducing a quadratic performance index function and adopting 2D Lyapunov-Krasovskii theory, the existence condition of the optimal fuzzy control law is given. Furthermore, its solvable condition, which depends on time-delay bounds, is constructed in terms of linear matrix inequalities, and its gain is obtained by using an optimization algorithm. This design has the advantages of faster tracking and better tracking performance. Finally, two different algorithms (with and without optimization) are used to control the water level of a triple-capacity water tank. The results show that the presented strategy is more effective and feasible.

In this paper, we consider networked control systems under Denial-of-Service (DoS) attacks. The control objective is to synthesize a quantized controller in which the quantizer is as coarse as possible for a networked control system subject to DoS attacks, while still guaranteeing (quadratic) stability. Our main result will explicitly show the trade-offs between system robustness against DoS and quantizer coarseness. A simulation example will demonstrate the strengths of the new method.

Global quadratic stabilization in probability is considered for both switched linear certain stochastic systems and switched linear uncertain stochastic systems where there are norm bounded uncertainties. Under the assumption that every single subsystem is NOT globally quadratically stable in probability (GQS-P), we propose both static and dynamic output based switching laws such that the switched system on hand is GQS-P. In the case of static output based switching, the condition is expressed by a set of matrix inequalities, while the design of dynamic output based switching is proposed with a convex combination of subsystems and a robust Luenberger observer for each subsystem. Numerical examples are presented to show validity of the design conditions and switching algorithms.

This paper proposes a gradient extremum seeking method to address locally quadratic static maps in the presence of time-varying delays. Accommodating nonconstant delays has a strong impact in the predictor construction in terms of the associated transport partial differential equation (PDE) with variable convection speeds beyond the restrictions imposed on the delay regarding its arbitrary duration but bounded variation. A novel predictor design using perturbation-based estimates of the unknown Gradient and Hessian of the map must be introduced to handle this variable nature of the delays, which can arise both in the input and output channels of the nonlinear map to be optimized. Local exponential stability and convergence to a small neighborhood of the unknown extremum point are guaranteed. This technical result is assured by using backstepping transformation and averaging theory in infinite dimensions. Implementation aspects of the presented predictor for variable delays as well as the extension to state-dependent delays are also discussed. At last, we introduce the first results in the topic of extremum seeking control for cascades of transport PDEs that are interconnected through boundary conditions. Such a PDE-PDE cascade is useful to represent simultaneous time- and state-dependent delays. A simulation example illustrates the effectiveness of the proposed predictor-based extremum seeking approach for time-delay compensation.

This paper presents the development of an indirect adaptive state-feedback controller to improve the disturbance-rejection capability of under-actuated multivariable systems. The ubiquitous Linear-Quadratic-Regulator (LQR) is employed as the baseline state-feedback controller. Despite its optimality, the LQR lacks robustness against parametric uncertainties. Hence, the main contribution of this paper is to devise and retrofit the LQR with a stable online gain-adjustment mechanism that dynamically adjusts the state weighting-coefficients of LQR's quadratic cost-function via state-error dependent nonlinear-scaling functions. An original self-mutating phase-based adaptive modulation scheme is systematically formulated in this paper to self-adjust the state weighting-coefficients. The scheme employs pre-calibrated secant-hyperbolic-functions whose waveforms are dynamically reconfigured online based on the variations in magnitude and polarity of state-error variables. This augmentation dynamically alters the solution of the Riccati-Equation which modifies the state-feedback gains online. The proposed adaptation flexibly manipulates the system's control effort as the response converges to or diverges from the reference. The efficacy of proposed adaptive controller is validated by conducting hardware-in-the-loop experiments to vertically stabilize the QNET 2.0 Rotary Pendulum system. As compared to the standard LQR, the proposed adaptive controller renders rapid transits in system's response with improved damping against oscillations, while maintaining its asymptotic-stability, under bounded exogenous disturbances.

