Dynamic State Feedback Control Research Articles

Anti-control of Hopf bifurcation for a chaotic system

Abstract The anti-control of Hopf bifurcation is a method used for bifurcation control. It can be used to realize the occurrence or delay of bifurcation at the specified position to meet the needs of engineering applications. In this study, a 4D chaotic system is studied, and a dynamic state feedback control method is proposed to realize the anti-control of Hopf bifurcation for the system. By adjusting the control parameters of the controller, the system Hopf bifurcation can be generated or delayed at the specified position to realize the anti-control of Hopf bifurcation. This control method avoids complicated calculation processes and has remarkable control effects. Through numerical simulation analysis, the correctness of this control method is verified.

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks

Abstract The objective of this paper is to develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network. It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network. For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed. In an event-triggered system, when an error signal exceeding a specified time-varying threshold it indicates the occurrence of a typical event. The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed. Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs. A simulation example is finally used to verify the effectiveness of such a control strategy can enhance the system performance.

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

In modern control theory applications, input–output feedback often arises and plays a crucial role in stabilizing any target control systems. However, in many practical applications, the knowledge of full information on the state of systems may not be available in general due to measurements. In order to control such types of systems, this paper uses a universal concept of real order calculus to stabilize by the method of dynamic output feedback control. Is it possible to design a dynamic output feedback stabilization for time-varying real order control systems? This work develops a new dynamic output feedback control method and proposes linear homogeneous time-varying control law to stabilize incommensurate nonlinear time-varying real order systems under the action of Caputo derivative with an addendum of ultimate random initial-time. We utilize the ideas of the comparison method and establish order-dependent asymptotic results associated with uniform Lipschitz continuous functions that provide stabilization by means of the dynamic output state feedback control method. We provide three examples that include a practical system and show the importance of some theoretical results in the demonstration to stabilize the problems by means of proposed control method.

Global state regulation of time-delay minimum-phase systems by delay-free dynamic compensation

This paper studies the global control problem, in the sense of “almost stabilization” or state regulation, for a class of time-delay minimum-phase nonlinear systems via delay-free dynamic compensation. Both dynamic state and output feedback control schemes are developed. By taking advantage of dynamic rather than static feedback, we design delay-independent dynamic state and output feedback compensators, respectively, to achieve asymptotic state regulation with global stability. In the case of dynamic state feedback, a structural condition is imposed on the inverse dynamics that are nonlinear yet imply linear zero dynamics. In the case of dynamic output feedback, more strict conditions on the nonlinearity are characterized to guarantee the existence of a dynamic output controller. In both cases, it is proved by the Lyapunov–Krasovskii functional method, combined with the Barbalat’s lemma, that all the states of the time-delay minimum-phase systems are regulated to zero and boundedness of the closed-loop system is ensured. Two examples are given to validate the proposed delay-free dynamic compensators.

Adaptive Prescribed-Time Control of Time-Delay Nonlinear Systems via a Double Time-Varying Gain Approach.

This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov-Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.

Robust PLL Synchronization Unit for Grid-Feeding Converters in Micro/Weak Grids

A grid-feeding voltage source converter (GFD-VSC) requires a phase-locked loop (PLL) synchronization unit to be connected to the grid. The PLL critically affects the dynamic performance and stability of the GFD-VSC. In particular, a PLL with pre/in-loop filtering, for working under distorted/polluted conditions, possesses a narrow stability margin and deficient performance in weak grid connections and fault ride-through (FRT) transients, also poor performance in frequency estimation. To address these problems, a robust PLL with several enhanced characteristics is proposed in this article. The robust PLL with a dynamic state feedback controller is designed using an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\bm{H}}}_\infty $</tex-math></inline-formula> robust control. The feedback controller is designed to improve the dynamic stability/response of the PLL, exposed to control uncertainties and exogenous disturbances, weak-grid connection, FRT transients and to improve its performance in frequency estimation. Numerical simulations validate the effectiveness of the proposed PLL.

Reset control and ℒ2-gain analysis of piecewise-affine systems

This paper is concerned with reset controller design and L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results.

Dynamic state feedback controller and observer design for dynamic artificial neural network models

Artificial neural networks are black-box models that can be used to model nonlinear dynamical systems. This article presents a synthesis method for full dynamic state feedback controllers and state and output observers that have guaranteed properties for systems approximated by dynamic artificial neural networks. The resulting control designs are applicable to the practical situation in which the steady-state values for the control input are not known. Dynamic artificial neural networks are written in the standard nonlinear operator form, also known in the literature as the Luré formulation. A generalized form of the Luré formulation is adopted to allow for the representation of deep ℓ-layer networks, ℓ≥1. Sufficient conditions for controller synthesis and observer design are derived in the form of linear matrix inequalities, using a quadratic Lyapunov function. The synthesis method is demonstrated for the control of pH in two tanks in series and a numerical example.

