Entire State Vector Research Articles

Adaptive Parameter Identification for a Class of Neural Mass Models with Application to Ergatic Systems

This paper considers one of the problems that arise in the developing of the ergatic brain-computer interfaces. This technology allows a person to control various mechatronic systems through the "power of thought", i.e. based on the registration of electrical activity of the brain. The problem is the complexity and poor knowledge of the brain. To describe the electrical activity of the brain, various models of neural ensembles are used, one of which is the neural mass model proposed by Jansen and Rit in 1995. To tune the parameters of this model according to real data, it is proposed to use an adaptive parameter identifier. An important condition for the synthesis of an adaptive identifier is that only the system output, which is the potential difference between two points of the head, can be measured. At the beginning, it is assumed that the entire state vector of the neural mass model is available for measurement. An identifier is synthesized to tune the parameters of such a system and its convergence is proved using the Lyapunov function method. Further, the obtained identifier is refined in such a way that it uses only the output of the system. To do this, using the finite difference method, the output derivative of the neural mass model is approximately calculated, which is used to make several replacements of the unknown components of the state vector. It is very difficult to analytically prove the convergence of the obtained adaptive parameter identifier, therefore, the possibility of using it to estimate the parameters of a neural mass model is checked using simulation. The synthesized identifier uses only the system output to tune the parameters, which in the future will allow us to consider real data instead of the system output. Thus, this identifier can be used to tune the parameters of the neural mass model based on real data.

Nonlinear optimal control of a multi-rotor wind power unit with PMSGs and AC/DC converters)

A nonlinear optimal (H-infinity) control method is developed for a wind power unit that comprises twin turbines, permanent magnet synchronous generators (PMSGs) and AC/DC converters. By proving differential flatness properties for this system the associated setpoints definition problem is solved. The dynamic model of the wind power unit being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearisation around a temporary operating point that is recomputed at each time-step of the control method. The linearisation relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearised state-space model of the wind power unit, a stabilising optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the wind power unit under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the wind power unit, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator.

Nonlinear optimal control for the rotary double inverted pendulum

AbstractThe control problem of the rotary double inverted pendulum (double Furuta pendulum) is nontrivial because of underactuation and strong nonlinearities in the associated state‐space model. The system has three degrees of freedom (one actuated and two unactuated joints) while receiving only one control input. In this article, a novel nonlinear optimal (H‐infinity) control approach is developed for the dynamic model of the rotary double inverted pendulum. First, the dynamic model of the double pendulum undergoes approximate linearization with the use of first‐order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a temporary operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. At a next stage a stabilizing H‐infinity feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation has to be solved at each time‐step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. To implement state estimation‐based control without the need to measure the entire state vector of the rotary double‐pendulum the H‐infinity Kalman filter is used as a robust state observer. The nonlinear optimal control method achieves fast and accurate tracking of setpoints by all state variables of the rotary double inverted pendulum under moderate variations of the control input.

Nonlinear optimal control for a gas compressor driven by an induction motor

The article proposes a nonlinear optimal control approach for the dynamic model of a gas centrifugal compressor being driven by an induction motor (IM). The dynamic model of the integrated compressor-induction motor system, being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the compressor-IM a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the compressor-IM under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the compressor-IM, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator. The differential flatness properties of the compressor-IM system are proven. The article’s method provides one of the few algorithmically simple and computationally efficient solutions for the nonlinear optimal control problem of the compressor-IM system.

Parametric design method for partial eigenstructure assignment of second-order linear systems via observer-based state feedback

In this article, a parametric method of observer-based partial eigenstrunt in second-order linear time-invariant (LTI) systems is explored. First, an observer is constructed to approximate the full sate vector when the entire state vector is not available for measurement. Meanwhile, the separation principle of the first-order linear systems is extended to second-order linear systems. Second, by partitioning the system matrix of the open-loop system into two parts, the satisfactory and unsatisfactory eigenstructures are selected. On the premise of retaining the satisfactory part in the open-loop system, the unsatisfactory eigenstructure assignment problem can be converted into the solutions of a type of generalized Sylvester equations (GSE). Third, by introducing a group of arbitrary parameters, complete parametric expressions of the proportional plus derivative (PD) state feedback controller can be obtained. The main advantage of the proposed method is that it provides all the design degrees of freedom and reduces the design complexity of the controller. Finally, the correctness of the proposed method is verified by two examples and simulation results. Using the degrees of freedom of the parameters, the gain matrices are optimized through the optimization index provided by the optimization function, and better performance is obtained.

