Kalman Yakubovich Popov Research Articles

Learning Deep Dissipative Dynamics

This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability, known to be valid across various systems including robotics, biological systems, and molecular dynamics. By analytically proving the general solution to the nonlinear Kalman–Yakubovich–Popov (KYP) lemma, which is the necessary and sufficient condition for dissipativity, we propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones and a learning method for the transformed dynamics. Utilizing the generality of dissipativity, our method strictly guarantee stability, input-output stability, and energy conservation of trained dynamical systems. Finally, we demonstrate the robustness of our method against out-of-domain input through applications to robotic arms and fluid dynamics.

Finite frequency H∞ control of discrete linear parameter-varying systems

This paper addresses the H ∞ control problem for discrete-time linear parameter-varying (LPV) systems within a specific frequency range. Using the generalized Kalman–Yakubovich–Popov (GKYP) lemma, a novel linear matrix inequality (LMI) condition is proposed, which depends on time-varying parameters. Furthermore, considering the system’s asymptotic stability and the time-domain constraints, a new H ∞ gain-scheduled state feedback controller design method is introduced. This method achieves the desired control objectives with a reduced number of LMI conditions. The proposed control method is validated through a 6-degree-of-freedom (DOF) half-car model with time-varying sprung mass. Simulation results demonstrate that the proposed control strategy is effective within the 4–8 Hz vibration frequency range, which corresponds to human sensitivity, while also ensuring compliance with actuator saturation constraints and suspension displacement time-domain limits.

Distributed Coordination D-Stabilization in Cyclic Pursuit Formations of Dynamical Multi-Agent Systems

In this study, the cyclic pursuit formation stabilization problem in target-enclosing operations by multiple homogeneous dynamic agents is investigated. To this end, a Lyapunov D-stability problem is first formulated to cover the transient performance requirements for multi-agent systems. Then, a simple diagrammatic Lyapunov D-stability criterion for cyclic pursuit formation is derived. The formation control scheme combined with a cyclic-pursuit-based distributed online path generator satisfying this condition guarantees both the required transient performance and global convergence properties with theoretical rigor. It is shown that the maximization of the connectivity gain in a cyclic-pursuit-based online path generator can be reduced to an optimization problem subject to linear matrix inequality constraints derived using the generalized Kalman-Yakubovich–Popov lemma. This approach provides a permissible range of connectivity gain, which not only guarantees global formation stability/convergence properties but also satisfies the required performance specification. Several numerical examples are provided to confirm the effectiveness of the proposed method.

Fault detection observer design for T-S fuzzy systems based on membership function-dependent mixed H−/H∞ performance in the finite-frequency domain

This paper focuses on the design of a fault detection observer for T–S fuzzy systems with faults and unknown disturbances, based on a membership function-dependent [Formula: see text] performance index. Currently, common methods for disturbance suppression and fault detection are based on traditional [Formula: see text] performance criteria. Traditional [Formula: see text] performance indices impose the same constraints on the entire system, which does not align with the characteristic that T–S fuzzy systems do not operate continuously in all linear subsystems. Therefore, aiming to improve the performance of the linear subsystems where the system operates for long periods, this paper proposes a membership function-dependent [Formula: see text] performance index and designs a fault detection observer based on this performance index. In addition, considering that the frequency of actual system faults and disturbances is not across the entire frequency domain, the design of the fault detection observer based on the membership function-dependent [Formula: see text] performance index is achieved through the generalized Kalman-–Yakubovich-–Popov lemma in a finite-frequency domain.

H−/L∞ UIO‐based fault detection and isolation design in finite‐frequency domain for nonlinear systems

AbstractThe issue of fault detection and isolation design in the finite‐frequency domain for discrete‐time Lipschitz nonlinear systems subjected to actuator faults and disturbances is investigated. A bank of H−/L∞ unknown input observers (UIOs) is established using the generalized observer scheme to generate residuals that are insensitive to a specific actuator fault but sensitive to the other actuator faults. Furthermore, in the finite‐frequency domain, the H− and L∞ performance indices are simultaneously used to improve the fault detection sensitivity and attenuate the influence of disturbances on the residuals, respectively. The design conditions for the bank of H−/L∞ UIOs are derived from the generalized Kalman–Yakubovich–Popov lemma and converted into an optimization problem constrained by linear matrix inequalities to solve the design matrices more easily. To diagnose actuator faults, a fault detection and isolation scheme is established using the time‐varying threshold from the L∞ performance analysis. Finally, the effectiveness of the fault detection and isolation scheme using the bank of H−/L∞ UIOs is validated by the simulation of two examples.