In this paper, a new optimal robust adaptive fuzzy controller is proposed for stabilization of the inverted pendulum (IP) system as a non-linear under-actuated quadratic dynamic model. To reach this goal, a fuzzy controller (FC) is utilized to generate a proper control effort to stabilize the system via a product inference engine, a singleton fuzzifier and a centre average defuzzifier. Since the IP is an under-actuated system, the decoupled sliding mode structure is utilized to find a general sliding surface and produce the adaptive laws based on the gradient descent method. The existing constant coefficients in the suggested control system are optimized by the multi-objective particle swarm optimization algorithm with regard to conflicting objective functions. The performance of the proposed strategy is compared with those of other controllers introduced in literature. The results demonstrate that the time integral of the absolute value of errors for the designed optimal robust adaptive fuzzy controller is much lower in comparison with those obtained by the other methods.

International audience; We investigate discrete-time closed-loop dynamics consisting of a linear plant, a linear controller and a wireless network that connects the sensors and the actuators to the control unit. The objective, and the main contribution of this work, is the static output feedback control synthesis under given network specifications. Precisely, the network features are formulated in terms of stochastic allowable transmission interval (SATI) which is a concept well-suited for the time-triggered control of wireless network control systems (WNCS). Given SATI parameters, we provide sufficient conditions in terms of linear matrix inequalities (LMIs) under which we can design a static output feedback controller that stabilizes the closed-loop WNCS in mean-square sense. Moreover, we guarantee that a quadratic control cost is less than a given bound. Consequently, the results can be used to ensure not only stability but also desired control performances for the WNCS and its SATI characteristics.

Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function, (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.

This study outlines the set of equations constituting the necessary conditions that should be solved to determine the optimal guidance command for a missile to intercept a stationary target along a desired impact direction at a prespecified final time. Unlike the earlier studies on nonlinear optimal guidance problems, the present study formalises the optimal control problem with both final time and final state fixed. The pure control effort quadratic norm is considered as the performance index to be minimised. A noticeable finding from the study of the necessary conditions is that the flight path angle of the optimal trajectory obeys the simple pendulum dynamics. Full characterisation of the exact optimal solution requires numerically solving a set of four nonlinear algebraic equations with respect to four unknowns.

In this paper, a simplest fractional-order hyperchaotic (SFOH) system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system, which possesses seven terms without any quadratic or higher-order polynomials. The numerical solution of the SFOH system is investigated based on the Adomian decomposition method (ADM). The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics. Dynamics of this system are demonstrated by means of phase portraits, bifurcation diagrams, Lyapunov exponent spectrum (LEs) and Poincaré section. The results show that the system has a wide chaotic range with order change, and large Lyapunov exponent when the order is very small, which indicates that the system has a good application prospect. Besides, the parameter a is a partial amplitude controller for the SFOH system. Finally, the system is successfully implemented by digital signal processor (DSP). It lays a foundation for the application of the SFOH system. Keywords: Chaos, Fractional calculus, Simplest fractional-order hyperchaotic system, Adomian decomposition method DSP implementation

With the high speed, the rotor of magnetically suspended permanent magnet synchronous motor (MSPMSM) suffers great thermal stress and mechanical stress resulting from the temperature rise problem caused by rotor losses, which leads to instability and inefficiency. In this paper, the mechanical–temperature field coupling analysis is conducted to analyze the relationship between the temperature field and structure, and multi-objective optimization of a rotor is performed to improve the design reliability and efficiency. Firstly, the temperature field is calculated by the 2D finite element model of MSPMSM and the method of applying the 2D temperature result to the 3D finite element model of the motor rotor equivalently is proposed. Then the thermal–structure coupling analysis is processed through mathematic method and finite element method (FEM), in which the 3D finite element model is established precisely in a way and approaches the practical operation state further. Moreover, the impact produced by the temperature and structure on the mechanical strength is analyzed in detail. Finally, the optimization mathematical model of the motor rotor is established with Sequential Quadratic Programming-NLPQL selected in the optimization scheme. Through optimization, the strength of the components in the motor rotor increases obviously and satisfies the design requirement, which to a great extend enhances the service life of the MSPMSM rotor. Keywords: FEM, MSPMSM, Multi-objective optimization, Thermal stress, Thermal–structure coupling analysis