Nonlinear Optimal Control for the Nine-Phase Permanent Magnet Synchronous Motor

Abstract Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They exhibit advantages comparing to three-phase motors because of achieving high power and torque rates under moderate variations of voltage and currents in their phases, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine-phase PMSM undergoes an approximate linearization process at each sampling instance. The linearisation procedure is based on first-order Taylor-series expansion and on the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion is satisfied, which signifies robustness of the control scheme against model uncertainty and perturbations. Moreover, under mild assumptions it is also proven that the control loop is globally asymptotically stable. Additionally it is experimentally confirmed through simulation tests, that the nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to apply state estimation-based control without the need to measure the entire state vector of the nine-phase PMSM, the H-infinity Kalman Filter is used as a robust state estimator.

Nonclassical properties of a deformed atom-cavity field state

We analyse here a nonclassical state produced by an atom-cavity field interaction. The two-level atom is passed through the single-mode electromagnetic cavity field. By deforming the field operators and introducing nonlinearity to the classic Jaynes–Cummings model, we explore the system in respect of a nonlinear Hamiltonian. Assuming that the atom is in an excited state and the field is in a coherent state initially, the analytic expression for the state vector of the entire system state vector is obtained. With the help of the derived state vector, we calculate the photon number distribution, Mandel's parameter, Wigner function, anti-bunching, squeezing properties and Q function etc.

A parametric design method of observer‐based state feedback controller for quasi‐linear systems

This paper designs an observer-based feedback controller for quasi-linear systems when the entire state vector is unavailable for measurement. First, based on the solution of a type of generalised Sylvester equations, general complete parameterisation of the full-order observer is proposed. Second, the traditional separation principle is applied to the quasi-linear systems. In other words, the design of a state feedback and the design of a state observer can be carried out independently. Further, general complete parameterisation of the state feedback controller is also established. Finally, numerical examples and simulations are adopted to verify the effectiveness of the proposed method.

ИДЕНТИФИКАЦИЯ ДЕФЕКТОВ В ПРИВОДАХ НА ОСНОВЕ МЕТОДОВ ОПТИМАЛЬНОГО УПРАВЛЕНИЯ

The paper exams the problem of identifying faults in the drives of robotic systems, the dynamicsmodel of which is described by linear differential equations. It is proposed to search for asolution to the fault identification problem based on the solution of an auxiliary optimal controlproblem for a dynamical system in which the role of an unknown vector function describingemerging faults is performed by some auxiliary control, which should provide a minimum for theresidual functional. Based on the solution of the auxiliary optimal control problem, a fault diagnosticobserver is proposed. In this case, the fault itself is found through the solution of the correspondingalgebraic Riccati equation and the differential equation for the auxiliary variable. Unlikepopular approaches to solving the problem of fault identification based on observers operatingin a sliding mode, the proposed method allows us to expand the class of systems for which theidentification problem can be solved. It is known that the methods of sliding mode observers designimpose certain restrictions on the systems under consideration. The proposed approach basedon optimal control can also give results for systems with nonlinear dynamics. In this case, methodsof approximate solution of optimal control problems based on the representation of the system inlinear form with state-dependent coefficients (the so-called State-dependent Riccati Equation,SDRE) are likely to be effective. The improvement of the proposed method in this direction will bethe subject of further research. The stated theory is shown on the example of fault identification ina DC drive. Different cases are considered for a system with complete observations (the entirestate vector is known) and with incomplete observations. It was shown during the simulation thatthe quality of faults identification can be improved by selecting the appropriate values of the penaltymatrices in the residual functional, while it is possible to achieve good diagnostics separatelythrough various channels of faults occurrence. The paper presents recommendations on the choiceof penalty matrices. The simulation results confirmed the operability of the diagnostic observerssynthesized using the proposed method.

A nonlinear optimal control approach for shipboard AC/DC microgrids

Shipboard AC/DC microgrids are used for power supply and electric propulsion in vessels. An indicative form of such a microgrid comprises diesel engines or gas turbines that provide power for the rotation of synchronous or asynchronous generators. Next, the AC output voltage of the generators is turned into DC voltage with the use of AC to DC converters and is distributed through DC voltage buses to the ship’s compartments. Besides, with the use of DC to AC inverters voltage excitation is provided to synchronous or asynchronous motors which can be used in turn for the vessel’s propulsion. The dynamic model of the considered shipboard AC/DC microgrid, being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the shipboard AC/DC microgrid a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the AC/DC microgrid under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the shipboard AC/DC microgrid, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator. The article’s method provides one of the few algorithmically simple and computationally efficient solutions for the nonlinear optimal control problem of shipboard microgrids.

