Gain Feedback Design Research Articles

Feedback Gain Design of Induction Machine Full-Order Flux Observer

In the field-oriented control of an induction machine, a full-order flux observer has been widely used to estimate the flux. It has several critical issues, such as discrete-time domain instability, dynamics deterioration, and another instability in a low-speed sensorless flux estimation. This paper addresses and analyzes these three issues. And it proposes a feedback gain design method for the full-order flux observer to solve the problems. Additionally, the parameter sensitivity in the flux estimation is analyzed with a frequency response function. The experiments were conducted with an EV-traction induction machine. The results show the performances of the proposed feedback gain design in the high-speed operation over the conventional discrete-time domain stability limit, the dynamics improvement in mid- and high-speed region, and the stable operation in the low-speed regeneration mode.

A survey on compressed sensing approach to systems and control

AbstractIn this survey paper, we review recent advances of compressed sensing applied to systems and control. Compressed sensing has been actively researched in the field of signal processing and machine learning. More recently, the method has been applied to systems and control problems, such as sparse feedback gain design, reduced-order control, and maximum hands-off control. This paper introduces these important applications of compressed sensing to systems and control. MATLAB programs for the numerical examples shown in this survey paper are available as supplementary materials.

Fuzzy-Resilient Distributed Optimal Coordination for Nonlinear Multiagent Systems Under Command Attacks

In this paper, we consider the problem of resilient distributed optimal coordination for uncertain nonlinear multi-agent systems, where each agent is remotely dominated by an associated instruction generator via an unreliable network channel which may be distorted by false data injection (FDI) attacks. To avoid evaluating the quality of decision variable or computing its high-order derivatives when applying the backstepping method, which is difficult in a distributed way, a new two-layer integrated design protocol with fuzzy-approximation-based adaptive dynamics compensation mechanism is designed. Through the local online estimation of the optimal solution and design of adaptive feedback gain, the fuzzy adaptive mechanism realizes the mutual compensation of cyber dynamics and physical dynamics. Resultantly, all the agents are shown to achieve the optimal consensus regardless of the FDI attacks and nonlinear uncertainties.

Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays

The stabilization problem is studied for memristive neural networks with interval delays under aperiodic switching event-triggered control. Note that, most of delayed memristive neural networks models studied are discontinuous, which are not the real memristive neural networks. First, a real model of memristive neural networks is proposed by continuous differential equations, furthermore, it is simplified to neural networks with interval matrix uncertainties. Secondly, an aperiodic switching event-trigger is given, and the considered system switches between aperiodic sampled-data system and continuous event-triggered system. Thirdly, by constructing a time-dependent piecewise-defined Lyapunov functional, the stability criterion and the feedback gain design are obtained by linear matrix inequalities. Compared with the existing results, the stability criterion is with lower conservatism. Finally, two neurons are taken as examples to ensure the feasibility of the results.

Design of input assignment and feedback gain for re‐stabilizing undirected networks with High‐Dimension Low‐Sample‐Size data

AbstractThere exists a critical transition before dramatic deterioration of a complex dynamical system. Recently, a method to predict such shifts based on High‐Dimension Low‐Sample‐Size (HDLSS) data has been developed. Thus based on the prediction, it is important to make the system more stable by feedback control just before such critical transitions, which we call re‐stabilization. However, the re‐stabilization cannot be achieved by traditional stabilization methods such as pole placement method because the available HDLSS data is not enough to get a mathematical system model by system identification. In this article, a model‐free pole placement method for re‐stabilization is proposed to design the optimal input assignment and feedback gain for undirected network systems only with HDLSS data. The proposed method is validated by numerical simulations.

Prescribed-Time Stabilization of Singularly Perturbed Systems

Dear Editor, This letter investigates the prescribed-time stabilization of linear singularly perturbed systems. Due to the numerical issues caused by the small perturbation parameter, the off-the-shelf control design techniques for the prescribed-time stabilization of regular linear systems are typically not suitable here. To solve the problem, the decoupling transformation techniques for time-varying singularly perturbed systems are combined with linear time-varying high gain feedback design techniques. A composite linear time-varying state feedback controller is designed, and the existence of the time-varying Chang transformation matrix for decoupling the slow and fast dynamics is guaranteed. As a result, the prescribed-time stability is ensured. Finally, a numerical example is provided to illustrate the effectiveness of the results.