In this paper, a fault severity estimation method is presented for high-resistance connection (HRC) in a permanent magnet synchronous machine drive system, being dependent upon the zero sequence voltage component (ZSVC) and stator currents. According to the relationship between the stator current, ZSVC and resistance deviations, a bivariate quadratic equation group is established with regard to the resistance deviations caused by HRC. The resistance deviations are obtained by solving the equation group. Based on the obtained resistance deviations, not only the fault is diagnosed and the faulty phase is identified, but also the HRC fault severity is estimated. Both the simulation and experiment are studied to validate the fault severity estimation method. The results verify the effectiveness and robustness of the proposed fault severity estimation method.

To avoid disrepair and over-repair and improve gas turbine reliability and availability, gas-path diagnosis is an effective technical means of disseminating early warning information for evolving or impending deterioration. Aiming at the problems of existing gas-path diagnosis methods (i.e., data-driven based gas-path diagnosis and a model-based gas-path diagnosis), this paper proposes a novel gas-path diagnosis method based on model-data hybrid drive, which is a forward solving mathematical process, to ensure real-time monitoring performance. Through case analysis, the proposed diagnostic method is not limited by the intrinsic nonlinear shape change of the characteristic maps of the actual component, which has good diagnostic applicability. And after the quadratic feature extraction of the two-dimensional entropy features (i.e., Shannon entropy and exponential entropy features), it is convenient to obtain visualized gas turbine gas-path diagnosis results for the operation and maintenance personnel. Moreover, although the extracted two-dimensional entropy values will change slightly when the operating conditions change, it can maintain good inter-class separation and intra-class aggregation performance.

This paper aims at providing two competitive solutions to the problem of estimating state as well as sensor and actuator faults. The development starts with a common system description, which is transformed into a nonlinear descriptor system-like form. The appealing property of such an approach is that the sensor fault is eliminated from the output equation by suitably extending the state vector. Subsequently, a novel fault estimation scheme is proposed and its error dynamics are carefully described. Having such a unified framework, two competitive design procedures are proposed. One is based on the celebrated $\mathcal {H}_{\infty }$ while the other employs the quadratic boundedness strategy. With the estimators, the paper provides a unified framework for assessing the uncertainty of the resulting estimates in the form of uncertainty intervals. Thus, both solutions can be compared from the theoretical perspective. The final part of the paper contains a numerical simulation example concerning a twin-rotor system that clearly shows the comparison and performance of the above approaches. Subsequently, an experimental study concerning a multi-tank system using real data is reported.

In this paper, an inverse optimal control problem of multi-agent systems is investigated based on partial stability and structured Lyapunov matrix. Agents with general linear dynamics are considered. The communication graph of the agents is assumed to be undirected and fixed. A cooperative optimal control protocol is designed to guarantee consensus based on static output feedback. It is demonstrated that, given the stabilizing static output feedback control input, a performance index function can be found such that the control input is optimal. A structured quadratic performance index is derived that is related to the topology of the communication graph. It allows for global optimal control that is implemented using the proposed distributed consensus protocol.

The application of modern control methods to automated driving of following vehicles on a highway can make the advanced transportation systems much more safe and efficient. This paper focuses on a computational approach to optimal control and stability analysis of the adjacent vehicles following in a single traffic lane of a highway in order to ensure the functional safety and assistance of automated driving systems. These vehicles are entirely automated as they have the ability to follow a line path at a high speed and reduce the distance that separates them while adjusting their responses automatically without intervention from humans (i.e. drivers). To meet such requirements for driving safety, this paper explores a new approach to string stability of following vehicles that travel in a straight line of a highway, using optimal control and Lyapunov stability theories. Consequently, sufficient conditions for string stability of a vehicle traffic using continuous-time Lyapunov function and matrix Riccati equation are presented. The search for a quadratic Lyapunov function is then formulated as a convex optimisation problem in terms of a linear invariant system towards a quadratic optimal criterion. The analysis of these methods for minimising the performance criterion is also given. Finally, the paper ends with a conclusion and perspective for future work.