Finite frequency H ∞ control for singular systems with application to a 2-machine 6-bus power network

This paper is concerned with the H ∞ control problem for singular systems over finite frequency ranges. The disturbance is assumed to be within low-/middle-/high-frequency ranges. Both the state feedback and static output feedback controllers are designed. First, by combining the Lyapunov function method and the generalized Kalman–Yakubovich–Popov lemma, a new finite frequency bounded real lemma (BRL) is proposed, which ensures the resulting closed-loop system to be regular, impulse free and stable with given finite frequency H ∞ performance bound. It is shown by theoretical analysis and numerical simulation that the proposed BRL has less conservatism than the existing ones in the literature. With the aid of the Finsler's Lemma, two improved finite frequency BRLs are further presented for the design of controllers. Then, by utilizing convexification techniques, sufficient conditions for solving the desired state feedback and static output feedback gains are presented in terms of linear matrix inequalities, respectively. Finally, the applicability and effectiveness of the proposed control methods are verified by a 6-bus power network system.

Hybrid Nonlinear Passivity-Based Control Approach to Magnetic-Impulsive Spacecraft Attitude Regulation

This paper proposes two novel passivity-based control design frameworks for hybrid nonlinear time-varying dynamical systems involving an interacting amalgam of continuous-time and discrete-time dynamics whose dynamical properties evolve periodically over time. In this regard, the hybrid Kalman–Yakubovich–Popov conditions are employed in tandem with the passivity theorem to construct a three-step control design algorithm to render closed-loop dynamics stable. The proposed control architectures are subsequently exploited to regulate the attitude motion of spacecraft with magnetic and impulsive modes of operation. Practical considerations involved in implementing the proposed hybrid algorithms are then discussed in detail. Simulation results show significant improvement in the performance of the attitude control system in terms of system response, robustness, and the required magnetic and impulsive control usage as compared to a hybrid linear approach.

Finite-frequency fuzzy fault-tolerant static output feedback H∞ control for Diesel engine air-path system

Finite-frequency fuzzy fault-tolerant static output feedback H∞ control for Diesel engine air-path system

On discrete-time dissipative port-Hamiltonian (descriptor) systems

Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for linear, completely causal, scattering passive dynamical systems based on the system coefficients. The relation of this formulation to positive and bounded real systems and the characterization via positive semidefinite solutions of Kalman–Yakubovich–Popov inequalities is also studied.

Design of robust pre‐compensators for decoupling polytopic linear systems

SummaryThis work proposes a new approach for designing dynamic pre‐compensators to reduce interactions of multivariable uncertain square systems. The proposed method is based on the minimization of the norm of the difference between the compensated system and a diagonal reference model. The main appeal of the technique is to propose a systematic procedure to obtain the reference model dynamics, in contrast to methods that use the identity matrix as a reference, and to obtain diagonal dominance in a frequency range of interest employing the generalized Kalman‐Yakubovich‐Popov (KYP) Lemma. The design conditions are expressed as linear matrix inequalities (LMI) thanks to a new general parametrization on the decision variables in bilinear products to reduce the conservatism of the solutions compared to standard approaches from the literature. Numerical examples verify the robustness of the proposed method, showing significant decoupling of the uncertain plant.

H ∞ negative imaginary static output feedback controller for low frequency networked control systems

In this paper, an H ∞ negative imaginary static output feedback (SOF) controller is designed for a low frequency (LF) networked control system (NCS) with time-delays. A difference operator is introduced to deal with the time-delays in a feedback configuration via integral quadratic constraints (IQCs). Both H ∞ performance and negative imaginariness are analysed via LF IQCs and a generalised Kalman–Yakubovich–Popov (GKYP) lemma. A two-stage algorithm is presented to obtain the H ∞ negative imaginary SOF controller for the LF NCS with time-delays. Simulation results are given to show the effectiveness and superiority of the H ∞ negative imaginary SOF controller.