Semiglobal Leader-Following Output Consensus of Discrete-Time Heterogeneous Linear Systems Subject to Actuator Position and Rate Saturation

Motivated by the fact that physical systems are usually subject to actuator position and rate saturation, we consider in this article the semiglobal leader-following output consensus problem of a group of discrete-time heterogeneous linear systems with position and rate-limited actuators by output feedback control law. Distributed observers are designed for followers to estimate the state of the leader and the follower itself, based on which a novel distributed control law is proposed. We show that, via the low gain feedback design technique and output regulation theory, the semiglobal leader-following output consensus of discrete-time heterogeneous linear systems can be achieved by the consensus protocol if each follower is reachable from the leader in a directed communication topology.

Model‐Free Cooperative Optimal Output Regulation for Linear Discrete‐Time Multi‐Agent Systems Using Reinforcement Learning

In this paper, an off‐policy model‐free algorithm is presented for solving the cooperative optimal output regulation problem for linear discrete‐time multi‐agent systems. First, an adaptive distributed observer is designed for each follower to estimate the leader’s information. Then, a distributed feedback‐feedforward controller is developed for each follower to solve the cooperative optimal output regulation problem utilizing the follower’s state information and the adaptive distributed observer. Based on the reinforcement learning method, an adaptive algorithm is presented to find the optimal feedback gains via online data collection from system trajectory. By designing a Sylvester map, the solution to the regulator equations is calculated via data collected from the optimal feedback gain design steps, and the feedforward control gain is found. Finally, an off‐policy model‐free algorithm is proposed to design the distributed feedback‐feedforward controller for each follower to solve the cooperative optimal output regulation problem. A numerical example is given to verify the effectiveness of this proposed approach.

Leader-following almost output consensus for discrete-time heterogeneous multi-agent systems in the presence of external disturbances

In this paper, we consider the problem of leader-following almost output consensus for discrete-time multi-agent systems with heterogeneous follower agents. Conditions on agent dynamics, the communication topology and how the disturbance enters the agent dynamics are established under which leader-following almost output consensus can be achieved, that is, the leader-following output consensus can be reached with any pre-specified level of accuracy and the effect of the disturbance on the leader-following consensus can be attenuated to any pre-specified level. A family of state feedback consensus protocols are constructed by using the low gain feedback design technique and a modified discrete-time Riccati equation. These consensus protocols are shown to achieve leader-following almost output consensus. Additional conditions are identified under which output feedback results are established. Simulation results demonstrate the effectiveness of the proposed consensus protocols.

Semi‐global weighted output average tracking of heterogeneous multi‐agent systems in the presence of actuator saturation and external disturbances

AbstractThis article studies the problem of semi‐global weighted output average tracking of a heterogeneous multi‐agent system in the presence of actuator saturation and external disturbances. The multi‐agent system contains a group of leader agents and a group of follower agents. Both the dynamics of leader agents and the dynamics of follower agents are allowed to be heterogeneous. Applying the classical output regulation theory and the low gain feedback design technique, we construct for each follower agent a state feedback control protocol and an output feedback control protocol, both parameterized in a scalar parameter. In both the state feedback case and the output feedback case, we construct distributed leader state observers for each follower agent that estimate the states of the leader agents. In the case of output feedback, we also construct for each follower agent state observer that estimates its own state. It is shown that, under these control protocols with a sufficiently small value of the parameter, each follower agent can track the weighted average of the outputs of the leader agents from an arbitrarily large bounded set of initial conditions and in the presence of actuator saturation and external disturbances if there exist directed paths from each leader agent to all the follower agents. Simulation results are given to illustrate the theoretical results.