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works This paper addresses the problem of replay attack detection in autonomous vehicles. Due to the strong presence of nonlinearities, traditional approaches based on linear approximations of the dynamics would not work effectively. For this reason, the proposed approach is based on a bank of quadratic parameter varying (QPV) observers, designed in such a way that each observer is insensitive to a replay attack that affects one specific sensor channel. This feature allows the development of a decision algorithm, whose effectiveness is validated by means of simulation results. This work was partially supported by the University of Stavanger through the project IN-12267. This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the projects SCAV (ref. MINECO DPI2017-88403-R) and DEOCS (ref. MINECO DPI2016-76493), and also by AGAUR ACCIO RIS3CAT UTILITIES 4.0 – P7 SECUTIL.

Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global stability, passivity property, and convergence time and accuracy are demonstrated. Also the control saturation case is explicitly analyzed. The suggested nonlinear damping is denoted as optimal since requiring no design additional parameters and ensuring a fast convergence, without transient overshoots for a non-saturated and one transient overshoot for a saturated control configuration., Comment: 7 figures

In practical model predictive control (MPC) implementations, constraints on the states are typically softened to ensure feasibility despite unmodeled disturbances. In this work, we propose a soft constrained MPC formulation supporting polytopic terminal sets in half-space and vertex representation, which significantly increases the feasible set while maintaining asymptotic stability in case of constraint violations. The proposed formulation allows for leveraging system trajectories that violate state constraints to iteratively improve the MPC controller’s performance. To this end, we apply convex optimization techniques to obtain a data-driven terminal cost and set, which result in a quadratic MPC problem. ISSN:2475-1456

This paper investigates the state feedback stabilization problem for a class of impulsive linear time-varying systems over specified time intervals and piecewise quadratic domains (PQDs). First, concepts related to finite-time stability and PQDs are given. Second, finite-time stability analysis over PQDs is implemented, and a variety of stability conditions involving differential linear matrix inequalities are investigated. Then, computationally tractable stability conditions are established for the control design. Finally, an illustrative example is presented to show the effectiveness of the designed state feedback control.

International audience; This paper deals with a control strategy for a DC-DC quadratic boost converter. In particular, a hybrid control scheme is proposed to encompass a control law and an observer for the estimation of the system states, based only on the measurements of the input and output voltages. Differently from classical control methods, where the controller is designed from a small-signal model, here the real model of the system is examined without considering the average values of the discrete variables. Using hybrid dynamical system theory, asymptotic stability of a neighborhood of the equilibrium point is established, ensuring practical stability of the origin, which contains estimation and tracking errors. Experimental results show the effectiveness of the proposed approach.

Operation and maintenance cost of wind turbine is intimately related to fatigue damage. However, considering fatigue directly in an optimization needs to be carefully done because its faithful model does not fit standard forms. Recent results have shown that the fatigue damage of a signal estimated using fatigue theory is non-linearly related to its corresponding variance. Therefore, this relationship is used to design a convex cost function approximating fatigue. In this paper, the sensitivity of open-loop optimizations using this fatigue-oriented non-quadratic cost function to the time horizon considered is studied, in terms of both fatigue and computational cost. Moreover, in order to alleviate the undesirable effects of the computational cost, an efficient fixed-point iteration-based way to optimize this fatigue-oriented cost function is presented. Results show that the fatigue-oriented cost function allows to obtain sensitive fatigue reduction compared to optimizations using a family of classical quadratic cost functions, especially for long optimization horizons. It is eventually, shown that the prediction horizon length required for the non-quadratic criterion to be efficient in an MPC makes its use prohibitive in such framework. However, prospects of reaping the benefits of the fatigue-oriented optimization using imitation learning are given.