Passivity‐based control design frameworks for hybrid nonlinear time‐varying dynamical systems

AbstractThis article proposes two novel passivity‐based control design frameworks for hybrid nonlinear dynamical systems involving an interacting mixture of continuous‐time and discrete‐time dynamics whose dynamical properties evolve periodically over time. By deriving the Kalman–Yakubovich–Popov (KYP) conditions characterizing dissipativeness for hybrid nonlinear time‐dependent dynamical systems, a hybrid computational algorithm, which alternates between continuous‐time and discrete‐time subsystems at an appropriate sequence of time instants, is then proposed to solve the resultant equations in an interacting manner. Two passivity‐based control schemes are then developed by utilizing the foregoing KYP conditions in tandem with the passivity theorem. The overall framework consists mainly of three steps. The hybrid output dynamics of the plant are first determined judiciously to satisfy the passivity specifications. A hybrid nonlinear controller is then designed to meet the input strict passivity requirements. The stability of the closed‐loop system is finally established by interconnecting the plant and the controller through negative feedback. Practical considerations for appropriately implementing the derived hybrid algorithms are then discussed in detail. The efficacy of the proposed control schemes is ultimately assessed via a multi‐dimensional system with a hybrid source of actuation.

Finite Frequency H∞ Control for Doubly Fed Induction Generators with Input Delay and Gain Disturbance

Due to the rapid development of wind power, the stable operation of doubly fed induction generators (DFIGs) has attracted much attention. This paper focuses on the finite frequency (FF) H∞ control for the DFIG with input delay, aiming to reduce the effects of current harmonic interferences and gain disturbances on the DFIG and improve the stability of the system. First, a DFIG state–space model with input delay under current harmonics was constructed. Second, based on the DFIG state–space model, an FF H∞ state-feedback controller was designed from the frequency domain perspective, which makes the DFIG stable and robust against harmonic interferences and gain disturbances. Third, via the generalized Kalman–Yakubovich–Popov (GKYP) lemma and the Lyapunov theory, the FF H∞ performance was evaluated in the form of linear matrix inequalities (LMIs), and then the state feedback FF H∞ controller was designed. Finally, the simulation results showed the efficiency of the proposed approach.

Fault detection in wind turbine transmission systems via finite frequency observers

AbstractThis paper addresses fault detection for wind turbine transmission system (WTTS) subject to actuator stuck faults and wind disturbances. Taking into account the frequency domain characteristics of such faults and disturbances, a modified observer is designed in terms of finite frequency (FF) performance indices that have detection performances superior to some formerly proposed ones. With the generalized Kalman–Yakubovich–Popov (GKYP) lemma and the Lyapunov theory, the FF performance indices are related to linear matrix inequalities (LMIs), and parametrization of the corresponding FF modified observer is completed by convex optimization under LMI constraints. One typical advantage of the modified observer is that fault and disturbance signals in distinctive FF domains can be dealt with simultaneously. This makes the residual system sensitive to actuator stuck faults and robust against external wind disturbances. Simulations are included to show that the design method achieves fault detection performances better than those of the entire frequency observers.

Vehicle Actuator Fault Detection With Finite-Frequency Specifications via Takagi-Sugeno Fuzzy Observers: Theory and Experiments

This article presents a new nonlinear observer-based method to detect the faults of both steering and torque actuators of autonomous ground vehicles. To this end, the nonlinear vehicle system is reformulated in a Takagi-Sugeno (TS) fuzzy model with both measured and unmeasured nonlinear consequents, called N-TS fuzzy model. Differently from the classical TS fuzzy technique with linear consequents, this N-TS fuzzy reformulation enables an effective use of differential mean value theorem to deal with unmeasured nonlinearities, which is known as a major challenge in TS fuzzy observer design. Moreover, the N-TS fuzzy form also allows reducing not only the design conservatism but also the numerical complexity of the design conditions as well as the observer structure, which is crucial for real-time vehicle application. To minimize the disturbance effect with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_\infty$</tex-math></inline-formula> performance and maximize the fault sensibility with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-$</tex-math></inline-formula> performance, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information on the disturbance/fault frequency ranges is taken into account in the N-TS fuzzy observer design via the generalized Kalman–Yakubovich–Popov (KYP) lemma. Based on Lyapunov stability theory, the design of the proposed multiobjective <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathscr {H}_-/\mathscr {H}_\infty$</tex-math></inline-formula> N-TS fuzzy fault detector is recast as an optimization problem with strict linear matrix inequality (LMI) constraints, which can be effectively solved with numerical solvers. Both numerical and experiments are performed under realistic driving conditions to demonstrate the theoretical and practical interests of the new finite-frequency fuzzy fault detection method.