Semi‐global leader–following output consensus of heterogeneous systems with all agents subject to input saturation

AbstractIn this paper, we consider the semi‐global leader–following output consensus of heterogeneous multi‐agent linear systems over a directed communication graph with both the leader agent and the follower agents subject to input saturation. Via the low gain feedback design technique, both the state feedback and output feedback consensus protocols are constructed. In the state feedback case, a fully distributed observer is given to estimate the state of the leader agent. In the output feedback case, for both the informed follower agents and the uninformed follower agents, a state observer and a distributed leader state observer for each follower are designed to estimate the state of the follower itself and the state of the leader agent, respectively. In the distributed leader state observer, additional discontinuous functions are designed to suppress the influence of the bounded input of the leader agent. In both consensus protocols, a term under a condition similar to that used in the robust control is used to compensate for the control input of the leader agent.

Semi-global stabilisation of fractional-order linear systems with actuator saturation by output feedback

This paper considers the problem of the semi-global asymptotic stabilisation of fractional-order (FO) linear systems subject to actuator saturation by output feedback. To solve the problem, a family of observer-based linear output feedback laws, parameterised in a positive scalar, is proposed by means of the low gain feedback design technique. The design applies to FO linear systems that are stabilisable and detectable, but not exponentially unstable. For such an FO system under the proposed observer-based linear low gain output feedback, the peak value of the control input for a given initial condition can be made arbitrarily small to avoid actuator saturation by decreasing the value of the parameter towards zero and thus semi-global asymptotic stabilisation is achieved. To obtain these results, we establish the properties of low gain feedback, derive asymptotic expansions and the bounds of high-order derivatives of the Mittag-Leffler (ML) functions to estimate the state responses of FO linear systems, and explicitly construct a Hermitian matrix to satisfy a linear matrix inequality (LMI) stability condition for FO linear systems. The results in this paper extend the corresponding results for integer-order (IO) linear systems.

Semi-global leader-following output consensus of heterogeneous systems subject to actuator position and rate saturation

We study in this paper a semi-global leader-following output consensus problem for multiple heterogeneous linear systems in the presence of actuator position and rate saturation over a directed topology. For each follower, via the low gain feedback design technique and output regulation theory, both a state feedback consensus protocol and an output feedback consensus protocol are constructed. In the output feedback case, different distributed observers are designed for the informed followers and uninformed followers to estimate the state of the leader and the follower itself. We show that the semi-global leader-following output consensus of heterogeneous linear systems can be achieved by the two consensus protocols if each follower is reachable from the leader in the directed communication topology.

Semi-global leader-following consensus-based formation flight of unmanned aerial vehicles

In this paper, we investigate a formation control problem of multi-agent systems (specifically a group of unmanned aerial vehicles) based on a semi-global leader-following consensus approach with both the leader and the followers subject to input saturation. Utilizing the low gain feedback design technique, a distributed static control protocol and a distributed adaptive control protocol are constructed. The former solves the problem under an assumption that the communication network is undirected, and it depends on the global information of the graph. For the latter, we relax the undirected graph to directed graph. Moreover, an adaptive updating gain is designed to avoid using the global information of the communication network. It is shown that the consensus protocols can solve the semi-global leader-following consensus problem if the leader agent is globally reachable. The results are verified successfully by both simulation and real flight tests.

Coordinated Time-Varying Low Gain Feedback Control of High-Speed Trains Under a Delayed Communication Network

The coordinated control problem for a multiple high-speed train (HST) system subject to unknown communication delays is systematically investigated in this paper. Taking into consideration the inertial lag of the servo motor, a third-order nonlinear control model is constructed to capture the dynamics of a train in real-world operations. By virtue of the backstepping linearization technique, the coordinated control of trains is formulated as a stabilization problem for a linear multiple-input multiple-output system with an unknown input delay. Distributed control laws with a time-varying low gain parameter are designed, besides solving the stabilization problem, to guarantee a fast convergency rate during the train status adjustment process. Numerical examples are provided to illustrate that the time-varying low gain parameter design achieves better control performance compared with the traditional constant low gain feedback design in terms of the convergency rate and the system overshot, and that the proposed control method is effective in train tracking distance adjustment.