In this paper, an improved recurrent neural network (RNN) scheme is proposed to perform the trajectory control of redundant robot manipulators using remote center of motion (RCM) constraints. Firstly, learning by demonstration is implemented to model the surgical operation skills in the Cartesian space. After that, considering the kinematic constraints associated with the optimization control of redundant manipulators, we propose a novel RNN-based approach to facilitate accurate task tracking based on the general quadratic performance index, which includes managing the constraints on RCM joint angle, and joint velocity, simultaneously. The results of the conducted theoretical analysis confirm that the RCM constraint has been established successfully, and accordingly. The corresponding end-effector tracking errors asymptotically converge to zero. Finally, demonstration experiments are conducted in a laboratory setup environment using KUKA LWR4+ to validate the effectiveness of the proposed control strategy.

Motivated by applications of multi-agent learning in noisy environments, this paper studies the robustness of gradient-based learning dynamics with respect to disturbances. While disturbances injected along a coordinate corresponding to any individual player's actions can always affect the overall learning dynamics, a subset of players can be disturbance decoupled---i.e., such players' actions are completely unaffected by the injected disturbance. We provide necessary and sufficient conditions to guarantee this property for games with quadratic cost functions, which encompass quadratic one-shot continuous games, finite-horizon linear quadratic (LQ) dynamic games, and bilinear games. Specifically, disturbance decoupling is characterized by both algebraic and graph-theoretic conditions on the learning dynamics, the latter is obtained by constructing a game graph based on gradients of players' costs. For LQ games, we show that disturbance decoupling imposes constraints on the controllable and unobservable subspaces of players. For two player bilinear games, we show that disturbance decoupling within a player's action coordinates imposes constraints on the payoff matrices. Illustrative numerical examples are provided.

International audience; This paper proposes a method to analyze, beyond stability, the performances of linear time-delay systems. Using robust analysis techniques, a sufficient condition that analyzes the location of eigenvalues in the complex plane is presented. More precisely, a set of quadratic inequality constraints are designed to define an admissible region for the infinitely many eigenvalues of a time-delay system and the quadratic separation theorem is applied to assess that the eigenvalues are effectively belonging to that stability region. This method is then used for the control of an active mass damper. A standard state feedback control is replaced with a static output feedback plus a static delayed output feedback. This strategy avoids the full measurement of the state and shows that delays in the dynamic may be helpful for stabilization. The closed-loop system is then expressed as a time-delay system and the performance criterion is exploited to analyze the stability and the damping properties. Simulations and experimental tests support the approach.

The paper is devoted to the problem of estimating simultaneously states, as well as actuator and sensor faults for Takagi&ndash, Sugeno systems. The proposed scheme is intended to cope with multiple sensor and actuator faults. To achieve such a goal, the original Takagi&ndash, Sugeno system is transformed into a descriptor one containing all state and fault variables within an extended state vector. Moreover, to facilitate the overall design procedure an auxiliary fault vector is introduced. In comparison to the approaches proposed in the literature, a usual restrictive assumption concerning fixed fault rate of change is removed. Finally, the robust convergence of the whole observer is guaranteed by the so-called quadratic boundedness approach which assumes that process and measurement uncertainties are unknown but bounded within an ellipsoid. The last part of the paper portrays an exemplary application concerning a nonlinear twin-rotor system.

We present a novel method of optimal robust control through quadratic programs that offers tracking stability while subject to input and state-based constraints as well as safety-critical constraints for nonlinear dynamical robotic systems in the presence of model uncertainty. The proposed method formulates robust control Lyapunov and barrier functions to provide guarantees of stability and safety in the presence of model uncertainty. We evaluate our proposed control design on dynamic walking of a five-link planar bipedal robot subject to contact force constraints as well as safety-critical precise foot placements on stepping stones, all while subject to model uncertainty. We conduct preliminary experimental validation of the proposed controller on a rectilinear spring-cart system under different types of model uncertainty and perturbations.