Nonlinear optimal control for a five-link parallel robotic manipulator

Control and stabilization of parallel robotic manipulators is a non-trivial problem because of nonlinearities and the multi-variable structure. In this article, a nonlinear optimal control approach is proposed for the dynamic model of such robotic systems, using as a case-study the model of a five-link parallel robot. The dynamic model of the parallel robotic manipulator undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands as a solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the parallel robotic manipulator, the H-infinity Kalman filter is used as a robust state estimator. Among the advantages of this control method, one can note that (i) unlike the popular computed-torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs and (ii) it achieves fast and accurate tracking of reference set points under minimal energy consumption by the robot’s actuators.

Nonlinear Optimal Control for the Translational Oscillator with Rotational Actuator

In this article, the problem of nonlinear optimal (H-infinity) control for a translational oscillator with rotating actuator (TORA) system is treated. The dynamic model of a translational oscillator with rotational actuator is generated through Euler-Lagrange analysis. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the TORA the H-infinity Kalman Filter is used as a robust state estimator.

Synchronization of the Electric Power Network in the Conditions of High-Frequency Measurement Noises

The problem of robust synchronization of the electrical power network with unknown parameters is considered in the present paper. The load angles of each generator with superimposed additive high frequency noises are available for measurement. An algorithm has been synthesized to reduce the influence of noises on measurement signals and to ensure synchronization of the network in normal mode and in emergency situations associated with a sudden change in the conuctivity of power lines. To synthesize the control algorithm, the new approach is used which makes it possible to independently control the quality of noise filtering and the quality of the stabilization error of the output variable. The conditions guaranteeing the stability of the system are obtained. The simulation results have shown that the designed control system of a network of electric generators, when only noisy indications of load angles are available for measurement, provides better transient quality indicators compared to schemes of R. Ortega (France) and D. Hill (Australia), where the entire state vector is available to measurements and the parameters of the generator model are partially known. Modeling also showed that the proposed algorithm ensures the stability of a closed-loop system if there are unmodeled dynamics in network model. We also note that under conditions of random measurement noises, the control goal cannot be guaranteed due to the unlimited nature of the noises, however, the simulation results illustrate the satisfactory quality of transients with nonzero random signals in noises.

Distributed Adaptive Consensus of Nonlinear Heterogeneous Agents With Delayed and Sampled Neighbor Measurements.

In this article, the adaptive output consensus problem of high-order nonlinear heterogeneous agents is addressed using only delayed, sampled neighbor output measurements. A class of auxiliary variables is introduced which are n -times differentiable functions and include the agent's output along with delayed, sampled output neighbor measurements. It is proven that if these variables are bounded and regulated to zero then asymptotic consensus among all agent outputs is ensured. In view of this property, an adaptive distributed backstepping design procedure is presented that guarantees boundedness and regulation of the proposed variables. This design procedure ensures not only the desired asymptotic output consensus but also the uniform boundedness of all closed-loop variables. The main feature of our approach is that, in the proposed control law for each agent, the entire state vector of the neighbors is not needed and only delayed sampled measurements of the neighbors' outputs are utilized. The simulation results are also presented that verify our theoretical analysis.

Implementation of a partially decentralized control architecture using wireless active sensors

This paper deals with the development of a vibration control architecture in which many stand-alone active dampers are involved. Each device is able to independently perform the control task, since it is embedded with sensors, an inertial actuator and a microcontroller, in which the control algorithm is implemented. The aim of this architecture is to improve the performance of a decentralized control strategy through a partial sharing of data between devices. The proposed control solution is based on the optimal control theory; the Linear Quadratic Regulator works with the full-state of the system, which is not available in many applications. In order to provide the entire state vector, state estimation is implemented in each device. A state recovery algorithm is adopted to improve the quality of the estimation without placing a hefty burden on the wireless channel. Numerical analysis is made in order to study the advantages of this method. Finally, the proposed solution is validated with experimental results from a clamped–clamped beam.