Fully Distributed Robust Formation Flying Control of Drones Swarm Based on Minimal Virtual Leader Information

This paper studies the robust formation flying problem for a swarm of drones, which are modeled as uncertain second order systems. By making use of minimal virtual leader information, a fully distributed robust control scheme is proposed, which includes three parts. First, the output based adaptive distributed observer is adopted to recover the global flying path vector as well as the coefficients of the minimal polynomial of the system matrix of the virtual leader system for each drone based on neighboring information from the communication network. Second, based on the estimated minimal polynomial of the system matrix of the virtual leader system, an asymptotic internal model is conceived to deal with uncertain system parameters. Third, by combining the asymptotic internal model and a certainty equivalent dynamic state feedback control law, a local trajectory tracking controller is synthesized to solve the robust formation flying problem. Numerical simulations are provided to validate the proposed control scheme.

Disturbance-Observer-Based Feedback Linearization Control for Stabilization and Accurate Voltage Tracking of a DC–DC Boost Converter

The nonminimum-phase property of the dc–dc boost converter can create difficulties in designing a stable, robust, and fast control for the output voltage. In this article, these difficulties are reduced by modifying the state model of the boost converter in such a way that it behaves like a minimum-phase system. More specifically, the control input entering the state equation for the output voltage is treated as an unknown disturbance to make the relative degree of the system equal the system’s order. As a result, the modified model does not exhibit zero dynamics, so that it can be treated as a minimum-phase system for the control design. The modified model is, then, used to derive a dynamic compensator for the output voltage regulation. More explicitly, the dynamic compensator is designed based on combining linearizing feedback control with a disturbance observer. The latter is employed to compensate for model uncertainties and unknown load with a view to ensure asymptotic regulation under the composite controller. The asymptotic regulation is achieved due to the integral action property characterizing the disturbance observer. More interestingly, after simple algebraic manipulation, it turns out that the composite controller reduces to a dynamic state feedback control plus an antiwindup scheme to mitigate the effect of control saturation during transients. The performance of the proposed controller is verified by experimental tests. The experimental results demonstrate the ability of the proposed controller to achieve good transient and steady-state performances.

Distributed robust group output synchronization control for heterogeneous uncertain linear multi-agent systems

This paper investigates the distributed robust group output synchronization problem of heterogeneous uncertain linear leader-follower multi-agent systems (MASs), whose followers have nonidentical and parameter uncertain dynamics. To achieve cooperative tracking with multiple targets, a new group synchronization framework based upon the output regulation technique is established. In the underlying directed communication topology, all nonidentical followers are divided into several subgroups. Meanwhile, each subgroup has its output tracking objective generated by an autonomous exosystem which is seen as the leader of each subgroup. Since not all followers can access their exosystems directly, the distributed exosystem observer based on the algebraic Riccati inequality (ARI) is designed to obtain the information of exosystems. Moreover, to compensate for parameter uncertainties for different group topologies, the p-copy internal model is synthesized into distributed control laws, i.e., dynamic state feedback control protocol under an acyclic directed graph and dynamic output feedback control protocol under a general directed graph. It is shown that group synchronization can be respectively achieved with these controllers under acyclic and general partitions regardless of parameter uncertainties. Finally, some examples are provided to verify the validity of the analytic results.

Hybridization of battery and ultracapacitor for electric vehicle application with dynamic energy management and non-linear state feedback controller

• Proposed a dynamic energy management system for hybrid sources in an electric vehicle. • Buck-boost H-bridge converters are introduced for bidirectional power flow control. • System non-linearities are addressed using a nonlinear state feedback controller. • The proposed system accurately delivers instantaneous vehicle speed and torque. This paper describes a methodology to control a multi-source battery-capacitor hybrid EV incorporating a dynamic power splitting strategy. Considering the requirement for precise speed control characteristics of the EV and the non-linear behavior of traction motor with system disturbances, a non-linear state feedback controller (NLSFC) with a disturbance observer is suggested as the speed control technique for the EV traction motor. To interface a parallel configured multi-source system, a non-inverted buck-boost H-bridge is proposed as the source side converter for effective recovery of the braking energy. Detailed control design for traction motor and converter is also presented for efficient control of EV. Besides, an adaptive energy management strategy considering power profile and dynamic source characteristics is incorporated into the overall control system. The simulation results from various case studies indicate that the proposed system can follow the required vehicle speed and torque despite the sudden change in EV load torque. Furthermore, the comparative analysis between NLSFC and PI controller shows improvement with steady-state error reduction from 0.43 to 0.0014 and peak overshoot drop from 12.07% to 3.51% during acceleration of the system when proposed NLSFC is adopted. The proposed solutions will be implemented in a prototype EV system in the future.