In this manuscript, we consider the finite-time H &infin, control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H &infin, controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H &infin, state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

International audience; This brief investigates a new consensus control methodology for nonlinear one-sided Lipschitz (OSL) multi-agents by considering the input saturation nonlinearity for each agent. Local design approaches are followed for dealing with the constrained consensus control of nonlinear agents by using the OSL dynamics, saturation nonlinearity, and quadratic inner-boundedness property. A region of initial conditions based on the consensus error is revealed, for which the proposed control approach guarantees the consensus error's convergence to the origin. A new design condition for computation of the consensus protocol gain is developed for the leader-following consensus. Then, simulation results on synchronization of mobile OSL are provided by considering input saturation.

This chapter aims to investigate the effectiveness of the nonlinear control-based model and the sampled-data design through the power system application. In particular, the study will focus on a model of a wind turbine system fed by a doubly fed induction generator (DFIG). First of all, a detail dynamical model of a DFIG-based wind-turbine grid-connected system is presented in the direct and quadratic synchronous reference frame. Afterward, mathematical modeling is performed for the nonlinear and sampled data systems. The nonlinear control will ensure the reproduction of the rotor direct and quadratic current that converge to the reference signal generated from. The proposed sampled-data system is built upon the nonlinear model and is introduced as an alternative of the classical discrete control which is known as emulation design. The simulation's results will show that implementing the approximate feedback will yield better results than the one obtained from the mere emulation.

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H &infin, design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method merges dissipation inequalities and integral quadratic constraints (IQCs) with both hard and soft IQC factorizations. Computational algorithms are presented using the generalized S-procedure and sum-of-squares techniques. The use of IQCs in backward reachability analysis allows for a variety of perturbations including parametric uncertainty, unmodeled dynamics, nonlinearities, and uncertain time delays. The method is demonstrated on two examples, including a 6-state quadrotor with actuator uncertainties., Submitted to L-CSS

In this paper, the Q-learning method for quadratic optimal control problem of discrete-time linear systems is reconsidered. The theoretical results prove that the quadratic optimal controller cannot be solved directly due to the linear correlation of the data sets. The following corollaries have been made: (1) The correlation of data is the key factor in the success for the calculation of quadratic optimal control laws by Q-learning method, (2) The control laws for linear systems cannot be derived directly by the existing Q-learning method, (3) For nonlinear systems, there are some doubts about the data independence of current method. Therefore, it is necessary to discuss the probability of the controllers established by the existing Q-learning method. To solve this problem, based on the ridge regression, an improved model-free Q-learning quadratic optimal control method for discrete-time linear systems is proposed in this paper. Therefore, the computation process can be implemented correctly, and the effective controller can be solved. The simulation results show that the proposed method can not only overcome the problem caused by the data correlation, but also derive proper control laws for discrete-time linear systems.

Recently, policy optimization for control purposes has received renewed attention due to the increasing interest in reinforcement learning. In this paper, we investigate the convergence of policy optimization for quadratic control of Markovian jump linear systems (MJLS). First, we study the optimization landscape of direct policy optimization for MJLS, and, in particular, show that despite the non-convexity of the resultant problem the unique stationary point is the global optimal solution. Next, we prove that the Gauss-Newton method and the natural policy gradient method converge to the optimal state feedback controller for MJLS at a linear rate if initialized at a controller which stabilizes the closed-loop dynamics in the mean square sense. We propose a novel Lyapunov argument to fix a key stability issue in the convergence proof. Finally, we present a numerical example to support our theory. Our work brings new insights for understanding the performance of policy learning methods on controlling unknown MJLS., Accepted to ACC 2020

Move blocking (MB) is a widely used strategy to reduce the degrees of freedom (DoFs) of the optimal control problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretisation steps. In this study, the authors focus on developing computationally efficient MB schemes for multiple shooting-based non-linear model predictive control (NMPC). The DoFs of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretisation accuracy and level of sparsity are maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretisation nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the non-uniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimisation accuracy and constraints fulfilment is shown by means of simulations with two different problems.