Improving Vibration Performance of Electric Vehicles Based on In-Wheel Motor-Active Suspension System via Robust Finite Frequency Control

This paper presents a robust finite frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> control strategy for improving vibration performance and ride comfort of electric vehicles through in-wheel motor-active suspension system(IWM-ASS). Since the human body is much sensitive to the vertical vibration of 4 -8 Hz, the main objective is dedicated to deal with the vibration challenge that matches the characteristics of the human body by applying the finite-frequency technique. Firstly, the uncertain quarter-vehicle active suspension model with dynamic damping in-wheel motor driven system is established, in which in-wheel motor is suspended as dynamic vibration absorber(DVA) to isolate the force transmitted to motor bearing in IWM-ASS. Based on the framework of generalized Kalman–Yakubovich–Popov lemma and stability theory, then the performance index of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> norm from external disturbance to controlled output for IWM-ASS is attenuated within the concerned frequency range while other system requirements such as parameter uncertainty, suspension deflection constraint and actuator saturation are also guaranteed in controller design. The resulting robust finite frequency state feedback <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H} _{\infty }$ </tex-math></inline-formula> controller is finally designed utilizing two new theorems, and solved via a set of linear matrix inequalities. Simulations for frequency-domain and time-domain responses are implemented and compared with the entire frequency control method to evaluate the effectiveness of the proposed strategy. It can be concluded from the results that the developed control strategy can effectively attenuate the negative vibration and enhance ride comfort and road-holding ability for electric vehicles of IWM-ASS.

Multi-Objective Finite-Frequency H ∞/GH 2 Static Output-Feedback Control Synthesis for Full-Vehicle Active Suspension Systems: A Metaheuristic Optimization Approach

In this paper, the problem of multi-objective control for active suspension systems with polytopic uncertainty is addressed via <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GH</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> static output feedback with a limited-frequency characteristic. For the overall analysis of the performance demanding both vehicle-ride comfort related to vertical- and transversal-directional dynamics and the time-domain constraints related to the driving maneuverability, a seven-degree-of-freedom full-vehicle model with an active suspension system is investigated. The robust static output-feedback control strategy is adopted because some state variables may not be directly measured in a realistic implementation. In designing this control, the finite-frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance using the generalized Kalman—Yakubovich—Popov lemma is optimized to improve the passenger’s ride comfort, while the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GH</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance is optimized to guarantee the constraints concerning the suspension deflection limitation, road-holding ability, and actuator saturation problem. This control synthesis problem is formulated as nonconvex bilinear matrix inequalities and requires simultaneous consideration of different finite-frequency domain ranges for vertical and transversal motions for evaluating the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. These design difficulties are overcome by the proposed multi-objective quantum-behaved particle swarm optimizer, which efficiently explores the relevant trade-offs between the considered multiple performance objectives and eventually provides the desired Pareto-optimal control set. Further, the numerical simulation cases of a full-vehicle active suspension system are presented to illustrate the effectiveness of the proposed control synthesis methodology in frequency and time domains.

Finite-frequency fixed-order dynamic output-feedback control via a homogeneous polynomially parameter-dependent technique

Finite-frequency fixed-order dynamic output-feedback control via a homogeneous polynomially parameter-dependent technique

Stability analysis and stabilisation of continuous-discrete fractional-order 2D Fornasini–Marchesini first model

This paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem solvable, based on the property of Kronecker product and the Generalized–Kalman–Yakubovich–Popov Lemma, the new sufficient and necessary stability conditions are established in the form of linear matrix inequalities. Thirdly, with the help of the Projection Lemma, the stabilisation conditions are obtained after introducing a state feedback controller, which can be solved with an iterative linear matrix inequality algorithm. In the end, the effectiveness of the proposed results is verified by two numerical examples.

Kalman–Yakubovich–Popov: Do We Need a New Proof? [From the Editor

Kalman–Yakubovich–Popov (KYP). The very historical heritage of our field is at war. Do we need a new proof?