Distributed Robust Containment Control of Linear Heterogeneous Multi-Agent Systems: An Output Regulation Approach

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders' measurable output was designed to estimate a convex combination of the leaders' states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders' convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

Optimal output consensus of second‐order uncertain nonlinear systems on weight‐unbalanced directed networks

AbstractThis article investigates the distributed optimal output consensus problem of second‐order uncertain nonlinear multiagent systems over weight‐unbalanced directed networks. Under the standard assumption that local cost functions are strongly convex with globally Lipschitz gradients, a novel distributed dynamic state feedback controller is developed such that the outputs of all the agents reach the optimal solution to minimize the global cost function which is the sum of all the local cost functions. The controller design is based on a two‐layer strategy, where a distributed optimal coordinator and a reference‐tracking controller are proposed to address the challenges arising from unbalanced directed networks and uncertain nonlinear functions respectively. A key feature of the proposed controller is that the nonlinear functions containing the uncertainties and disturbances are not required to be globally Lipschitz. Furthermore, by exploiting adaptive control technique, no prior knowledge of the uncertainties or disturbances is required either. Two simulation examples are finally provided to illustrate the effectiveness of the proposed control scheme.

Adaptive friction compensation for a class of mechanical systems based on LuGre model

AbstractThis paper deals with the problem of friction compensation for a class of uncertain mechanical systems based on LuGre model. The objective is to develop control laws such that the position variable of the system tracks a periodic desired signal or a constant desired signal. Since the friction behavior of the system with periodic desired signals is largely different from that of the system with constant desired signals, two different adaptive control methods are presented for the two cases, respectively. For the case of periodic desired signals, an adaptive repetitive learning control method is presented, and for the case of constant desired signals, an adaptive dynamic state feedback control method is presented. Both the control laws can guarantee that all the signals in the closed loop system are bounded and the tracking errors converge to zero. Several numerical simulations are carried out to show effectiveness of the proposed control algorithms.

Dissipative stabilization of linear input delay systems via dynamical state feedback controllers: an optimization based approach

In this note, we present an effective solution to the stabilization of linear input delay systems subject to dissipative constraints while all the effect of input delay is compensated by a controller with novel structure. The method is inspired by the recent development in the mathematical treatment of distributed delays and predictor controllers, which are critical for the derivation of the solution. An important conceptual innovation is the use of a parameterized dynamical state feedback controller (DSFC), where the dimension of the controller equals the dimension of the control input. A sufficient condition for the existence of a dissipative DSFC is obtained via the Krasovskii functional approach, where the condition includes a bilinear matrix inequality (BMI). To solve the BMI, we apply an inner convex approximation algorithm which can be initialized based on an explicit construction of a predictor controller gain. The proposed DSFC can be considered as an extension of the classical predictor controller, thereby capable of compensating all the effects of the pointwise input delay while satisfying dissipative constraints. A numerical example is given to illustrate the effectiveness of our proposed methodology.

Regional Eigenvalue Assignment in Cooperative Linear Output Regulation

The contribution of this paper is a regional eigenvalue assignment method for cooperative output regulation of heterogeneous linear multiagent systems with an internal model-based distributed dynamic state feedback control law. The proposed method offers an agent-wise local approach to synthesize distributed control gains while assigning, for example, the minimal decay rate and the minimal damping ratio of the overall closed-loop system as desired. Numerical examples demonstrate the efficacy of the proposed method by assigning the eigenvalues of a large-scale system to different regions, specifically, disks, shifted half-planes, and conic sectors.

Hopf bifurcation control of the ML neuron model with Hc bifurcation type

&lt;abstract&gt;&lt;p&gt;It is shown that many neurological diseases are caused by the changes of firing patterns induced by bifurcations. Therefore, the bifurcation control may provide a potential therapeutic method of these neurodegenerative diseases. In this paper, we investigate the Hopf bifurcation control of the Morris-Lecar (ML) model with Homoclinic (Hc) bifurcation type by introducing a dynamic state-feedback control. The results indicate that the linear term can change the ML model from Hc bifurcation type to SNIC bifurcation type without changing the firing patterns. The cooperation of linear and cubic term can transform the ML model from the Hc bifurcation type to the Hopf bifurcation type, resulting in the transformation of firing patterns from type I to type II. Besides, we utilize the Poincare Birkhoff (PB) normal form method to derive the analytical expression of the bifurcation stability index for the controlled ML model with Hc bifurcation type, and the results show that the cubic term can regulate the criticality of the Hopf bifurcation. Numerical simulation results are consistent with the theoretical analysis.&lt;/p&gt;&lt;/abstract&gt;

State Observer for Linear Systems with Explicit Constraints: Orthogonal Decomposition Method.

In this paper, an orthogonal decomposition-based state observer for systems with explicit constraints is proposed. State observers have been an integral part of robotic systems, reflecting the practicality and effectiveness of the dynamic state feedback control, but the same methods are lacking for the systems with explicit mechanical constraints, where observer designs have been proposed only for special cases of such systems, with relatively restrictive assumptions. This work aims to provide an observer design framework for a general case linear time-invariant system with explicit constraints, by finding lower-dimensional subspaces in the state space, where the system is observable while giving sufficient information for both feedback and feed-forward control. We show that the proposed formulation recovers minimal coordinate representation when it is sufficient for the control law generation and retains non-minimal coordinates when those are required for the feed-forward control law. The proposed observer is tested on a flywheel inverted pendulum and on a quadruped robot Unitree A1.