In this paper, a model reference control strategy is proposed in order to perform trajectory tracking in Takagi–Sugeno–Lipschitz (TSL) systems. Since the state vector is assumed not to be completely available for measurement, a proportional observer is added to the control scheme in order to apply an estimate-feedback control action instead of a state-feedback one. The overall design of both the controller and the observer gains are performed using a Lyapunov-based quadratic boundedness specification, in order to improve the robustness against unknown exogenous disturbances. It is shown that the conditions that ensure convergence within ellipsoidal regions of the tracking and estimation errors can be expressed in the form of a linear matrix inequality (LMI) formulation. The effectiveness of the developed control strategy is demonstrated by means of simulation results.

This paper proposes a nonlinear unit root test based on the autoregressive neural network process for testing unemployment hysteresis. In this new unit root testing framework, the linear, quadratic and cubic components of the neural network process are used to capture the nonlinearity in a given time series data. The theoretical properties of the test are developed, while the size and the power properties are examined in a Monte Carlo simulation study. Various empirical applications with unemployment and inflation rates across a number of countries are carried out at the end of the article. pre-print 437 KB

Today's semi-autonomous vehicles are gradually moving towards full autonomy. This transition requires developing effective control algorithms for handing complex autonomous tasks. Driving as a group of vehicles, referred to as a convoy, on automated highways is a highly important and challenging task that autonomous driving systems must deal with. This paper considers the control problem of a vehicle convoy modeled with linear dynamics. The convoy formation requirement is presented in terms of a quadratic performance index to minimize The convoy formation control is formulated as a receding horizon linear-quadratic (LQ) optimal control problem. The receding horizon control law is innovatively defined via the solution to the algebraic Riccati equation. The solution matrix and therefore the receding horizon control law are obtained in the closed-form. A control architecture consisting of four algorithms is proposed to handle formation size/shape switching. The closed-form control law is at the core of these algorithms. Simulation results are provided to justify the models, solutions, and proposed algorithms. Web of Science 33 11 2180 2174

In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example.

Persistently excited nonlinear time-varying systems are considered in this paper. Two new quadratic, time-varying, Lyapunov functions are presented, whose time-varying matrices—solutions to suitable linear time-varying matrix differential equations—are causal (nonanticipating) and, thus, differently from related results in the literature, available at runtime. They allow for directly addressing and successfully achieving further adaptation goals, when uncertain parameters affect the system dynamics.

This paper investigates the nonlinear vehicle platoon control problems with external disturbances. The quadratic spacing policy (QSP) is applied into the platoon control, in which the desired intervehicle distance is a quadratic function in terms of the vehicle’s velocities. Comparing with the general constant time headway policy (CTHP), the QSP is more suitable to the human driving behaviors (HDB) and can improve the traffic capacity. Then, a novel platoon control scheme is proposed based on the distributed integrated sliding mode (DISM). Since the external disturbances are taken into consideration, the sliding mode method is employed to handle the disturbances. Moreover, the stability and string stability of the proposed platoon control system are strictly analyzed. In final, numerical simulations are provided to verify the proposed approaches.

In this paper, an MPC solution is devised for linear time-periodic optimal regulation problems requiring the minimization of a sum of vector norms. Such type of problems arise for instance in aerospace applications, in which it is desired to trade-off fuel consumption and state regulation performance, while limiting as much as possible the control activation time. Closed-loop stability is guaranteed by embedding in the design a terminal set and a terminal cost, both of which are periodically time-varying. Differently from quadratic MPC, the terminal cost is in the form of a weighted 2-norm. A systematic method to construct such a function is presented. The proposed design is demonstrated on a spacecraft rendezvous case study with periodic dynamics.