A delay‐independent output feedback law for discrete‐time linear systems with bounded unknown input delay

AbstractBounded input delay frequently arises in discrete‐time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay‐independent truncated predictor state feedback design, an observer‐based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete‐time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open‐loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open‐loop poles of a system are at z = 1 or inside the unit circle, stabilization can be achieved for an arbitrarily large bounded delay as long as the value of the low gain parameter is chosen small enough.

An exploration of the Razumikhin stability theorem with applications in stabilization of delay systems

In this paper, we establish a new evolution property of Lyapunov functions that satisfy the Razumikhin Stability Theorem conditions. The derived property is shown to be a valid alternative criterion to prove the asymptotic stability of a delay system without calculating the derivative of the Lyapunov function, and it is especially useful in solving stabilization problems for time delay systems when the delay is unknown. As an example application of this derived property, we investigate the stabilization of continuous-time linear systems with an unknown time-varying delay, by proposing a switched low gain feedback control technique that utilizes the derived property. Existing literature on stabilization of continuous time delay systems all require some knowledge, such as an upper bound, of the delay. In this work, by proposing a switched low gain feedback control law utilizing the derived property, we are able to achieve asymptotic stabilization of the system without any knowledge of the delay. Furthermore, the proposed switched low gain feedback law also significantly improves the closed-loop system performance in terms of overshoot and convergence speed, in comparison with the traditional fixed gain low gain feedback design. Simulation study verifies the theoretical results.

Eigenvalue Optimization of the Energy-Balancing Feedback for Modular Multilevel Converters

Despite its potential impact on the balancing performance, current literature on the modular multilevel converter (MMC) energy-balancing feedback gain design and tuning process seem incomplete. In order to close this research gap, the energy-balancing feedback gain tuning of an ac current controlled MMC with half-bridge cells and isolated star point is considered in this paper. The tuning is difficult, because each energy error adds its own dedicated component to the circulating current reference that leads to a strong coupling that evades common tuning approaches. This problem is solved in two steps: at first, the relevant error dynamics is extracted and validated to model the time domain behavior of the energy balancing. Second, a theorem from Wu (1975) is invoked to easily calculate the closed-loop eigenvalues that finally allow for an easy optimization of the energy-balancing performance. Despite the radical simplifications during the modeling and error dynamics extraction, the acquired model is able to adequately reproduce the energy errors and the balancing circulating current of the converter. Simulation and measurement results on a grid-side MMC demonstrate a considerable performance improvement in contrast to the traditional gain estimation on the open loop. This is verified with and without a second harmonic in the circulating currents.

A Sampled-Data Approach to Pyragas-Type Delayed Feedback Stabilization of Periodic Orbits

A sampled-data Pyragas-type delayed feedback control framework is proposed for stabilizing both periodic solutions of linear periodic systems and unstable periodic orbits of nonlinear systems. The proposed framework uses the difference between two consecutive samples of the state as a feedback input. Furthermore, the controller is turned on and off periodically in an alternating fashion, allowing one to obtain a monodromy matrix for the closed-loop system. Asymptotic behavior of the closed-loop system state trajectories is investigated through an analysis of the obtained monodromy matrix. Then, an efficient feedback gain design method is developed by exploiting the properties of the monodromy matrix. Finally, the efficacy of the proposed framework is demonstrated with a numerical example.

Event-based cooperative global practical output regulation of multi-agent systems with nonlinear leader

This paper presents a distributed event-based high gain feedback design for the cooperative global practical output regulation problem of nonlinear multi-agent systems with unit relative degree subject to the general nonlinear leader system. We first convert global practical output regulation problem into global practical stabilization problem, then prove the input-to-state stability of the closed-loop system by regarding the sampling error and the steady-state of the actuator together as the external input. Based on the high gain feedback technique, the input-to-state gain function can be made sufficiently small, and hence the tracking error can converge to an arbitrary predefined small residual set around the origin. A distinguishing feature of our result is that, our controller is static and purely digital, thus, giving rise to quite a simple structure.