Stability conditions for infinite networks of nonlinear systems and their application for stabilization

We introduce a new concept of ℓ∞-input-to-state stability for infinite networks composed of a countable set of interconnected nonlinear subsystems of ordinary differential equations. We suppose that the entire state vector is an element of ℓ∞ and each subsystem is input-to-state stable whereas the dimension of its entire disturbance input including possible interconnections with other subsystems is finite. Our first main result provides conditions for ℓ∞-input-to-state stability of such infinite-dimensional networks. In our second main result, we solve the problem of decentralized ℓ∞-ISS stabilization for such networks composed of interconnected lower-triangular form subsystems with uncontrollable linearization. To apply our first main result and obtain the second one, we construct a feedback for each individual agent, which satisfies our new stability conditions. This yields the stabilization of the entire network. Our design is also new for finite networks and this can be considered as an important special case.

Validation of OCO-2 error analysis using simulated retrievals

Abstract. Characterization of errors and sensitivity in remotely sensed observations of greenhouse gases is necessary for their use in estimating regional-scale fluxes. We analyze 15 orbits of the simulated Orbiting Carbon Observatory-2 (OCO-2) with the Atmospheric Carbon Observations from Space (ACOS) retrieval, which utilizes an optimal estimation approach, to compare predicted versus actual errors in the retrieved CO2 state. We find that the nonlinearity in the retrieval system results in XCO2 errors of ∼0.9 ppm. The predicted measurement error (resulting from radiance measurement error), about 0.2 ppm, is accurate, and an upper bound on the smoothing error (resulting from imperfect sensitivity) is not more than 0.3 ppm greater than predicted. However, the predicted XCO2 interferent error (resulting from jointly retrieved parameters) is a factor of 4 larger than predicted. This results from some interferent parameter errors that are larger than predicted, as well as some interferent parameter errors that are more strongly correlated with XCO2 error than predicted by linear error estimation. Variations in the magnitude of CO2 Jacobians at different retrieved states, which vary similarly for the upper and lower partial columns, could explain the higher interferent errors. A related finding is that the error correlation within the CO2 profiles is less negative than predicted and that reducing the magnitude of the negative correlation between the upper and lower partial columns from −0.9 to −0.5 results in agreement between the predicted and actual XCO2 error. We additionally study how the postprocessing bias correction affects errors. The bias-corrected results found in the operational OCO-2 Lite product consist of linear modification of XCO2 based on specific retrieved values, such as the CO2 grad del (δ∇CO2), (“grad del” is a measure of the change in the profile shape versus the prior) and dP (the retrieved surface pressure minus the prior). We find similar linear relationships between XCO2 error and dP or δ∇CO2 but see a very complex pattern of errors throughout the entire state vector. Possibilities for mitigating biases are proposed, though additional study is needed.

Nonlinear optimal control for DC industrial microgrids

ABSTRACTDC industrial microgrids can assure uninterrupted and free-of-perturbations power supply to industrial units. Besides the solution of the related optimal control problem can result in minimisation of electric power consumption by such units. In this article, the problem of nonlinear optimal (H-infinity) control for industrial microgrids is treated. The dynamic model of an indicative microgrid that comprises photovoltaic units, batteries and supercapacitors is considered. This model undergoes approximate linearisation around a temporary operating point that is recomputed at each time-step of the control method. The linearisation relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearised state-space model of the system, a stabilising optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the DC microgrid the H-infinity Kalman Filter is used as a robust state estimator.

Robust Functional Interval Observer for Multivariable Linear Systems

The study of a continuous-time multivariable linear system may not need the knowledge of the entire internal state vector, but only of a linear function of it. In this case, instead of designing a complete observer, only a functional (also called reduced order) observer is used. In this field of research, this paper focuses on robust functional cooperative interval observers. Such an observer is proposed and its properties (in particular, its convergence) are established. Then, a design procedure is given for practical use. Finally, the theoretical contributions are illustrated in examples.

Nonlinear optimal control for wind power generators comprising a multi-mass drivetrain and a DFIG

The article proposes a nonlinear optimal (H-infinity) control method for a wind power generation system comprising a two-mass drivetrain and a Doubly-Fed Induction Generator (DFIG). Comparing to the 6-th order dynamic model of the DFIG, the state-space model of the considered power generation unit is extended after including in it the dynamics of the drivetrain. To solve the associated control problem, the dynamic model of the power generation unit undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control algorithm. The linearization procedure relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space description of the power unit, an H-infinity controller is developed. This stands for the solution of the optimal control problem for the wind power system under model uncertainty and external perturbations. For the computation of the controller’s feedback gain an algebraic Riccati equation is repetitively solved at each iteration of the control method. Moreover, with the use of Lyapunov analysis the global asymptotic stability of the control scheme is proven. Finally, to implement state estimation-based control without the need to measure the entire state vector of the power unit, the H-infinity Kalman Filter is used as a robust observer.